modelling, integration and optimisation for recirculating
TRANSCRIPT
Modelling Integration and Optimisation for
Recirculating Cooling Water System Operation
A thesis submitted to The University of Manchester for the degree of
Doctor of Philosophy
In the Faculty of Science and Engineering
2016
Fei Song
School of Chemical Engineering and Analytical Science
2
Table of Contents
List of Figures 3
Abstracthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4
Declaration 5
Copyright Statement 6
Acknowledgement 7
Chapter 1 Introduction 8
11 Background 8
111 Recirculating cooling water systems 8
112 Operation of recirculating cooling water systems 12
113 Interactions between cooling water systems and processes 13
114 Operation management of cooling water systems 14
12 Motivation 14
13 Aims and objectives 15
14 Thesis outline 16
Chapter 2 17
Publication 1 Operational Optimisation of Mechanical Draft Wet Cooling Towers 17
Chapter 3 18
Publication 2 Operational Optimisation of Recirculating Cooling Water Systems 18
Chapter 4 19
Publication 3 Operational Optimisation of Recirculating Cooling Water Systems for
Improving the Performance of Condensing Turbines 19
Chapter 5 Conclusions and Future Work 20
51 Conclusions 20
52 Future work 21
References 23
Word Count 33521
3
List of Figures
Figure 11 A recirculating cooling water systemhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8
4
Abstract
The University of Manchester
Fei Song
PhD Chemical Engineering and Analytical Sciences
Modelling Integration and Optimisation for Recirculating Cooling Water System
Operation
2016
Recirculating cooling water systems are extensively used for heat removal from
processes in the process industry Two aspects are focused on to improve the economic
performance of cooling water systems and processes with cooling demand the
integration of key components in cooling water systems including cooling towers
cooler networks and piping networks and the integration of cooling water systems and
processes with cooling demand
For the internal integration of cooling water systems integration models were
established for the operation of cooling water systems in the literature [1] [2] [3]
There are some limitations in the literature they were limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored in the literature [2]
and [3] To overcome those limitations in the literature in this thesis a nonlinear
integration model of cooling water systems is developed for multiple cooling towers
and cooler networks in both parallel and complex configuration The model includes
cooling tower modelling cooler network modelling and hydraulic modelling In cooling
tower modelling correlation expressions of tower characteristics air inlet conditions
and water inlet conditions are developed to predict temperature of water leaving towers
and humidity of air leaving towers respectively In cooler network modelling detailed
heat transfer in individual coolers is considered In hydraulic modelling pressure drop
in both coolers and pipes are taken into account The nonlinear model is solved by the
solver CONOPT in GAMS to determine the optimal water distribution and air flowrate
For the integration of cooling water systems and processes with cooling demand a new
equation-based simultaneous optimisation method is proposed in which an integration
model of cooling water systems and processes is developed Condensing turbines are
taken as an example to illustrate the method
Case studies prove that the models are effective to solve the problems The standalone
optimisation of cooling water systems reduces the operating cost by 56 compared
with the base case The simultaneous optimisation increases the total profit by 337 kpoundyr
compared with focusing only on maximising the power generation of condensing
turbines
5
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institution of learning
Fei Song
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any
relevant Thesis restriction declarations deposited in the University Library the
University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy
on Presentation of Theses
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
2
Table of Contents
List of Figures 3
Abstracthelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip4
Declaration 5
Copyright Statement 6
Acknowledgement 7
Chapter 1 Introduction 8
11 Background 8
111 Recirculating cooling water systems 8
112 Operation of recirculating cooling water systems 12
113 Interactions between cooling water systems and processes 13
114 Operation management of cooling water systems 14
12 Motivation 14
13 Aims and objectives 15
14 Thesis outline 16
Chapter 2 17
Publication 1 Operational Optimisation of Mechanical Draft Wet Cooling Towers 17
Chapter 3 18
Publication 2 Operational Optimisation of Recirculating Cooling Water Systems 18
Chapter 4 19
Publication 3 Operational Optimisation of Recirculating Cooling Water Systems for
Improving the Performance of Condensing Turbines 19
Chapter 5 Conclusions and Future Work 20
51 Conclusions 20
52 Future work 21
References 23
Word Count 33521
3
List of Figures
Figure 11 A recirculating cooling water systemhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8
4
Abstract
The University of Manchester
Fei Song
PhD Chemical Engineering and Analytical Sciences
Modelling Integration and Optimisation for Recirculating Cooling Water System
Operation
2016
Recirculating cooling water systems are extensively used for heat removal from
processes in the process industry Two aspects are focused on to improve the economic
performance of cooling water systems and processes with cooling demand the
integration of key components in cooling water systems including cooling towers
cooler networks and piping networks and the integration of cooling water systems and
processes with cooling demand
For the internal integration of cooling water systems integration models were
established for the operation of cooling water systems in the literature [1] [2] [3]
There are some limitations in the literature they were limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored in the literature [2]
and [3] To overcome those limitations in the literature in this thesis a nonlinear
integration model of cooling water systems is developed for multiple cooling towers
and cooler networks in both parallel and complex configuration The model includes
cooling tower modelling cooler network modelling and hydraulic modelling In cooling
tower modelling correlation expressions of tower characteristics air inlet conditions
and water inlet conditions are developed to predict temperature of water leaving towers
and humidity of air leaving towers respectively In cooler network modelling detailed
heat transfer in individual coolers is considered In hydraulic modelling pressure drop
in both coolers and pipes are taken into account The nonlinear model is solved by the
solver CONOPT in GAMS to determine the optimal water distribution and air flowrate
For the integration of cooling water systems and processes with cooling demand a new
equation-based simultaneous optimisation method is proposed in which an integration
model of cooling water systems and processes is developed Condensing turbines are
taken as an example to illustrate the method
Case studies prove that the models are effective to solve the problems The standalone
optimisation of cooling water systems reduces the operating cost by 56 compared
with the base case The simultaneous optimisation increases the total profit by 337 kpoundyr
compared with focusing only on maximising the power generation of condensing
turbines
5
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institution of learning
Fei Song
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any
relevant Thesis restriction declarations deposited in the University Library the
University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy
on Presentation of Theses
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
3
List of Figures
Figure 11 A recirculating cooling water systemhelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphelliphellip8
4
Abstract
The University of Manchester
Fei Song
PhD Chemical Engineering and Analytical Sciences
Modelling Integration and Optimisation for Recirculating Cooling Water System
Operation
2016
Recirculating cooling water systems are extensively used for heat removal from
processes in the process industry Two aspects are focused on to improve the economic
performance of cooling water systems and processes with cooling demand the
integration of key components in cooling water systems including cooling towers
cooler networks and piping networks and the integration of cooling water systems and
processes with cooling demand
For the internal integration of cooling water systems integration models were
established for the operation of cooling water systems in the literature [1] [2] [3]
There are some limitations in the literature they were limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored in the literature [2]
and [3] To overcome those limitations in the literature in this thesis a nonlinear
integration model of cooling water systems is developed for multiple cooling towers
and cooler networks in both parallel and complex configuration The model includes
cooling tower modelling cooler network modelling and hydraulic modelling In cooling
tower modelling correlation expressions of tower characteristics air inlet conditions
and water inlet conditions are developed to predict temperature of water leaving towers
and humidity of air leaving towers respectively In cooler network modelling detailed
heat transfer in individual coolers is considered In hydraulic modelling pressure drop
in both coolers and pipes are taken into account The nonlinear model is solved by the
solver CONOPT in GAMS to determine the optimal water distribution and air flowrate
For the integration of cooling water systems and processes with cooling demand a new
equation-based simultaneous optimisation method is proposed in which an integration
model of cooling water systems and processes is developed Condensing turbines are
taken as an example to illustrate the method
Case studies prove that the models are effective to solve the problems The standalone
optimisation of cooling water systems reduces the operating cost by 56 compared
with the base case The simultaneous optimisation increases the total profit by 337 kpoundyr
compared with focusing only on maximising the power generation of condensing
turbines
5
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institution of learning
Fei Song
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any
relevant Thesis restriction declarations deposited in the University Library the
University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy
on Presentation of Theses
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
4
Abstract
The University of Manchester
Fei Song
PhD Chemical Engineering and Analytical Sciences
Modelling Integration and Optimisation for Recirculating Cooling Water System
Operation
2016
Recirculating cooling water systems are extensively used for heat removal from
processes in the process industry Two aspects are focused on to improve the economic
performance of cooling water systems and processes with cooling demand the
integration of key components in cooling water systems including cooling towers
cooler networks and piping networks and the integration of cooling water systems and
processes with cooling demand
For the internal integration of cooling water systems integration models were
established for the operation of cooling water systems in the literature [1] [2] [3]
There are some limitations in the literature they were limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored in the literature [2]
and [3] To overcome those limitations in the literature in this thesis a nonlinear
integration model of cooling water systems is developed for multiple cooling towers
and cooler networks in both parallel and complex configuration The model includes
cooling tower modelling cooler network modelling and hydraulic modelling In cooling
tower modelling correlation expressions of tower characteristics air inlet conditions
and water inlet conditions are developed to predict temperature of water leaving towers
and humidity of air leaving towers respectively In cooler network modelling detailed
heat transfer in individual coolers is considered In hydraulic modelling pressure drop
in both coolers and pipes are taken into account The nonlinear model is solved by the
solver CONOPT in GAMS to determine the optimal water distribution and air flowrate
For the integration of cooling water systems and processes with cooling demand a new
equation-based simultaneous optimisation method is proposed in which an integration
model of cooling water systems and processes is developed Condensing turbines are
taken as an example to illustrate the method
Case studies prove that the models are effective to solve the problems The standalone
optimisation of cooling water systems reduces the operating cost by 56 compared
with the base case The simultaneous optimisation increases the total profit by 337 kpoundyr
compared with focusing only on maximising the power generation of condensing
turbines
5
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institution of learning
Fei Song
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any
relevant Thesis restriction declarations deposited in the University Library the
University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy
on Presentation of Theses
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
5
Declaration
No portion of the work referred to in this thesis has been submitted in support of an
application for another degree or qualification of this or any other university or other
institution of learning
Fei Song
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
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7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
6
Copyright Statement
The author of this thesis (including any appendices andor schedules to this thesis) owns
certain copyright of related rights in it (the ldquoCopyrightrdquo) and she has given The
University of Manchester certain rights to use such Copyright including for
administrative purposes
Copies of this thesis either in full or in extracts and whether in hard or electronic copy
may be made only in accordance with the Copyright Designs and Patents Act 1988 (as
amended) and regulation issued under it or when appropriate in accordance with
licensing agreements which the University has from time to time This page much form
part of any such copies made
The ownership of certain Copyright patents designs trademarks and other intellectual
property (the ldquoIntellectual Propertyrdquo) and any reproductions of copyright works in the
thesis for example graphs and tables (ldquoReproductionsrdquo) which may be described in this
thesis may not be owned by the author and may be owned by third parties Such
Intellectual Property and Reproductions cannot and must not be made available for use
without the prior written permission of the owner (s) of the relevant Intellectual
Property andor Reproductions
Further information on the conditions under which disclosure publication and
commercialisation of this thesis the Copyright and any Intellectual Property University
IP Policy (see httpdocumentsmanchesteracukDocuInfoaspxDocID=487) in any
relevant Thesis restriction declarations deposited in the University Library the
University Libraryrsquos regulations (see
httpwwwlibrarymanchesteracukaboutusregulations) and in the Universityrsquos policy
on Presentation of Theses
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
7
Acknowledgement
I would like to express my gratitude to all those who helped supported and guided me
during my study and the writing of this thesis
I would like to express my sincere gratitude to my supervisor Dr Nan Zhang for his
great patience and constant guidance throughout this process His rigorous attitude
toward research and life has a significant impact on me Special thanks to Prof Robin
Smith and Dr Megan Jobson who give me valuable advice on my writing
I also owe thanks to my dear friends and my colleagues in the CPI who give me support
and help all through these years Special thanks to Yuhang Lou whose rigorous attitude
to her job inspired me Special thanks to my friends and colleagues Chengjun Qian
Luyi Liu Kunpeng Guo and Xiao Yang who provided me advice and helps on my
research and gave me encouragement In addition my special thanks would go to my
best friend Niantai Li
Last but not least I owe my thanks to my beloved parents who gave me both spiritual
and financial support for my study Without them I will not be who I am today Thanks
for their understanding and the wonderful life they provided to me
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
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Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
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[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
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28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
Chapter 1 Introduction
8
Chapter 1 Introduction
11 Background
111 Recirculating cooling water systems
Recirculating cooling water systems are widely used to reject process heat to keep
processes running efficiently and safely in chemical petrochemical and petroleum
processes refrigeration and air conditioning plants and power stations etc Cooling
water systems consume a large amount of water and power According to the data
collected from some refineries a recirculating cooling water system with 20000 th of
circulating water consumes about 260 th of make-up water and about 4000 kW of
electricity The make-up water consumption and power consumption of the cooling
water system are about half of the total water consumption and about 30 [4] of the
total power consumption of the refinery respectively
Figure 11 A recirculating cooling water system
The basic features of recirculating cooling water systems are shown in Figure 11 There
are three major components in a recirculating cooling water system namely wet cooling
towers cooler networks and piping networks Cooling water used as the cooling
Chapter 1 Introduction
9
medium is pumped and distributed by a piping network to individual coolers that form a
cooler network Cooling water removes the heat from processes and thereby gets a
temperature rise Then hot cooling water from the cooler network is sent to the wet
cooling towers to reject the heat obtained from processes The cold cooling water from
the cooling towers mixed with makeup water is pumped into individual coolers to cool
down processes again
Wet cooling towers are facilities where cold cooling water is produced Hot cooling
water is sent to the top of towers and air is blown to towers from the bottom The
downwards flowing water directly contacts the upwards flowing air As the moisture
content of the saturated air at the water temperature is greater than that of the air a
small portion of cooling water evaporates The latent heat needed by evaporation is
supplied by the remaining water which results in the reduction of water temperature
Besides heat convection occurs due to the temperature difference between water and air
The combination of water evaporation and heat convection is responsible for the final
decrease of water temperature About 80 of the total heat rejected by cooling water is
caused by evaporation [5] Because of the water evaporation contaminants in the
remaining water are concentrated In order to prevent cooling towers coolers and pipes
from fouling corrosion and biological growth some water known as blowdown is
removed to take away some impurities Besides some water known as drift is entrained
by the air Those water losses caused by evaporation blowdown and drift are
compensated by make-up water to keep the flowrate of circulating cooling water
constant Sometimes in order to reduce the heat load of cooling towers some hot
cooling water is discharged as hot blowdown which is shown in Figure 11 In this case
make-up water compensates for the water loss caused by not only evaporation
blowdown and drift but also hot blowdown
Chapter 1 Introduction
10
Wet cooling towers are categorised as natural draft wet cooling towers and mechanical
draft wet cooling towers according to the ways of drawing air through the towers In
natural draft wet cooling towers the buoyancy of the air rising in a tall chimney
provides the driving force for air flowing through towers which results in the large
sizes of towers while fans are used to blow air through the mechanical draft wet cooling
towers As generally used for water flowrate of 45000 th [6] and above natural draft
wet cooling towers are usually used in power stations Natural draft cooling towers
cannot optionally change air flowrate into cooling towers without the help of fans The
advantage of natural draft wet cooling towers is that no power is consumed to blow air
Mechanical draft wet cooling towers are categorised as forced draft wet cooling towers
and induced draft cooling towers by the location of fans Fans are located at the bottom
of forced draft wet cooling towers while they are located at the top of induced draft wet
cooling towers Air flowrate into mechanical draft cooling towers can be adjusted by the
control of fan speed on-off fans operation and use of automatically adjustable pitch
fans [1] which provides a degree of freedom for the operation of cooling water systems
The range and the approach are two important factors that affect cooling tower
performance Range is defined as the difference between the temperature of water
entering and leaving cooling towers Approach is the difference between the
temperature of water leaving cooling towers and ambient wet-bulb temperature that is
an indicator of how much moisture is in the air [1]
Cooler networks used in plants are either in a parallel arrangement or a series and
parallel arrangement Coolers or condensers where cooling water removes heat from
processes are usually shell and tube heat exchangers When cooling water used in
individual coolers is from cooling towers the cooler network is in a parallel
arrangement When cooling water used in coolers is not only that from cooling towers
but also the reuse water from coolers the cooling network is in a series and parallel
Chapter 1 Introduction
11
arrangement Cooler networks in a parallel arrangement are easier to control and
manage than those in a series and parallel arrangement However some cooling water
can be reused in cooler networks in a series and parallel arrangement which reduces the
usage of circulating water and increases the cooling water inlet temperature to cooling
towers
Piping networks distribute cooling water to individual coolers A piping network
consists of pipes pumps valves and pipe fittings When water flows in pipes valves
pipe fittings and coolers friction loss occurs in the cooling water Pumps provide the
energy for the cooling water to overcome the friction and keep the cooling water
circulating in cooling water systems Valves can be adjusted to change the cooling water
flowrate which provides another degree of freedom for the operation of cooling water
systems
The thermal or hydraulic behaviour of individual components is complex In cooling
towers both mass transfer and heat transfer are involved which makes it complicated to
simulate the thermal behaviour of cooling towers In cooler networks except for the
thermal behaviour of individual coolers there are thermal interactions between coolers
for cooler networks in a series and parallel arrangement The hydraulic behaviour of the
network includes pressure drop in both pipes piping fitting valves and coolers In
addition to the complexity of individual components there are strong interactions
between the components of cooling water systems The performance of cooling towers
and piping networks influences the performance of cooler networks The performance
of cooler networks and piping networks has an impact on the performance of cooling
towers The performance of cooling towers and cooler networks provides a requirement
for water distribution determined by piping networks Therefore when the operation of
cooling water systems is determined for a specified process cooling demand cooling
towers cooler networks and piping networks should be considered simultaneously
Chapter 1 Introduction
12
Besides ambient air conditions also have an impact on the thermal performance of
cooling towers The temperature of water leaving cooling towers varies with the
inevitable oscillations of ambient air conditions The ambient air conditions include dry-
bulb temperature wet-bulb temperature and humidity Dry-bulb temperature is ambient
temperature Wet-bulb temperature is an indicator of the moisture content in air The
humidity of air can be calculated with dry-bulb temperature wet-bulb temperature and
pressure
112 Operation of recirculating cooling water systems
The investigation of the operation of cooling water systems in this project includes
cooling water flowrate in individual towers and coolers air flowrate in individual
cooling towers and the resulting make-up water and power consumption Water flowrate
can be adjusted by valves and pumps and air flowrate can be adjusted by fans In a
given cooling tower the ratio of water inlet mass flowrate and air inlet mass flowrate
has an influence on the water outlet temperature Therefore the temperature of water
leaving towers can be altered by changing cooling water flowrate or air flowrate The
adjustable cooling water flowrate and temperature result in that various operations of a
cooling water system achieve the same process cooling demand Different operations
consume the different quantity of make-up water and power The total operating cost
incurred by make-up water and power consumption varies with the change of water
inlet flowrate and air inlet flowrate Therefore the economic performance of a given
cooling water system for a given process cooling load can be improved by changing
water inlet flowrate and air inlet flowrate As the change of power consumption caused
by the change of cooling water flowrate is opposite to the change in power consumption
caused by the change of air flowrate the most economic operation is determined by the
trade-off between cooling water flowrate and air flowrate
Chapter 1 Introduction
13
A study reveals that the energy consumption by a cooling water system can be saved by
about 11 through optimising cooling water flowrate air flowrate and water
distribution in cooling water systems in a petrochemical plant [7] According to the
study [7] for a cooling water system with 20000 th of circulating water in a refinery
the power consumption can be reduced by about 3200 MWh per year and the resulting
economic saving can be as much as 320 kpoundyr
113 Interactions between cooling water systems and processes
Water flowrate in individual coolers and water temperature produced by cooling towers
have a significant influence on the performance of some processes with cooling demand
such as condensing turbines compressor inter-cooling condensation of light
components for distillation pre-cooling for refrigeration compression and so on For
example the decrease in water temperature increases the power generation of
condensing turbines and reduces pressure in distillation columns power consumption
by compressors and refrigerator consumption However the decrease in water
temperature increases the operating cost of cooling water systems Consequently the
improvement in the performance of those processes increases the operating cost of
cooling water systems If the operation of cooling water systems is determined by
minimising the operating cost of cooling water systems only it may have a negative
impact on the performance of processes On the other hand if the operation of cooling
water systems is determined by optimising the performance of processes only the
operating cost of cooling water systems is likely to increase Therefore there is a trade-
off between the economic performance of cooling water systems and that of processes
with cooling demand to improve the overall economic performance
Condensing turbines with surface condensers using cooling water are typical users of
cooling water systems The power generation rate of condensing turbines is impacted by
cooling water flowrate and temperature In this work they are taken as an example of
Chapter 1 Introduction
14
processes with cooling demand to develop a systematic approach to determine the
optimal operation of cooling water systems for the improvement of overall economic
performance of cooling water systems and processes
114 Operation management of cooling water systems
In practice utility sectors manage the operation of cooling towers to achieve the desired
cooling water outlet temperature and process sectors manage the operation of cooler
networks based on the process cooling demand The two sectors do not exchange
detailed information about the behaviour of the overall systems They do not take the
interactions within cooling water systems and the interactions between cooling water
systems and processes into consideration when they manage their operation The
resulting operation of cooling water systems is not always the most cost effective
12 Motivation
The economic performance of cooling water systems can be improved by operational
optimisation of cooling water systems Due to strong interactions between cooling
towers cooler networks and piping networks the operational optimisation of cooling
water systems should be determined by the integration of cooling towers cooler
networks and piping networks Some studies [1] [2] [3] [8] [9] [10] [11] focused on
the design and operation of cooling water systems with the consideration of the
interactions between cooling towers and cooler networks Most of them were carried out
for design optimisation and only a few were performed for operational optimisation of
cooling water systems Some studies [8] and [12] employed the cooling tower models
that are differential equations based on the mass and heat transfer mechanism Although
they provide the accurate prediction the differential equations are difficult to handle in
an optimisation program Some studies [9] and [11] employed simple cooling tower
models that provide less accurate predictions than rigorous models Besides there is no
Chapter 1 Introduction
15
model developed for cooling water systems in those studies that considers all the factors
including detailed heat transfer in coolers pressure drop in coolers and pipes multiple
cooling towers and cooler networks in a complex arrangement
As mentioned above there are interactions between cooling water systems and
processes The focus of economic performance of cooling water systems only is very
likely to miss the opportunity of improving the performance of those processes
Therefore when the optimal operation of cooling water systems is determined the
performance of those processes should be considered with cooling water systems
simultaneously
13 Aims and objectives
The aims of this work include
To determine the optimal operation of cooling water systems for minimising the
operating cost of cooling water systems without affecting process performance
To determine the optimal operation of cooling water systems for improving the
overall performance of cooling water systems and condensing turbines
The steps to achieve the first aim include
Data analysis for the operation of cooling water systems
Model development of mechanical draft wet cooling towers with accurate
prediction for water evaporation rate and cooling water outlet temperature
To develop a cooler network model that considers detailed heat transfer in
coolers and interactions between coolers and cooling towers in which multiple
cooling towers and cooler networks in a series and parallel arrangement are
included
To develop a piping network model including pressure drop in coolers pipes
Chapter 1 Introduction
16
pipe fittings and valves
To develop a model of cooling water systems by integration of cooling towers
cooler networks and piping networks
To solve the problem with the objective of minimising the operating cost of
cooling water systems
The steps to achieve the second aim include
To integrate the models of cooling water systems and processes (eg condensing
turbines)
To optimise cooling water systems and condensing turbines simultaneously for
maximising the total profit
14 Thesis outline
The thesis consists of three papers to cover three main research areas for cooling water
systems In the first paper a regression model of mechanical draft wet cooling towers is
proposed and validated which is then subject to optimisation to minimise the operating
cost of cooling towers for fixed process cooling demand In the second paper a model
of cooling water systems with the integration of cooling towers cooler networks and
piping networks is developed and the operation of cooling water systems is optimised
for minimising the operating cost of cooling water systems again under fixed process
cooling demand In the third paper a model of cooling water systems and condensing
turbines is developed for the operational optimisation of cooling water systems to
maximise the total net profit of cooling water systems and condensing turbines Finally
conclusions and future work are presented
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Chapter 2
Publication 1 Operational Optimisation of Mechanical
Draft Wet Cooling Towers
(Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical
Draft Wet Cooling Towers)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
1
Operational Optimisation of Mechanical Draft Wet
Cooling Towers
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Mechanical draft wet cooling towers are widely used in process industries to reject
process heat into the atmosphere Varying operations of cooling towers can achieve the
same process cooling demand with different total operating cost Therefore water and
air mass flowrate entering cooling towers are optimised to improve the economic
performance of cooling towers A nonlinear model of cooling towers is developed for
the operational optimisation In the model correlation expressions of tower
characteristics ambient air conditions air flowrate and inlet water conditions are
proposed to predict air outlet humidity and cooling water outlet temperature The
correlation equation to predict air outlet humidity refers to a correlation proposed by
Qureshi et al [1] The correlation equation to calculate water outlet temperature is
proposed through analysing the effect of key factors on the temperature The correlation
equations are validated with the measured data presented in Simpson and Sherwood [2]
To optimise the operating variables of towers the model is solved by the solver
CONOPT in GAMS The model is proven to be effective to improve the economic
performance of cooling towers by a case study In the case study through optimisation
the operating cost of the cooling tower is reduced by about 69 compared with the
base case
Key words mechanical draft wet cooling towers correlation operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
2
Highlights
A regression model of cooling towers is developed and validated
The regression model is effective to reduce the operating cost of cooling towers
The effect of ambient air conditions on the performance of cooling towers is
investigated
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
atmosphere through cooling water in chemical petrochemical and petroleum processes
and power stations etc The basic features of recirculating cooling water systems are
presented in Figure 1 Wet cooling towers are one of the key components in
recirculating cooling water systems as they play a major role in the recycling of cooling
water in recirculating cooling water systems In a recirculating cooling water system
cooling water removes heat from processes resulting in a rise in cooling water
temperature The hot cooling water is sent to wet cooling towers after heat exchange
with processes In wet cooling towers cooling water is cooled down by direct contact
with air After that cold cooling water from wet cooling towers is pumped to remove
heat from processes again As a result cooling water consumption is reduced to about 5
that of a once-through system [3] In addition cooling water can be cooled to below
ambient temperature by the employment of wet cooling towers Compared with the
cooling water temperature created by dry cooling towers the cooling water temperature
produced by wet cooling towers can achieve cooling requirement of most industrial
processes Mechanical draft wet cooling towers are the most common especially in the
petrochemical chemical and petroleum industries and refrigeration and air conditioning
plants The fundamentals of wet cooling towers can be referred to references [4] [5]
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
3
Figure 1 Recirculating cooling water systems
Inlet air flowrate and inlet cooling water flowrate are two adjustable elements in the
operation of mechanical draft wet cooling towers The inlet air flowrate is adjusted by
fans in mechanical draft wet cooling towers The inlet cooling water flowrate is the
same as the cooling water flowrate that is needed by process heat removal when all the
cooling water used to remove heat from processes enters cooling towers to be cooled
down The cooling water flowrate used to remove process heat can be adjusted by
valves and pumps Therefore the inlet cooling water flowrate of cooling towers is
adjustable According to the fact that the cooling water temperature produced by
cooling towers is affected by the ratio of air mass flowrate and cooling water mass
flowrate into cooling towers recorded in the literature [6] [7] [8] the cooling water
temperature produced by cooling towers is variable when inlet air flowrate or inlet
cooling water flowrate changes Since they are variables cooling water flowrate and
cooling water temperature can be adjusted to satisfy the cooling requirement of
processes in many ways such as a relatively low cooling water flowrate coupled with a
relatively large range or a relatively high cooling water flowrate coupled with a
relatively small range
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
4
Even though different operations of cooling towers can achieve the same cooling
requirement of processes different operations consume the different quantity of power
and make-up water resulting in the different operating cost that consists of power cost
and make-up water cost Therefore the economic performance of cooling towers can be
improved by optimising inlet cooling water mass flowrate and inlet air mass flowrate
For a given mechanical draft wet cooling tower with a given cooling requirement of
processes when the inlet cooling water mass flowrate is increased the cooling water
temperature difference caused by heat exchange with processes will decrease
accordingly The decrease in the cooling water temperature difference reduces the
demand for air in cooling towers The increase of cooling water flowrate increases
power consumption of water pumps while the decrease of inlet air mass flowrate
reduces power consumption of fans Due to the opposite effect of the change of cooling
water flowrate and air flowrate on power consumption there is a trade-off between inlet
cooling water mass flowrate and inlet air mass flowrate to improve the economic
performance of cooling towers Questions are what the most cost effective operation is
and how it is obtained for an existing cooling tower with specified process cooling
demand Those questions can be solved systematically by the operational optimisation
subject to the model of cooling towers
It is not straightforward to obtain the optimal operation for cooling towers to fulfil the
cooling duty imposed by processes because of the complex thermal behaviour of
cooling towers The operation of cooling towers is not only affected by the tower
characteristics but also the process cooling requirement For one thing the cooling
water outlet temperature of cooling towers is influenced by the air inlet mass flowrate
the cooling water inlet mass flowrate the cooling water inlet temperature and the
characteristic of cooling towers For the other the cooling water inlet flowrate and the
cooling water inlet temperature are adjusted to remove the specified heat from processes
according to cooling water outlet temperature from cooling towers Therefore the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
5
interacted air inlet flowrate cooling water inlet flowrate cooling water inlet
temperature and outlet temperature are constrained by both the cooling load of
processes and the thermal behaviour of cooling towers Besides the ambient air
conditions that include dry-bulb temperature wet-bulb temperature and humidity have
an influence on water temperature produced by cooling towers As a result the heat
rejected by processes will vary in accordance with the oscillations of ambient air
conditions when a fixed operation of cooling towers is implemented
Many thermal models were developed for cooling towers in the literature Differential
equations were used to describe heat and mass transfer in cooling towers for design
rating and analytical purposes in the literature [3] [9] [10] [11] [12] [13] [14]
Cooling tower models were based on the film theory in [3] [9] and [11] Merkel [9] was
the first to develop a model for cooling towers with differential equations In this model
water evaporation was neglected to simplify the model and the outlet air was assumed
to be saturated to determine the characteristic of cooling towers Due to the assumptions
water evaporation rate cannot be predicted accurately Kloppers et al [10] provided the
detailed governing equations for mechanical draft counter flow wet cooling towers
based on the Poppe method [11] In this method three governing differential equations
were developed to predict the humidity and enthalpy of outlet air and the transfer
characteristics of towers Without assumptions as made by Merkel the Poppe method
[11] estimates water evaporation rate outlet temperature of cooling water and
characteristics of cooling towers more accurately than the Merkel method [9] The
Poppe method did not consider the heat resistance in the water film while Khan et al [3]
considered the heat resistance in the water film in their model Fisenko et al [12] and
Qureshi et al [13] described evaporative cooling of both water film and water droplets
Qureshi et al [13] employed the model for evaporative cooling of water droplets
developed by Fisenko et al [12] However the model for the water film in the literature
[12] was developed to predict film temperature and thickness averaged temperature of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
6
the moist air and density of the water vapour in the air while that in Qureshi et al [13]
was to predict the enthalpy and the humidity of the air In addition Qureshi et al [13]
considered the effect of fouling on the thermal performance of cooling towers in their
model Jaber and Webb [14] extended the effectiveness-NTU method to cooling towers
As it makes the same assumptions as those in the Merkel method [9] the effectiveness-
NTU method provides the estimation close to that of the Merkel method In the
literature optimisation of cooling towers in terms of operation and design was carried
out with different cooling tower models The Merkel method was transformed into an
algebraic equation using the four-point Chebyshev integration technique and applied in
an optimisation program for cooling tower design [15] Rubio-Castro et al [16] applied
the Poppe method to the same optimisation program as that in [15] by using the fourth-
order Runge-Kutta algorithm The application of the Poppe method makes it more
difficult to solve the optimisation problem than that of the Merkel method But the
prediction by the Poppe method is more practical that by the Merkel method as the
assumptions that simplify the Merkel method are not made in the Poppe method Castro
et al [17] employed a correlation model of cooling towers for operational optimisation
of cooling water systems In this model the inlet air flowrate is determined based on the
assumption that the outlet air from cooling towers is saturated and water evaporation
rate was related to the cooling duty of cooling towers only regardless of the effect of
ambient air conditions on water evaporation In addition there were some correlations
established for the transfer characteristics in the literature [18] [19] [20] [21] [22]
[23] [24] for the range of cooling towers in the literature [25] and for the evaporation
ratio in the literature [1]
In summary a detailed phenomenological model of a cooling tower is expressed as
differential equations which cannot be directly used in an optimisation program When
it is applied in an optimisation program with the help of the Runge-Kutta algorithm the
number of variables and equations in the problem will be increased The Merkel method
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
7
is widely used in optimisation programs because of the simplicity However some
assumptions made in the Merkel method reduce the accuracy of predictions So do the
other models that make the same assumptions as in the Merkel method To overcome
those limitations a regression model of cooling towers will be developed for the
optimisation for cooling tower operation
In this paper the operational optimisation of cooling towers is carried out to determine
the optimal cooling water inlet mass flowrate and air inlet mass flowrate for a given
cooling tower with specified process cooling demand A nonlinear model is developed
for the operational optimisation The model includes mass and energy balance for
cooling towers correlation equations characteristics of fans and pumps and an equation
for the cooling demand In order to make the optimisation program less difficult to solve
correlation functions are developed to estimate the cooling water outlet temperature the
water evaporation and the number of transfer units of mechanical draft wet cooling
towers Power consumption by fans and pumps is determined by the characteristics of
fans and pumps The hydraulic characteristics of cooling towers and piping networks
are not considered here Then the model is applied to optimise cooling water mass
flowrate and air mass flowrate for a given cooling tower subject to the variation of
ambient air conditions in case studies
2 Mechanical Draft Wet Cooling Tower Modelling
Mathematical models are developed for optimising the operation of a given cooling
tower with given cooling requirement of processes The specified cooling requirement
of processes is the target of the operation of cooling towers The operation consists of
cooling water inlet mass flowrate and air inlet mass flowrate Cooling water inlet
temperature cooling water outlet temperature make-up water consumption power
consumption and the resulting operating cost will be changed with the variation of
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
8
operations Ambient air conditions have an influence on the thermal performance of
cooling towers
As the cooling requirement of processes is satisfied by the operation and the thermal
performance of cooling towers caused by the operation a thermal model of cooling
towers and cooling requirement of processes are used as constraints for the prediction of
the cooling water inlet mass flowrate and the air inlet flowrate Then an objective
function is employed to select the optimum operation among the feasible solutions
In this section a thermal model of cooling towers is established as constraints in the
optimisation model Number of transfer units (NTU) as the transfer characteristic of
cooling towers is one of the main factors that influence the thermal performance of
cooling towers The cooling water outlet temperature of cooling towers indicating the
thermal performance of cooling towers plays a vital role in heat removal from processes
The air outlet humidity is important to predict water evaporation rate and air outlet
conditions Therefore three correlation functions are established to relate the three
variables to other variables and parameters individually An energy balance between
process streams and cooling water is used to make sure the process cooling demand is
satisfied Last but not least the objective function is established to determine the
optimal operation of a given cooling tower which is to minimise the total operating cost
In order to estimate the total operating cost power consumption and make-up water
consumption are calculated
There are some assumptions for the model of cooling towers developed in this paper
The system is at steady state
Negligible heat through the tower walls to the environment
Negligible heat transfer from the tower fans to air or water streams
Constant specific heat capacity of water water vapour and dry air throughout the
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
9
tower
Uniform cross-sectional area of the tower
No supersaturated air from cooling towers
21 Thermal model of cooling towers
211 Mass and energy balance
In a wet cooling tower water loss in the water stream caused by evaporation is
equivalent to the increase of moisture content in the air which is expressed in equation
(1)
( ) (1)
where and are cooling water inlet and outlet mass flowrate respectively
is dry air mass flowrate and and are air inlet and outlet humidity ratio based on
dry air mass flowrate respectively
The energy balance in towers is carried out by equation (2)
( ) (2)
where is the specific heat capacity of cooling water and are cooling water
inlet and outlet temperature respectively and and are specific enthalpy of air
entering and leaving cooling towers based on the dry air mass flowrate respectively
Water evaporation is considered in both mass balance and energy balance
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
10
212 Correlation expressions for cooling towers
(1) Characteristics of cooling towers
The Merkel number and the number of transfer units (NTU) are two representations of
transfer characteristics of cooling towers The relationship between NTU and the
Merkel number is shown in equation (A6) in the Appendix The Merkel number can be
calculated by the correlation equation proposed by Johnson [23] which is presented as
equation (A7) in the Appendix Therefore the correlation expression of NTU can be
presented as equation (A8) according to the correlation equation of the Merkel number
With the assumption that the cross section covered by air and water is constant a
correlation equation of the NTU is simplified as
(3)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and are coefficients
(2) Cooling water outlet temperature
The outlet water temperature of cooling towers needs to be predicted as the outlet water
temperature have an impact on heat removal from processes It is indicated in the
literature [3] that the outlet water temperature is influenced by inlet water temperature
inlet water mass flowrate dry air mass flowrate and inlet wet-bulb temperature The
effect of those factors on the range that is the difference between water inlet temperature
and water outlet temperature is analysed and the results are displayed in Figure 2 All
the calculation for the analysis is implemented by the Poppe method [10] Figure 2 (a) is
a plot between the range and NTU for different value of the mass flowrate ratio
( frasl ) The follow set of input data is used to draw the plot
In Figure 2 (b) a plot between
the range and inlet mass flowrate of cooling water for different value of water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
11
temperature is shown The following set of input data is used to draw the plot
In Figure 2 (c) a plot between the range and dry air mass flowrate for different value of
water inlet temperature is generated with the input data
Figure 2 (d) is a
plot between the range and the difference between water inlet temperature and ambient
wet-bulb temperature for different value of the mass flowrate ratio ( frasl ) The plot
is generated with the input data
(a)The range versus NTU
(b)The range versus inlet mass flowrate of cooling water
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
12
(c)The range versus mass flowrate of dry air
(d)The range versus difference between water inlet temperature and ambient wet-bulb
temperature
Figure 2 Variation of the range versus NTU (a) water inlet mass flowrate (b) dry air mass
flowrate (c) and difference between water inlet temperature and ambient wet-bulb
temperature (d)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
13
According to the plots in Figure 2 equation (4) is proposed to predict the outlet
temperature of cooling water from an existing cooling tower
( ) (4)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature is ambient wet-bulb temperature NTU is the
number of transfer units and are coefficients
(3) Air outlet humidity
The air outlet humidity is important for the estimation of water evaporation and air
outlet conditions Therefore the correlation model is developed for the air outlet
humidity A correlation equation for water evaporation percentage was proposed and
validated by Qureshi et al [1] which is presented as equation (A17) in the Appendix
The water evaporation ratio (ER) can be expressed as equation (5)
( )
w (5)
where is cooling water inlet mass flowrate is dry air mass flowrate and and
are air inlet and outlet humidity ratio based on dry air mass flowrate respectively
Combining equations (5) and (A17) equation (6) is obtained
( )
w ( ) ( ) ( ) (6)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
14
where and are cooling water inlet and outlet temperature respectively and
and are ambient dry-bulb temperature and ambient wet-bulb temperature
respectively
Equation (6) is rearranged to be equation (7)
( ( ) ( ) ( )) (7)
According to equation (7) equation (8) is proposed to predict air outlet humidity
( ( ) ( ) ( ))
(8)
where γ -γ are coefficients
213 Cooling requirement of processes
The cooling water from a cooling tower mixed with make-up water is distributed into
individual coolers to remove heat from processes The cooling water temperature into
coolers can be determined by equation (9)
( ) (9)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water outlet temperature is the mass flowrate of the
make-up water is the temperature of the make-up water and is the temperature of
the water stream after make-up
The process cooling demand achieved by cooling water can be presented as equation
(10)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
15
( ) (10)
where is the specific heat capacity of cooling water is cooling water inlet
mass flowrate is cooling water inlet temperature and is the temperature of the
water stream after make-up
The equations for thermal properties of cooling water and air are presented in Appendix
Those thermal properties of cooling water and air related to temperature are calculated
at the mean temperature of water entering and leaving towers
22 Economic performance of cooling towers
221 Make-up water consumption
When there is no hot blowdown removed the make-up water is consumed to
compensate for the water losses mainly caused by water evaporation Water evaporation
rate is calculated by the humidity difference between inlet air and outlet air as
represented by equation (11) The humidity of air leaving a tower is predicted by
equation (8)
( ) (11)
where is water evaporation rate is dry air mass flowrate and and are air
inlet and outlet humidity ratio based on dry air mass flowrate respectively
The consumption of make-up water is expressed as equation (12)
(12)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
16
where is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water [26] The cycles of
concentration are taken as parameters
222 Power consumption
Power consumption of mechanical draft wet cooling towers consists of power
consumption of fans and pumps The power needed by fans is related to the air mass
flowrate and characteristics of fans In general form the power needed by a given fan
can be written as equation (13)
( ) (13)
where is power consumption of fans and is dry air mass flowrate
Power consumed by pumps to compensate for the friction loss of cooling water is
determined by cooling water volumetric flowrate and characteristics of the pumps
Equations (14) - (16) are used to calculate power consumption by pumps [27]
(14)
( ) (15)
w
(16)
where is the volumetric flowrate of water flowing through the pump is the
mass flowrate of water flowing through the pump is the pressure head provided by
the pump is the pump efficiency and is the power consumed by the pump
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
17
Note that it is assumed that the pressure head provided by fans and pumps satisfies the
head requirement within the limitation boundary of cooling water flowrate and dry air
flowrate
23 Practical constraints
The practical constraints include the limitation boundary of cooling water inlet mass
flowrate air inlet mass flowrate the ratio of cooling water inlet mass flowrate and air
inlet mass flowrate the cooling water inlet temperature and the cooling water outlet
temperature
(17)
(18)
w
w
w
(19)
(20)
(21)
where is cooling water inlet mass flowrate is dry air mass flowrate is
cooling water inlet temperature and is cooling water outlet temperature
24 Objective function
In this problem the objective function is to minimise the operating cost expressed as
equation (22) The operating cost (TOC) includes make-up water cost and power cost
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
18
( ) (22)
where is mass flowrate of make-up water is power consumption of fans is
power consumption of pumps and C1 and C2 are unit cost of make-up water and power
respectively
3 Model validation
A cooling tower presented in Simpson and Sherwood [2] is used to illustrate the
accuracy of those correlation equations The coefficients in the correlations are
regressed for the cooling tower with the least square method
Measured data for cooling water inlet mass flowrate dry air mass flowrate and cooling
water inlet temperature and the corresponding calculated value of NTU are required to
determine the coefficients (α1-α4) in the correlation for NTU The value of NTU cannot
be measured directly but it can be predicted by the phenomenological models of
cooling towers In this paper the Poppe method presented in [10] is used to calculate
the value of NTU When the Poppe method is applied to calculate the value of NTU the
interface temperature is assumed to be 05 K less than water temperature in cooling
towers [28]
The coefficients (β -β ) in equations (4) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
mass flowrate dry air mass flowrate and air inlet wet-bulb temperature as well as the
calculated value of NTU
The coefficients (γ -γ ) in equations (8) are regressed by the least square method with
the measured data of cooling water inlet and outlet temperature cooling water inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
19
mass flowrate dry air mass flowrate and air inlet dry-bulb temperature wet-bulb
temperature and humidity
The measured data used to predict the coefficients in equations (3) (4) and (8) is
presented in Table A1 in the Appendix The coefficients in the regression model of the
cooling tower are presented in Table 1
Table 1 Coefficients for the cooling tower in Simpson and Sherwood [2]
(a) Coefficients in equation (3)
α1 α2 α3 α4
95846 06568 -12569 -04216
(b) Coefficients in equation (4)
β1 β2 β3 β4 β5
40099 -17177 08672 -21377 08165
(c) Coefficients in equation (8)
γ1 γ2 γ3 γ4 γ5 γ6 γ7
-2176E-03 1089E-03 3715E-04 2322E-04 9006E-01 -6731E-01 1074E+00
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
20
(a) Predicted outlet water temperature versus measured outlet water temperature
(b) Predicted outlet air humidity versus measured outlet air humidity
Figure 3 Measured versus predicted values
A good agreement between predicted values by regression models and the measured
data is reached which is shown in Figure 3 With the regressed coefficients the cooling
water outlet temperature and the air outlet humidity can be calculated for any operating
y=x
y=x
R2=0992
R2=0996
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
21
conditions within the range of measurement The accuracy of these regressed equations
is validated with other measured data for the cooling tower that is not used for the
coefficient regression The comparison results are listed in Table 2
Table 2 Comparison of wo and two between the regressed model and the measured data
provided by Simpson and Sherwood [2]
No 1 2 3 4 5 6
Measured
data
(degC) 2933 3667 4100 3889 4033 3572
(degC) 2966 3192 3550 3111 3361 3311
(degC) 2111 2111 2388 2388 2667 2944
(kgs) 1186 1178 1157 1174 1157 1156
(kgs) 1132 1132 0881 1132 1008 1258
Calculated
data
(degC)
Measured 2433 2633 2800 2844 3044 3122
Correlation 2415 2642 2818 2851 3016 3106
Relative
difference () 073 -036 -065 -024 092 051
(10-2
kgkg
dry air)
Measured 2192 2835 3108 3223 3454 3301
Correlation 2168 2878 3119 3229 3419 3305
Relative
difference
()
111 -151 -037 -017 103 -011
The relative differences between the correlations and the measured data in terms of the
cooling water outlet temperature and the air outlet humidity are no more than 10 and
20 respectively Therefore the correlation equations predict the cooling water outlet
temperature and the air outlet humidity accurately
4 Solution Method
Before the model is applied the coefficients in equations (3) (4) and (8) are regressed
for the given cooling tower by the least square method with measured data or operation
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
22
data After that the objective function is minimised with the input data of the given
process cooling demand unit cost of make-up water and power the cycles of
concentration and the ambient air conditions (dry-bulb temperature wet-bulb
temperature and humidity) subject to the constraints composed of equations (1) - (4)
and (8) - (16) and the practical constraints including equations (17) - (21) As the model
includes nonlinear equations the optimisation problem is a nonlinear problem
Therefore the problem is solved by the solver CONOPT in software GAMS as
CONOPT is well suited for models with nonlinear constraints Before solving the
problem the initial values are assigned to the variables After optimisation the optimal
cooling water inlet mass flowrate and dry air mass flowrate into the cooling tower are
determined for the specified cooling load and the consequent cooling water outlet
temperature of the cooling tower power consumption make-up water consumption and
operating cost are obtained
5 Case Studies
Two case studies are presented to illustrate the application of the model developed
above to determine the optimal operation of a cooling tower in various ambient air
conditions In Case 1 the base case is optimised for a given cooling tower with
specified process cooling demand The variation of ambient air conditions causes the
change of the thermal performance of cooling towers The variation of the thermal and
economic performance of the cooling tower with the change of ambient air conditions is
examined in Case 2 Then operating variables of the cooling tower are optimised
corresponding to individual ambient air conditions In Case 2 it is investigated whether
it is worthwhile to optimise the operating variables when the ambient air conditions
change
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
23
51 Base case
A cooling tower with a fan and a pump is employed to complete the specified cooling
requirement of processes The specified process cooling demand is 9928 MW The
ambient air conditions are listed in Table 3 which include dry-bulb temperature wet-
bulb temperature humidity and enthalpy 7920 th cooling water and 7200 th dry air
are used to cool down the processes The make-up water temperature is assumed to be
the same as the ambient temperature The unit cost of make-up water is 03 poundt and the
unit cost of electricity is 01 poundkWh 4 cycles of concentration are used There are some
practical constraints listed in Table 4 such as the upper bound of cooling water inlet
and outlet temperature and limitation boundary of cooling water and dry air mass
flowrate The thermal and economic performance of the cooling tower is presented in
Table 6
Table 3 Ambient air conditions and process cooling demand
Cases Base case Case 1 Case2
Condition 1 Condition 2 Condition 3
Ambient air
conditions
tdbi (degC) 3028 3028 3533 2950 2600
twbi (degC) 2565 2565 2944 2500 2250
wi (10
-2kgkg dry air)
190 190 239 183 158
ii (kJkg) 7913 7913 9688 7636 6645
Process cooling demand (MW) 9928
Table 4 Practical constraints
Cooling water inlet temperature (degC) Upper bound 4800
Cooling water outlet temperature (degC) Upper bound 3500
Cooling water mass flowrate (th) Upper bound 8640
Lower bound 4320
Dry air mass flowrate (th) Upper bound 9720
Lower bound 3600
Upper bound 17
Lower bound 07
Approach (degC) Lower bound 33
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
24
52 Case study 1
The mass flowrate of cooling water and dry air entering the tower is optimised with the
model developed and the proposed solution method in last section The objective is to
minimise the operating cost of the tower Before optimisation the coefficients in the
regression models of the cooling tower the fan and the pump are regressed The
regression models are provided in Table 5 There are 20 equations and 22 variables in
this optimisation problem
Table 5 Models of the cooling tower the pump and the fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan [17]
( )
The optimisation results are presented in Table 6 Through optimisation the cooling
requirement of processes is satisfied and the total operating cost is reduced by 175 poundh
(approximately equivalent to 140 kpoundyr) when the cooling water inlet flowrate reduces
from 7920 th to 5760 th and the dry air flowrate increases from 7200 th to around
9187 th As the water mass flowrate is decreased the range that is the temperature
difference between the inlet water and the outlet water is supposed to increase to
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
25
achieve the cooling requirement The range is increased from 108 degC to 149 degC by the
increase of the air mass flowrate Therefore the cooling requirement of processes is
achieved by the decrease of inlet cooling water flowrate and the increase of the air mass
flowrate Although the cooling requirement of processes is fixed the cooling duty of the
cooling tower is slightly increased as the change of the operating variables results in a
slight increase of evaporation rate The increase of the evaporation rate leads to 47 th
more make-up water consumption than that in the base case In respect of power
consumption the decrease of water flowrate results in the decrease of power
consumption of the pump by around 290 kW while the increase of the air flowrate
increases the power consumption of the fan by about 100 kW As a result the overall
power consumption reduces by about 190 kW through optimisation As the increase in
the cost of make-up water is less than the decrease in the cost of power the total
operating cost decreases
Table 6 Optimisation results
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Operating
conditions
Inlet water
flowrate (th) 7920 5760 5760 6280 5641 7137
Inlet dry air
flowrate (th) 7200 9187 9187 7533 9441 4996
Cooling
water
Inlet
temperature
(degC)
4100 4385 4385 4644 4351 4062
Outlet
temperature
(degC)
3020 2895 3166 2849 2676 3274 2830 2869
Range (degC) 1080 1490 1219 1536 1709 1370 1521 1193
Cooling duty of cooling
towers (MW) 1039 1041 858 1071 1188 1052 1039 1029
Heat rejected by processes
(MW) 9928 8079 10240 11442 9928
Evaporation rate (th) 1304 1339 1181 1368 1466 1404 1331 1226
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
26
Cases Base
case
Case
1
Case 2
Before optimisation After optimisation
Condition
1
Condition
2
Condition
3
Cond
1
Cond
2
Cond
3
Make-up water
consumption (th) 1738 1785 1575 1824 1955 1872 1775 1635
Power
consumption
(kW)
Fan 353 450 450 450 450 377 462 240
Pump 1631 1344 1344 1344 1344 1396 1333 1503
Total 1984 1794 1794 1794 1794 1773 1795 1743
Cost (poundh)
Make-up
water 522 536 473 547 587 561 532 490
Power 1983 1794 1794 1794 1794 1773 1795 1743
Total 2505 2330 2267 2341 2381 2334 2327 2233
53 Case study 2
In this case three different ambient air conditions are used to investigate the effect of
the ambient air conditions on the thermal and economic performance of the cooling
tower The ambient air conditions are listed in Table 3 The optimal value of operating
variables of the cooling tower obtained in Case 1 is implemented under individual air
conditions The resulting thermal and economic performance of the cooling tower is
presented in Table 6
It is noticed that the process cooling demand cannot be satisfied by the fixed operation
when the ambient air becomes hot and humidity while excessive heat is removed by the
fixed operation when the ambient air becomes cold and dry In the condition 1 the heat
rejected by processes is around 81 MW which is about 18 MW less than the cooling
requirement In conditions 2 and 3 the heat rejected by processes is around 104 MW
and 114 MW respectively which are about 5 and 15 MW more than the cooling
requirement That is because the cooling water outlet temperature is increased with the
increase of inlet dry-bulb temperature wet-bulb temperature and humidity when the
cooling water inlet flowrate the dry air flowrate and the cooling water inlet temperature
are fixed as shown in Table 6
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
27
A fixed operation of cooling towers under different ambient air conditions results in that
either the cooling demand is not satisfied or the excessive heat is removed from
processes Therefore the operating variables of towers are supposed to be adjusted for
individual ambient air conditions to complete the cooling demand and to reduce the
operating cost at the same time Operational optimisation of the tower is performed
under individual ambient air conditions The optimisation results are listed in Table 6
Through optimisation the specified cooling demand is satisfied no matter what the
ambient air conditions are and the operating cost is minimised In the condition 1
through optimisation the cooling water inlet mass flowrate is increased by about 520 th
while the dry air mass flowrate is decreased by around 1654 th compared with the
operation obtained in Case 1 As the cooling load is increased from about 81 MW to
around 99 MW the cooling water flowrate is increased to complete the cooling demand
The large decrease of air flowrate is caused by the reduction of the range of cooling
water and the increase of cooling water inlet temperature which results in the reduction
of the total power consumption The optimal operation of the cooling tower leads to the
increase of evaporation rate and thereby the make-up water consumption is increased
As a result the overall operating cost is higher than that in Case 1 The dry-bulb
temperature the wet-bulb temperature and the humidity in conditions 2 and 3 are lower
than those in case 1 Through optimisation the cooling water inlet mass flowrate is
decreased by approximate 120 th while the air mass flowrate is increased by about 250
th in condition 2 The increase of the air mass flowrate is mainly caused by the increase
of the range The increase of power consumed by the fan is more than the decrease of
power consumed by the pump and thereby the total power consumption is increased
Due to the reduced water evaporation rate the make-up water consumption is decreased
As a result the total operating cost is reduced by 03 poundh The operating cost in
condition 2 is quite close to that in case 1 as the ambient air conditions are almost the
same In condition 3 the cooling water inlet mass flowrate is increased which results in
the decrease of the range The dry air mass flowrate is largely reduced which is caused
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
28
by the large reduce of the range and the favourable ambient air conditions The overall
power consumption is reduced by about 50 kW As the water evaporation rate decreases
the make-up water consumption is reduced by 32 th Therefore the total operating cost
is decreased by nearly 10 poundh In summary the operational optimisation of a cooling
tower carried out for each air condition allows the cooling demand to be completed with
the minimum total operating cost no matter how the ambient air conditions change The
benefit from the optimisation is obvious when ambient air conditions change a lot
while the benefit from the optimisation is little when ambient air conditions change
slightly
6 Conclusions
Various operating conditions of a given cooling tower can achieve the cooling
requirement of processes resulting in different total operating cost Therefore the
operational optimisation of cooling towers is necessary to improve the economic
performance A model of mechanical draft wet cooling towers is developed for an
operational optimisation program to optimise water inlet flowrate and air inlet flowrate
of cooling towers to improve the economic performance of cooling towers In this
model correlation functions are established to predict water outlet temperature air
outlet humidity and number of transfer units The regression functions correlate tower
characteristics air conditions and water conditions to predict water outlet temperature
and water evaporation rate The model considers more factors that influence water
outlet temperature and water evaporation rate than the regression model developed in
Castro et al [17] The correlation expressions are verified with the literature data [2]
The solver CONOPT is proposed to solve the NLP problem in GAMS The model is
proven to be effective to determine the optimal operating conditions and to improve the
economic performance of cooling towers by a case study In the case study the total
operating cost is improved by 69 through optimisation compared with that in the
base case
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
29
In addition the effect of the ambient air conditions on the operation and the resulting
thermal and economic performance of the cooling tower are investigated The results
reveal that a fixed operation of the cooling tower cannot satisfy the cooling requirement
of processes when the ambient air becomes hot and humidity while it removes
excessive heat when the ambient air becomes cold and dry The optimisation of the
cooling tower under different ambient air conditions not only completes the specified
cooling demand but also reduces the operating cost
The model of cooling towers is based on mechanical draft wet cooling towers
Therefore the application of the model is appropriate to mechanical draft wet cooling
towers The model of nature draft wet cooling towers is not developed here but can refer
to the model proposed in this paper The operation of cooling towers is determined with
the consideration of the transfer characteristic of cooling towers and the process cooling
demand regardless of the effect of cooler networks and piping networks on the
operation In fact the cooling water inlet temperature is determined by the structure of
individual coolers and the arrangement of cooler networks besides the factors
considered in this paper In future work therefore the detailed cooler network will be
taken into account when the operation of cooling towers is optimised
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
30
Nomenclature
Parameters
A cross sectional area of fill in a cooling tower (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
ifgwo latent heat of water evaluated at 27315K (Jkg)
ii enthalpy of inlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
Lfi the height of fill in a cooling tower (m)
Q the cooling load of processes (W)
tm temperature of makeup water (degC)
tdbi air inlet dry-bulb temperature of a cooling tower (degC)
twbi air inlet wet-bulb temperature of a cooling tower (degC)
wi humidity ratio of inlet air into cooling towers (kgkg dry air)
Variables
Cpa the specific heat of dry air (JkgdegC)
Cpv specific heat of saturated water vapor (JkgdegC)
Cpw the specific heat of cooling water (JkgdegC)
ER evaporation ratio
Hp pressure head provided by pumps (m)
ifgw latent heat of water (Jkg)
ima enthalpy of the airndashwater vapour mixture per unit mass of dry air (Jkg dry
air)
imasw enthalpy of saturated air evaluated at the local bulk water temperature (Jkg
dry air)
io enthalpy of outlet air-water vapour mixture per unit mass of dry air (Jkg
dry air)
iv enthalpy of the water vapour at the bulk water temperature (Jkg)
Lef the Lewis factor
ma mass flowrate of dry air in a cooling tower (kgs)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
31
Mep Merkel number
me evaporation rate (kgs)
mm mass flowrate of makeup water (kgs)
mw mass flowrate of cooling water in a cooling tower (kgs)
mwi mass flowrate of inlet cooling water into a cooling tower (kgs)
mwo mass flowrate of outlet cooling water from a cooling tower (kgs)
NTU number of transfer units
p pressure (Pa)
ps vapour pressure of saturated water vapour (Pa)
pswb vapour pressure of saturated water vapour evaluated at the wet-bulb
temperature (Pa)
Pf power consumed by fans (kW)
Pp power consumed by pumps (kW)
Qw volumetric flowrate of cooling water (m3s)
T temperature K
tdb dry-bulb temperature (degC)
tc inlet temperature of cooling water into coolers (degC)
TOC total operating cost (poundh)
tw cooling water temperature in a cooling tower (degC)
twb wet-bulb temperature (degC)
twi inlet temperature of cooling water into cooling towers (degC)
two outlet temperature of cooling water from cooling towers (degC)
w humidity ratio (kgkg dry air)
wo humidity ratio of outlet air from a cooling tower (kgkg dry air)
wsw humidity ratio of saturated air at water temperature (kgkg dry air)
ηp pump efficiency
Subscripts
a air
db dry-bulb
e evaporation
f fans
i inlet
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
32
m make-up water
o outlet
p pumps
P Poppe method
s saturation
v vapor
w cooling water
wb wet-bulb
References
[1] Qureshi BA and Zubair SM 2006 Prediction of Evaporation Losses in Wet Cooling
Towers Heat Transfer Eng 27(9) pp 86-92
[2] Simpson WM and Sherwood TW 1946 Performance of Small Mechanical Draft Cooling
Towers Refrigerating Engineering 52 (6) pp 525-543 and 574-576
[3] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter Flow
Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[4] Singham JR 1983 Heat Exchanger Design Handbook Hemisphere Publishing Corporation
New York USA
[5] Mills AE 1999 Basic Heat and Mass Transfer Prentice Hall Upper Saddle River USA
[6] Lemouari M Boumaza M and Mujtaba IM 2007 Thermal Performances Investigation of
a Wet Cooling Tower Applied Thermal Engineering 27 pp 902ndash909
[7] Lemouari M and Boumaza M 2010 Experimental Investigation of the Performance
Characteristics of a Counter Flow Wet Cooling Tower International Journal of Thermal
Sciences 49 pp2049-2056
[8] Alwan DAlDH Maid IW and Soheel AH 2013 Numerical and Experimental Study of
Counter Flow Cooling Tower Performance with Difference Packs Porosity and Configuration
Al-Rafidain Engineering 21 (6) pp 101-115
[9] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash128
[10] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[11] Poppe M and Rogener H 1991 Berechnung von Ruckkuhlwerken VDI-Warmeatlas Mi 1ndash
Mi 15
[12] Fisenko SP Petruchik AI and Solodukhin AD 2002 Evaporative Cooling of Water In a
Natural Draft Cooling Tower Int J Heat Mass Transfer 45 pp 4683ndash4694
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
33
[13] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[14] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU Method
ASME J Heat Transfer 111(4) pp 837ndash843
[15] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical Engineering
Research and Design 88 (5-6) pp 614-625
[16] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A 2011
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a Rigorous
Model Applied Thermal Engineering 31 pp 3615-3628
[17] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in Cooling
Water Systems Trans IChemE 78 (part A) pp 192-201
[18] Baker DR and Shryock HA 1961 A Comprehensive Approach to the Analysis of Cooling
Tower Performance Journal of Heat Transfer pp 339ndash350
[19] Kroumlger DG 2004 Air-Cooled Heat Exchangers and Cooling Towers PennWell Corp Tulsa
Oklahoma
[20] Milosavljevic N and Heikkilauml P 2001 A Comprehensive Approach to Cooling Tower
Design Applied Thermal Engineering 21 pp 899ndash915
[21] Goshayshi HR and Missenden JF 2000 The Investigation of Cooling Tower Packing in
Various Arrangements Applied Thermal Engineering 20 pp 69ndash80
[22] Kloppers JC and Kroumlger DG 2005 Refinement of the Transfer Characteristic Correlation
of Wet-Cooling Tower Fills Heat Transfer Engineering 26(4) pp 35-41
[23] Johnson BM 1989 Cooling Tower Performance Prediction and Improvement Volume 1
Applications Guide EPRI Report GS-6370 Volume 2 Knowledge Base EPRI Report GS-
6370 EPRI Palo Alto
[24] Singla RK Singh K and Das R 2016 Tower Characteristics Correlation and Parameter
Retrieval in Wet Cooling Tower with Expanded Wire Mesh Packing Applied Thermal
Engineering 96 pp 240ndash249
[25] Shahali P Rahmati M Alavi SR and Sedaghat A 2016 Experimental Study on
Improving Operating Conditions of Wet Cooling Towers Using Various Rib Numbers of
Packing International Journal of Refrigeration 65 pp 80ndash91
[26] Mc Kelvey KK and Brooke M 1959 The Industrial Cooling Tower Elsevier Publishing
Amsterdam
[27] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of Pump of a Pump Group Journal of Water Resources Planning and
Management 134 pp88-93
[28] Webb R L 1984 A Unified Theoretical Treatment for Thermal Analysis of Cooling Towers
Evaporative Condensers and Fluid Coolers ASHRAE Trans 90(2) pp 398ndash415
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
34
Appendix
1) Data information
The data used to validate the correlations of cooling towers are presented in Table A1
Table A1 Measured data for the regression of coefficients in equations (3) (4) and (8) for a
cooling tower in Simpson and Sherwood [2]
No twi
(degC)
two
(degC)
tdbi
(degC)
twbi
(degC)
wi
(kgkg dry air)
ma
(kgs)
mwi
(kgs)
wo
(kgkg dry air)
1 4144 2600 3411 2111 00104 1158 0754 00284
2 2872 2422 2900 2111 00125 1186 1259 00215
3 3450 2622 3050 2111 00119 1186 1259 00271
4 3878 2933 3500 2667 00188 1264 1008 00323
5 3878 2933 3500 2667 00188 1250 1008 00323
6 3967 2622 3400 2111 00105 1174 0881 00284
7 3500 2867 3461 2667 00190 1156 0881 00285
8 4361 2789 3500 2388 00141 1158 0754 00316
9 4306 2972 3572 2667 00185 1155 0754 00337
10 3806 3089 3594 2944 00236 1142 0754 00321
11 4778 3217 3617 2944 00235 1142 0754 00400
12 3378 2472 3250 2111 00110 1179 0881 00238
13 4144 3000 3617 2667 00183 1156 0881 00340
14 4061 3172 3417 2944 00244 1147 0881 00359
15 4350 3217 3533 2944 00239 1147 0881 00383
16 3672 3139 3272 2944 00250 1155 1008 00329
17 3322 2550 2883 2111 00126 1186 1008 00244
18 3844 2678 2950 2111 00123 1186 1008 00290
19 3661 2944 3250 2667 00199 1161 1132 00314
20 4100 3050 3294 2667 00197 1161 1132 00364
21 3611 2972 3111 2667 00204 1166 1258 00314
22 4022 3078 3133 2667 00203 1166 1258 00364
23 3956 3011 3206 2667 00200 1008 1008 00349
24 3950 3006 3106 2667 00205 1051 1008 00344
25 3944 3000 3333 2667 00195 1108 1008 00341
26 3978 2967 3167 2667 00202 0947 1008 00357
2) The Poppe method [10]
There are some basic assumptions in the Poppe method listed as follows
bull The system is at steady state
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
35
bull Heat and mass transfer in a direction normal to the flows only
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Constant heat and mass transfer coefficients throughout the tower
bull Water lost by drift is negligible
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
bull No resistance to heat flow in the interface
The governing equations of the Poppe method are expressed as equations (A1) ndash (A3)
w
( w ) w
w ( ) w ( w ) v- ( w ) w (A1)
w
w
( w ) w
w ( ) w ( w ) v- ( w ) w
(A2)
w
( w ) ( w ) ( ) v ( w ) w (A3)
where is enthalpy of the airndashwater vapour mixture per unit mass of dry air is
enthalpy of saturated air evaluated at the local bulk water temperature is humidity
of saturated air at water temperature is the Lewis factor is enthalpy of the water
vapour at the bulk water temperature is humidity of cooling water is temperature
of cooling water is the Merkel number calculated by the Poppe method is
mass flowrate of cooling water and is mass flowrate of dry air
w
w
(
w ( )) (A4)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
36
The Lewis factor is expressed as equation (A5)
w w
w
0 w w
w 1
(A5)
The relationship of NTU and the Merkel number is expressed by equation (A6)
w
(A6)
The correlation expression for the prediction of the Merkel number is expressed by
equation (A7) according to Johnson [23]
w
( ) (A7)
The correlation expression for the prediction of NTU is expressed by equation (A8)
combining equations (A6) with (A7)
w
(A8)
where is the height of fill is the cross sectional area of fill and c1- c4 are
coefficients
The equations for properties of water and air
The enthalpy of the air-water vapor mixture per unit mass of dry air is
( ) [ ( )] (A9)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
37
The specific heat of dry air at constant pressure is
times times times times 7 (A10)
The water vapor pressure is
(A11)
7
7
times [ ( 7 frasl ) +]
times [ 7 ( 7 frasl ) ] (A12)
The specific heat of saturated water vapour is
times times times (A13)
The specific heat of water is
times times times times (A14)
The latent heat of water is
times times times (A15)
is obtained from above equation where T=27315K
The humidity ratio of air is
( w )
w w
( w )
77 w (A16)
Chapter 2 Operational Optimisation of Mechanical Draft Wet Cooling Towers
38
The correlation equation of evaporation ratio of cooling towers proposed by Qureshi et
al [1] is presented as equation (A17)
( ) ( ) ( ) (A17)
where ER is evaporation ratio and are cooling water inlet and outlet
temperature respectively and and are ambient dry-bulb temperature and wet-
bulb temperature respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
Chapter 3
Publication 2 Operational Optimisation of
Recirculating Cooling Water Systems
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
1
Operational Optimisation of Recirculating Cooling
Water Systems
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
Recirculating cooling water systems are extensively used for heat removal in the
process industry The economic performance can be improved by integration of key
components in cooling water systems The integration of cooling water systems was
carried out for the cooling water system operation in the literature [1] [2] [3] Models
were developed for cooling water systems in [1] [2] [3] which is limited to one
cooling tower and cooler networks with a parallel configuration In addition the model
in the literature [1] did not consider the detail heat transfer in coolers and the model in
the literature [2] and [3] did not include the pressure drop in coolers To overcome those
limitations in this paper an NLP model is developed for operational optimisation of
cooling water systems The model takes multiple cooling towers and cooler networks in
both parallel and complex configurations into account The model developed by Song et
al [4] is employed for cooling tower modelling The detailed heat transfer in coolers is
expressed The hydraulic model takes pressure drop in coolers pipes and pipe fittings
into consideration The NLP model is solved by the solver CONOPT in GAMS for
minimising the total operating cost A case study proves that the model is effective to
improve the economic performance by integration of cooling water systems In the case
study through optimisation the operating cost is reduced by about 6 compared with
the base case
Key words recirculating cooling water systems integration model operational
optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
2
Highlights
An integration model of recirculating cooling water systems is developed
Multiple cooling towers and cooler networks in parallel and series configurations
are considered
Detailed heat transfer in coolers and pressure drop in coolers and pipes are taken
into account
The model is effective to improve the economic performance
The effect of ambient air conditions on the performance of cooling water systems is
investigated
1 Introduction
The recirculating cooling water systems are commonly used to reject process heat to the
atmosphere in order to keep processes running efficiently and safely in chemical
petrochemical and petroleum processes power stations etc A typical recirculating
cooling water system consists of three key components that are mechanical draft wet
cooling towers cooler networks and piping networks as shown in Figure 1 Cooling
water is pumped and distributed by piping networks to individual coolers for process
heat removal After heat exchange in coolers cooling water is heated while processes
are cooled Hot cooling water from cooler networks formed by coolers is sent to wet
cooling towers In wet cooling towers when the cooling water directly contacts air
blown by fans water evaporation and heat convection occur resulting in the
temperature reduction of cooling water Due to water evaporation some cooling water
is lost which is replenished by make-up water The cold cooling water from cooling
towers mixed with the make-up water is pumped to individual coolers again In this way
cooling water recirculates in cooling water systems
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
3
Figure 1 A recirculating cooling water system
The operation of cooling water systems includes circulating water flowrate in cooling
water systems cooling water flowrate through individual coolers and air flowrate into
cooling towers Circulating water flowrate in cooling water systems and cooling water
flowrate into individual coolers can be adjusted by valves and pumps Air flowrate into
cooling towers can be adjusted by fans Cooling water outlet temperature of cooling
towers which determines the cooling water inlet temperature of individual coolers can
be changed by the adjustment of circulating water flowrate and air flowrate into cooling
towers The same cooling requirement of processes can be satisfied by various
operations of cooling water systems as cooling water flowrate and temperature into
individual coolers are alterable The same cooling requirement can be achieved by
either a relatively low flowrate of circulating water in cooling water systems
accompanied by a large temperature increase of cooling water after heat removal or a
relatively high flowrate of circulating water in cooling water systems accompanied by a
small temperature increase of cooling water after heat removal When cooling water
temperature change after heat removal is small the cooling water temperature recovery
in cooling towers is achieved by low air flowrate When cooling water temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
4
change is large the cooling water temperature recovery in cooling towers is attained by
high air flowrate Therefore the specified cooling requirement can be achieved by
increasing circulating water flowrate with decreasing air flowrate into cooling towers or
by decreasing circulating water flowrate with increasing air flowrate into cooling towers
Although various operations can achieve the same cooling requirement the resulting
make-up water consumption and power consumption are probably different Because
the change of circulating water flowrate is contrary to the change of air flowrate the
change of power consumption by pumps is contrary to the change of power
consumption by fans When the decrease in power consumption cannot offset the
increase in power consumption the total power consumption will change with
operations of cooling water systems In addition make-up water consumption depends
on the operation as well as water evaporation depends on the operation of cooling water
systems Therefore the total operating cost caused by power and make-up water
consumption varies with the change of operations The economic performance of
cooling water systems can be improved by a trade-off between circulating water
flowrate and air flowrate
In the operation of cooling water systems circulating water flowrate and cooling water
into individual coolers are determined by the characteristics of piping networks and
pumps Any change of cooling water flowrate in one of the coolers influences not only
the cooling water outlet temperature from the cooler but also the cooling water flowrate
through other coolers and their cooling water outlet temperature
The thermal interaction between cooling towers and cooler networks is complex Cold
cooling water from cooling towers mixed with make-up water is distributed to
individual coolers Therefore the cooling water outlet temperature of cooling towers
determines the cooling water inlet temperature of coolers For given coolers the cooling
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
5
water inlet temperature and flowrate determine the process outlet temperature and the
cooling water outlet temperature from coolers when the flowrate and the inlet properties
of processes are constant For the given cooling requirement the cooling water flowrate
and temperature into individual coolers must allow processes to achieve their specified
temperature After heat exchange the hot cooling water from cooler networks is sent to
cooling towers Therefore the cooling water into cooling towers is the same as the
cooling water out of cooler networks in terms of flowrate and temperature In given
cooling towers cooling water outlet temperature of cooling towers depends on cooling
water inlet temperature cooling water inlet flowrate and air inlet flowrate The cooling
water outlet temperature of cooling towers must achieve the requirement for cooling
water inlet temperature of coolers which affects the air flowrate into cooling towers in
turn
In addition ambient air conditions including dry-bulb temperature wet-bulb
temperature and humidity have an impact on the thermal performance of cooling towers
The variation of ambient air conditions changes the performance of cooling towers and
thereby that of the overall cooling water system
In practice the operation of cooling towers and the operation of cooler networks are
usually carried out by two separate sectors Utility sectors in charge of cooling towers
adjust the air flowrate to cool down the cooling water to the desired temperature that
usually relies on the design data Process sectors operating cooler networks changes the
cooling water flowrate into coolers until the temperature of processes reaches their
requirement Both sectors do not concern about the effect of their operations on the
other components of cooling water systems The operation of cooling water systems is
hardly the most economical without considering the interactions between different
sectors
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
6
Many studies on cooling towers and cooler networks were carried out separately in
previous studies Some models of cooling towers were proposed in [4] [5] [6] [7] [8]
[9] [10] [11] The optimisation of cooling towers based on different models was
studied in [12] [13] [14] [15] Besides the previous studies on cooling towers some
studies on cooler network design modelling and optimisation were investigated in [16]
[17] [18] [19] [20] [21] The stage-wise superstructure was developed for cooler
networks by Ponce-Ortega et al [16] which allowed bypass and splitting of cooling
water The number of processes determined the number of stages in order to include
arrangements completely in series Mass balance and energy balance are carried out for
cooler networks Film heat transfer coefficients of processes and cooling water were
treated as parameters The pressure drop and cooler configuration were not considered
The stage-wise superstructure of cooler networks developed in [16] was applied by
Ponce-Ortega et al [17] The detailed cooler design and pressure drop in coolers were
included in the model Two-step sequential approach was proposed for the optimisation
of cooling water systems by Sun et al [18] The first step is to determine the optimal
cooler network with a superstructure of a cooler network For the purpose of simplicity
and operability there is a limit to the serial number of coolers in each parallel branch
pipe Mass balance and energy balance were performed for cooler networks The second
step is to determine the optimal pump network for the optimal cooler network with the
method developed by Sun et al [19] An analytical methodology was developed to
target and design cooler networks by Shenoy et al [20] Firstly the Unified Targeting
Algorithm was applied to decide the target of the minimum cooling water flowrate
Then the Nearest-Neighbors Algorithm was used to design the cooler network with the
maximum cooling water reuse This method did not consider energy consumption
Picoacuten-Nuacutentildeez et al [21] developed a thermal-hydraulic model of cooling networks for
flexible design and operation of cooling networks
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
7
Due to strong interactions between the components in cooling water systems there has
been a growing interest in the integration of cooling water systems for analysis and
optimisation of cooling water systems In 2000 Castro et al [1] established an
optimisation model for a cooling water system to determine the optimum operating
conditions of cooling water systems The model was developed for a cooling water
system with one cooling tower and a cooler network in a parallel configuration
including a regressed model of cooling towers an energy balance of coolers and a
hydraulic model of piping networks The detailed heat transfer in heat exchangers was
not expressed Cortinovis et al [2] developed a mathematical model for the systematic
performance analysis of cooling water systems with a cooling tower and a cooler
network in a parallel arrangement The model included a phenomenological model of
cooling towers with an empirical model of mass transfer coefficient a detailed heat
transfer model of individual coolers and a hydraulic model of piping networks The
pressure drop in heat exchangers was not considered in the hydraulic model Later on
Cortinovis et al [3] extended the model developed in [2] to optimise the operation of
cooling water systems Picoacuten-Nuacutentildeez et al [22] introduced a simplified model to
investigate the steady state response of cooling networks to temperature disturbances
The model was established on the basis of cooling tower thermal effectiveness and
cooler network thermal effectiveness The hydraulic performance of the network was
not considered Kim and Smith [23] developed a methodology to design the cooling
water network and a methodology to debottleneck cooling water systems with the
consideration of the interaction of cooler networks and cooling towers In their work
pinch analysis was applied to determine the target of cooling water flowrate in cooling
water network Pinch analysis is a graphical method that is unable to take pressure drop
in piping networks cost and forbidden connections into account Therefore the method
developed by Kim and Smith [23] can be used to design a cooling water system with the
minimum cold utility usage rather than a cooling water system with the minimum total
cost Afterwards Kim and Smith [24] developed a mathematical model for the retrofit
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
8
design of cooling water systems In their work the pressure drop in both heat
exchangers and pipes was considered Ponce-Ortega et al [25] developed an MINLP
model for the optimisation of cooling water system design The model included detailed
design model of cooling towers a stage-wise superstructure of cooler networks detailed
design model of coolers and pressure drop calculation in coolers It should be noted that
the models mentioned above were developed for cooling water systems with a single
cooling tower However cooling water systems in most large-scale industries contain
multiple cooling towers Some studies on the design of the cooling water system with
multiple cooling towers were made in the literature [26] [27] [28] In the literature [26]
[27] a superstructure of cooler networks was developed which included all the possible
connections between cooling towers and coolers and all the possibilities of cooling
water reuse between coolers Mass balance and energy balance of cooler network were
implemented Multiple cooling towers were represented by their inlet temperature
outlet temperature and maximum capacity rather than the model of cooling towers in
the literature [26] while a phenomenological model of cooling towers developed by
Kroumlger et al [29] was employed to predict the performance of cooling towers in
Literature [27] Rubio-Castro [28] developed an MINLP model for optimisation of
cooling water system design The model included a model for sizing the cooling towers
based on the Merkel method [5] in which pressure drop characteristics of the types of
packing were considered and a stage-wise superstructure for cooler network design was
employed However the pressure drop in piping networks was not considered
Although so many studies have been made on either individual components of cooling
water systems or the integration of cooling water systems for analysis and optimisation
of cooling water systems most studies solved the design problems of cooling water
systems and few studies worked on the operational optimisation of existing cooling
water systems In the few articles [1] [2] [3] on the investigation of cooling water
system operation models developed are limited to single cooling towers and cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
9
networks in parallel configurations The model in the literature [1] overlooked the
detailed heat transfer in coolers and the model in the literature [2] [3] did not consider
the pressure drop in coolers when the hydraulic modelling was carried out
In this work therefore an NLP model is developed with the integration of cooling
towers cooler networks and piping networks for the operational optimisation of cooling
water systems to improve the economic performance of cooling water systems The
operation of cooling water systems includes the flowrate of water into individual
coolers and cooling towers and the flowrate of air into individual cooling towers Cooler
networks both in a parallel arrangement and in a complex arrangement are considered in
the model Multiple cooling towers are included in the model as well The model
developed by Song et al [4] is employed for cooling tower modelling The prediction of
water evaporation takes the ambient air conditions into consideration A detailed heat
transfer model is used for cooler modelling with the consideration of the effect of
cooling water flowrate on the overall heat transfer coefficients of individual coolers
The pressure drop of cooling water side in coolers and the pressure drop in pipes piping
fittings and valves are included in the hydraulic model of piping networks The effect of
cooling water flowrate on the pressure drop is taken into account The cooling
requirement of processes is represented by the outlet temperature of processes from
coolers The process outlet temperature is required to be either fixed or flexible in a
range which is decided by the process requirement When the process outlet
temperature can be flexible in a range the cooling requirement is satisfied as long as the
target temperature of processes after heat rejection is in the specified range The effect
of process outlet temperature from coolers on the performance of processes is not
considered
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
10
2 Recirculating Cooling Water System Modelling
As the three major components in cooling water systems have strong interactions the
model of cooling water systems consists of models of cooling towers cooler networks
and piping networks The detailed models are presented below
21 Cooling tower modelling
The model of cooling towers developed by Song et al [4] is employed which is
presented as equations (A1) - (A8) in Appendix A (A) The model includes regression
models of number of transfer units air outlet humidity and cooling water outlet
temperature mass and heat balance of cooling towers and a regression model of
characteristics of fans The cooling water outlet temperature is an important element for
heat transfer in coolers The air outlet humidity can be used to predict water evaporation
The fan characteristic model is used to calculate power consumption by fans
22 Cooler network modelling
The cooler network model consists of models of coolers interactions between coolers
and interactions between cooling towers and coolers The model of coolers includes
energy balance and heat transfer equations Both the parallel arrangement and the series
and parallel arrangement of cooler networks are taken into account in the cooler
network model as they are commonly used in plants
221 Cooler modelling
1) The model of coolers
There are some assumptions made in cooler modelling
bull The properties of cooling water related to temperature are calculated at the
mean temperature of inlet and outlet of individual coolers
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
11
bull Heat transfer coefficient of processes is constant
bull The properties of processes are constant
bull Heat losses to the environment are negligible
bull Cooling water is set to flow in the tube side and hot streams are set to flow in
the shell side
bull The fouling resistant of cooling water and processes are constant
Heat balance and heat transfer equations are used to simulate individual coolers which
is referenced as equations (B1) - (B9) in Appendix A (B) They are used to estimate the
cooling water outlet temperature and process outlet temperature of individual coolers
and at the same time to make sure the cooling requirement of processes is satisfied in
given coolers The process heat capacity flowrate and inlet temperature of coolers are
taken as parameters as they cannot be changed by cooling water systems When the
process outlet temperature is flexible in a specified range the process outlet temperature
is variable
The effect of cooling water flowrate on the heat transfer coefficient and the pressure
drop of cooling water is considered Heat transfer coefficient and pressure drop of the
tube side are calculated by the equation developed by Wang et al [30] which are
presented as equations (B9) and (B10) respectively in Appendix A (B) In calculation of
the overall heat transfer coefficient the fouling resistance of both processes and cooling
water is considered with a fixed value The validation of heat transfer coefficient and
pressure drop developed by Wang et al [30] is presented in Appendix A (B)
222 Network modelling
The network model reflects both interactions between cooling towers and cooler
networks and interactions between coolers The network model is developed for cooler
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
12
networks in parallel arrangements shown in Figure 2 and those in series and parallel
arrangements shown in Figure 3
Figure 2 A cooling water system with a cooler network in a parallel arrangement
Figure 3 A cooling water system with a cooler network in a series and parallel
arrangement
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
13
1) Cooler networks in parallel arrangements
In parallel arrangements cooling water from cooling towers is the source of cooling
water into coolers and cooling towers are the sinks of cooling water from coolers In the
modelling j is the set of cooling towers and q is the set of coolers
(1) Mass balance
The water from cooling tower j mixed with make-up water is distributed to cooler q
Therefore the mass flowrate of water flowing through point a in Figure 2 is the sum of
water from cooling tower j to cooler q which is represented by equation (1)
( ) sum ( ) (1)
where ( ) is mass flowrate of water entering cooling tower j and ( ) is mass
flowrate of water from cooling tower j to cooler q
The mass flowrate of water entering cooling tower j is the sum of water from cooler q to
cooling tower j which is represented by equation (2)
( ) sum ( ) (2)
where ( ) is mass flowrate of water from cooler q to cooling tower j
The mass balance of inlet and outlet of coolers is expressed as equations (3) - (4)
( ) sum ( ) (3)
( ) sum ( ) (4)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
14
where m (q) is mass flowrate of water flowing through cooler q
(2) Energy balance
The temperature of cooling water provided by cooling tower j is calculated by equation
(5) as the cooling water provided by cooling tower j is the mixture of cooling water
from cooling tower j and its corresponding make-up water
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
(5)
where ( ) is mass flowrate of make-up water for cooling tower j ( ) is the
specific heat capacity of circulating water in tower j ( ) is the specific heat
capacity of make-up water for tower j ( ) is temperature of water leaving tower j
( ) is temperature of make-up water for tower j and ( ) is water temperature at point
a in Figure 2
The cooling water inlet temperature of cooling tower j is predicted by equation (6)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (6)
where ( ) is the specific heat capacity of water going through cooler q ( ) is
temperature of water entering cooling tower j and ( ) is temperature of water
leaving cooler q
If the cooling tower j provides cooling water for the cooler q then the inlet temperature
of cooling water into the cooler q is calculated by the following equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
15
where ( ) is mass flowrate of water flowing through cooler q ( ) is the
specific heat capacity of water going through cooler q ( ) is temperature of water
entering cooler q ( ) is mass flowrate of water from cooling tower j to cooler q
( ) is the specific heat capacity of circulating water in tower j and ( ) is water
temperature at point a in Figure 2
2) Cooler networks in series and parallel arrangements
In series and parallel arrangements there are two kinds of sources for cooling water into
coolers which are cooling water from cooling towers and that from coolers (reuse
cooling water) and two kinds of sinks for cooling water from coolers which are cooling
towers and coolers The equations describing the mass and energy balance for point a
and b in Figure 2 are used to present the mass and energy balance for point arsquo and brsquo in
Figure 3 respectively The difference between the series and parallel arrangements and
the parallel arrangements is coolers that use cooling water from other coolers and that
provide cooling water to other coolers Mass balance and energy balance for those
coolers are presented as follows
(1) Mass balance
In the case of using reuse cooling water as the only source cooling water into a cooler q
is the mixture of cooling water from other cooler k which is expressed by equation (8)
( ) sum ( ) ( ) (8)
where m (q) is mass flowrate of water flowing through cooler q and ( ) is mass
flowrate of water from cooler k to cooler q
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
16
In the case that a cooler q uses both cooling water from cooling tower j and cooling
water from cooler k the flowrate of cooling water into the cooler q is expressed by
equation (9)
( ) sum ( ) sum ( ) ( ) (9)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler k to cooler q and ( ) is mass flowrate of water from
cooling tower j to cooler q
Equations (10) and (11) are used to carry out the mass balance for the outlet of cooler q
discharging water to another cooler k only and both other cooler k and cooling tower j
respectively
( ) sum ( ) ( ) (10)
( ) sum ( ) sum ( ) ( ) (11)
where m (q) is mass flowrate of water flowing through cooler q ( ) is mass
flowrate of water from cooler q to cooler k and ( ) is mass flowrate of water from
cooler q to cooling tower j
(2) Energy balance
For a cooler q receiving cooling water from other cooler k the energy balance for the
inlet of these coolers is developed as equation (12)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (12)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
17
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) is temperature of water entering cooler q and ( ) is temperature of water
leaving cooler k
For a cooler q using cooling water from both cooling tower j and other cooler k the
energy balance for the inlet of these coolers is developed as equation (13)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( ) ( )) ( )
(13)
where m (q) is mass flowrate of water flowing through cooler q ( ) and ( )
are the specific heat capacity of water going through cooler k and cooler q respectively
( ) temperature of water entering cooler q ( ) is temperature of water leaving
cooler k ( ) is mass flowrate of water from cooling tower j to cooler q ( ) is
the specific heat capacity of circulating water in tower j and ( ) is water temperature at
point a in Figure 2
23 Piping network modelling
The model of piping networks includes mechanical energy balance and the
characteristics of pumps With this model water distribution in individual coolers is
determined and power consumption by pumps is predicted
231 Water distribution
There are some assumptions made in piping network modelling
bull There is no heat loss from pipes pipe fittings and valves to the environment
bull There is one splitter corresponding to each cooling tower which provides
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
18
cooling water to coolers and one mixer corresponding to each cooling tower that
mixes hot water from coolers
In the piping network modelling inlet (S1) and outlet (S2) of individual coolers inlet
(S5) and outlet (S6) of individual cooling towers individual splitters (S3) and individual
mixers (S4) are taken as nodes respectively as shown in Figure 4 Mechanical energy
balance between the nodes is carried out by employing the Bernoulli equation
Figure 4 A piping network
Mechanical energy balance is conducted between the outlet (S6) of cooling tower j and
its corresponding splitter (S3) which is expressed as equation (14)
( ) ( )
( )
w( ) ( ) ( )
( )
( )
w( ) ( ) (14)
where ( ) and ( ) are elevation of the outlet of cooling tower j (at node S6) and
splitter j (at node S3) respectively ( ) and ( ) are velocity of water leaving
cooling tower j and that of water going through splitter j respectively ( ) and ( )
are pressure of water at the outlet of cooling tower j and that of water at splitter j
respectively ( ) is density of water ( ) is the friction loss between node s6 of
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
19
cooling tower j and splitter j ( ) is energy provided by pump j and g is gravitational
constant
Mechanical energy balance between splitter j and the inlet (S1) of the cooler q which
uses cooling water from splitter j is presented as equation (15)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (15)
where ( ) is elevation of the inlet of cooler q ( ) is velocity of water going
through cooler q ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
For cooler q using cooling water from other cooler k mechanical energy balance
between outlet (S2) of cooler k and inlet (S1) of cooler q is presented as equation (16)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (k q) (16)
where ( ) is elevation of the outlet of cooler k ( ) is velocity of water going
through cooler k ( ) is pressure of water at the inlet of cooler q ( ) is density of
water and ( ) is the friction loss between splitter j and inlet of cooler q
Mechanical energy balance between outlet (S2) of cooler q and the mixer j (S4) which
is receiving cooling water from cooler q is expressed as equation (17)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (17)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
20
where ( ) is elevation of mixer j ( ) is velocity of water going through mixer j
( ) is pressure of water at mixer j ( ) is density of water at the mixer j and
( ) is the friction loss between outlet of cooler q and mixer j
Mechanical energy balance between the inlet (S5) of cooling tower j and the
corresponding mixer (S4) is expressed as equation (18)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (18)
where ( ) is elevation of the inlet of cooling tower j ( ) is velocity of water
entering cooling tower j ( ) is pressure of water at the inlet of cooling tower j ( )
is density of water at the inlet of cooling tower j and ( ) is the friction loss
between the mixer j and the inlet of cooling tower j
Pressure drop in cooler q is calculated to express the relationship between the pressure
of inlet (S1) of cooler q and that of outlet (S2) of cooler q
( ) ( ) ( ) (19)
where ( ) is pressure of water at the inlet of cooler q ( ) is pressure of water at
the outlet of cooler q and ( ) is pressure drop in cooler q
The calculation of pressure drop in cooling water side of coolers applies the equation
developed by Wang et al [30] which is presented as equation (B10)
The Darcy-Weisbach equation is used to estimate friction loss in pipes pipe fittings and
valves Equivalent length is used to calculate friction loss in pipe fittings and valves
The Colebrook-White equation [31] is applied for friction factor calculation
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
21
232 Pump modelling
The characteristics of pumps and the characteristics of piping networks are combined to
determine water distribution in individual coolers and the power consumed by pumping
cooling water
A model developed by Ulanicki et al [32] is used to represent the characteristics of
pumps which is shown in Appendix A (C) The coefficients (a1-a3 and b1-b3) in the
model are needed to be corrected for a given pump
24 Practical constraints
Besides models mentioned above some practical constraints are presented as equations
(20) - (28)
The temperature difference between process streams and cooling water is no less than
the minimum temperature approach
( ) ( ) (20)
( ) ( ) (21)
where ( ) and ( ) are temperature of process stream entering cooler q and
leaving cooler q respectively ( ) and ( ) are temperature of water entering cooler
q and leaving cooler q respectively and is the minimum temperature difference
There is an upper bound for the temperature of cooling water entering cooling towers to
avoid fouling scaling and corrosion
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
22
( ) ( ) (22)
In practice the approach which is the difference between the temperature of cooling
water leaving cooling towers and the wet-bulb temperature of inlet air should be no less
than 28 degC [33]
( ) (23)
The cooling water in individual coolers is in the turbulent region
( ) (24)
where ( ) is the Reynolds number of cooling water in cooler q
For a given cooling tower there are limits for cooling water flowrate and air flowrate to
keep cooling tower working properly
( ) ( ) ( )
(25)
( ) ( ) ( )
(26)
The pressure drop in individual coolers is no greater than the maximum allowance
( ) ( ) (27)
The assumption that outlet air of cooling tower j is not supersaturated is satisfied by
equation (28)
( ) ( ) (28)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
23
where ( ) and ( ) are dry-bulb temperature and wet-bulb temperature of air
leaving cooling tower j respectively
25 Objective function
The objective of operational optimisation is to minimise the operating cost The
operating cost (TOC) includes cost of makeup water and cost of power needed by fans
and pumps which is expressed as
Min sum ( ) sum ( ( ) ( )) (29)
where C1 and C2 are unit cost of make-up water and electricity respectively ( ) is
make-up water for cooling tower j ( ) is power consumption of pump j and ( ) is
power consumption of fan j
3 Solution Method
Before the model is applied to optimise the operation of cooling water systems model
correction for cooling towers pumps and fans is carried out with the measured data or
the operating data of the given equipment The coefficients in the model can be
achieved by the regression of coefficients in the models with the least square method
After that the objective function is minimised subject to the model constraints and the
practical constraints If the cooler network is in a parallel configuration equations (8) -
(13) and (16) are excluded If the cooler network is in a series and parallel configuration
all the equations mentioned above are included As there are nonlinear equations in the
model the NLP problem is formed The solver CONOPT is employed to solve the
problem in software GAMS as the solver CONOPT is well suited for models with very
nonlinear constraints Before optimisation initial values are assigned to the variables
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
24
such as mass flowrate of cooling water entering individual coolers and towers air
flowrate entering individual towers and so on
4 Case Studies
Two case studies are used to illustrate the application of the proposed model The
operational optimisation is carried out for a simplified subset of a refinery cooling water
system to cool down nine processes in which there are two forced draft wet cooling
towers two pumps and nine coolers The specifications of the cooling water system are
illustrated below in detail
The specifications of process streams are presented in Table 1 which include the
temperature of process streams entering and leaving coolers (represented as inlet
temperature and outlet temperature respectively) the heat capacity flowrate and heat
transfer coefficient as well as fouling resistance
Table 1 Specifications of processes
Process
streams
Inlet temp
degC
Outlet temp
degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degCW
C1 60 Upper 450
1704 987 000018 Lower 420
C2 120 Upper 795
482 286 000018 Lower 750
C3 95 500 586 732 000018
C4 100 Upper 595
707 448 000035 Lower 550
C5 105 Upper 545
447 748 000053 Lower 500
C6 90 Upper 595
1004 488 000018 Lower 550
C7 75 Upper 445
602 913 000018 Lower 400
C8 150 Upper 1000
394 180 000018 Lower 950
C9 125 Upper 645
513 346 000053 Lower 600
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
25
The specifications of coolers are presented in Table 2 in terms of area number of tubes
tube passes tube diameter and length of tube
Table 2 Cooler specifications
Coolers Area
(m^2)
Number
of tubes
Tube
passes
Tube inside
diameter
(mm)
Tube outside
diameter
(mm)
Length of
tube
(m)
Thermal
conductivity of tube
wall (wmdegC)
C1 3506 1006 2 15 19 60 50
C2 1589 610 2 15 19 45 50
C3 2135 610 2 15 19 60 50
C4 2539 980 4 15 19 45 50
C5 1685 366 2 20 25 60 50
C6 2606 1006 2 15 19 45 50
C7 2004 588 4 20 25 45 50
C8 1641 468 2 15 19 60 50
C9 2539 980 4 15 19 45 50
The pipe specifications in terms of equivalent length of pipes and pipe fittings diameter
and roughness are given in Table 3
Table 3 Pipe specifications
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S6(1)-S3(1) 600 046 00002 S4(1)-S5(1) 1300 046 00002
S6(2)-S3(2) 400 041 00002 S4(2)-S5(2) 1300 041 00002
S3(1)-S1(C1) 600 027 00002 S2(C1)-S4(1) 800 014 00002
S3(1)-S1(C3) 800 023 00002 S2(C2)-S4(1) 1000 023 00002
S3(1)-S1(C4) 700 015 00002 S2(C3)-S4(1) 1400 023 00002
S3(1)-S1(C5) 1000 021 00002 S2(C4)-S4(1) 1000 021 00002
S3(2)-S1(C6) 400 021 00002 S2(C5)-S4(1) 1000 021 00002
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
26
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
Pipe Equivalent
Length
(m)
Diameter
(m)
Roughness
(m)
S3(2)-S1(C7) 1200 024 00002 S2(C6)-S4(2) 1000 015 00002
S3(2)-S1(C9) 1000 046 00002 S2(C7)-S4(2) 1200 021 00002
S2(C9)-S4(2) 1400 024 00002 S2(C8)-S4(2) 800 023 00002
S2(C1)
-S1(C2) 1200 023 00002
S2(C6)
-S1(C8) 1300 023 00002
The cycles of concentration are set to be 4 for blowdown discharge The fouling
resistance of cooling water is assumed to be 528e-4 msup2degCW The unit cost of make-up
water and the unit cost of electricity are 03 poundt and 01 poundkWh respectively
41 Base case
The cooling water system is operated in the ambient air conditions listed in Table 4 The
operating conditions in the base case are provided in Figure 5 which include the
cooling water inlet flowrate of individual cooling towers the temperature of cooling
water entering individual towers the temperature of cooling water leaving individual
cooling towers dry air flowrate in individual cooling towers and cooling water
distribution in individual coolers The data at the top in Figure 5 is the operating
conditions in the base case The thermal and economic performance of the cooling water
system determined by the operation is shown in Table 6 and the outlet temperature of
individual processes from coolers is listed in Table 7
Table 4 Ambient air conditions
Ambient air conditions
Make-up water
temperature (degC) Dry-bulb temperature
(degC)
Wet-bulb
temperature (degC)
Humidity (kgkg
dry air)
Enthalpy
(kJkg)
318 271 205 855 318
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
27
Figure 5 Comparison of optimal operation and operation in base case
42 Case study 1
Before optimisation the coefficients in the regression models of cooling towers pumps
and fans are regressed and presented in Table 5
Table 5 Models of cooling towers pumps and fans
Units Models
Cooling
towers 1
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
28
Units Models
2
( ) ( ) ( )
( )
( ) times times ( ( ) ( )) times
( ) times ( ( ) ) ( ) 7
( )
( ) ( ) ( ) ( ) ( )
7
( ( ) )
Pumps
1
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
2
( ) ( ) ( ) ( )
( ) ( ( ) )
( ) ( ) ( )
( )
Fans
1 ( ) ( ) ( )
( )
2 ( ) ( ) ( )
( )
In this case the operating cost of the cooling water system is to be minimised with the
same process cooling requirement satisfied by adjusting cooling water distribution in
individual coolers and dry air flowrate into individual coolers The model of cooling
water systems developed for cooler networks in a series and parallel arrangement is
applied and solved by CONOPT in GAMS with the objective of the operating cost
minimisation There are 438 variables and 412 equations in this optimisation problem
The optimal operating conditions are presented in Figure 5 which are the data at the
bottom The resulting thermal and economic performance of the cooling water system is
listed in Table 6 and the outlet temperature of individual processes from coolers is
shown in Table 7
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
29
Through optimisation the operating cost of the cooling water system is decreased by 28
kpoundyr which is shown in Table 6 and the temperature of process streams leaving coolers
satisfies the requirement which is shown in Table 7 The cooling water flowrate in the
tower 1 is decreased by 107 th which results in a decrease of the range of the tower 1
The temperature of water entering the tower 1 is increased by 08 ordmC which results in a
decrease of air flowrate The decrease of both water flowrate and air flowrate reduces
the power consumption by about 25 kW compared with the base case The cooling
water flowrate of the tower 2 is reduced by around 100 th which leads to the increase
of the range of the tower 2 The increased range of the tower 2 requires a larger air
flowrate of the tower 2 The resulting dry air flowrate is increased by around 130 th
The decrease of power consumption caused by the decrease of cooling water flowrate of
the cooling tower 2 is 9 kW more than the increase of power consumption by the
increase of air flowrate of the tower 2 Therefore the total power consumption of the
cooling tower 2 is saved by 9 kW The total power consumption of the cooling water
system is reduced by about 34 kW The total make-up water consumption in the cooling
water system after optimisation is almost the same as before optimisation Consequently
the total operating cost of the cooling water system is reduced mainly because of the
reduction of power consumption in this case
The cooling water flowrate entering the coolers that use water from cooling towers only
is reduced to enhance the temperature of water leaving coolers and thereby the
temperature of water entering towers The coolers that reuse cooling water from other
coolers take full advantage of the cooling water that can be reused Therefore the
overall cooling water flowrate is reduced
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
30
Table 6 Comparison of the optimal operating conditions and the operating conditions in
the base case
Base case Case 1 Difference
Cooling
towers
The range (degC) Cooling tower 1 110 118 -08
Cooling tower 2 109 124 15
The approach
(degC)
Cooling tower 1 38 38 00
Cooling tower 2 41 34 -07
Make-up water flowrate (th)
Cooling tower 1 231 222 -09
Cooling tower 2 178 181 03
Total 409 403 -06
Power
consumption
(kW)
Pumps
Cooling tower 1 2369 2172 -197
Cooling tower 2 1815 1657 -158
Total 4184 3829 -355
Fans
Cooling tower 1 512 461 -51
Cooling tower 2 353 421 68
Total 865 882 17
Total 5049 4711 -338
Cost
Water(poundh) 1227 1209 -018
Electricity(poundh) 5049 4711 -338
Total operating cost (poundh) 6276 5920 -356
Total operating cost (poundyr) 502k 474k 28k
Table 7 Comparison of outlet temperature of process fluid from individual coolers
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C1 450 450
C2 795 795
C3 500 500
C4 595 595
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
31
Hot streams
Outlet temperature of process fluids from individual coolers
(degC)
Base case Optimisation
C5 545 545
C6 595 595
C7 445 445
C8 1000 1000
C9 645 645
43 Case study 2
The thermal performance of cooling towers is affected by ambient air conditions In this
case the thermal performance of cooling water systems under different ambient air
conditions with the same operation of cooling water systems is studied After that the
operating variables of cooling water systems are optimised for each ambient air
condition with the aim of minimising the operating cost Three different ambient air
conditions listed in Table 8 are used to investigate the effect of air conditions on the
performance of cooling water systems The cooling requirement is kept the same as
stated in Table 1
Table 8 Ambient air conditions
Condition 1 Condition 2 Condition 3
Ambient air
conditions
Dry-bulb temperature (degC) 355 275 325
Wet-bulb temperature (degC) 290 242 280
Humidity (kgkg dry air) 229 178 223
Enthalpy (kJkg) 946 731 898
Make-up water temperature (degC) 355 275 325
The optimal operation of the cooling water system obtained in Case 1 is implemented in
individual air conditions The thermal performance of the operation under the three
ambient air conditions is listed in Table 9 In the conditions 1 and 3 the process streams
cannot be cooled down to the upper bound of the temperature requirement which means
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
32
that the operation cannot achieve the specified cooling requirement of processes The
ambient air conditions in the conditions 1 and 3 are less favourable to mass and heat
transfer in cooling towers than the air conditions in Case 1 as they have higher dry-bulb
temperature wet-bulb temperature and humidity than the air conditions in Case 1
Therefore the operation of the cooling water system obtained for certain ambient air
conditions probably may not achieve the cooling requirement of processes when
ambient air conditions become disadvantageous to water evaporation and heat
convection in cooling towers In the condition 2 the temperature of the process streams
leaving coolers are below the upper bound of the temperature when the optimal
operation of the cooling water system obtained in Case 1 is carried out As the ambient
air conditions in the condition 2 have lower dry-bulb temperature wet-bulb temperature
and humidity than the ambient air conditions used in Case 1 the ambient air conditions
in the condition 2 is more favourable to water evaporation and heat convection in the
cooling towers than the ambient air conditions in Case 1 Therefore the operation of the
cooling water system obtained in Case 1 reduces the process temperature to the value
below the upper bound of the requirement when the ambient air conditions become
more favourable to water evaporation and heat convection than the ambient air
conditions used to determine the operation Comparing the process outlet temperature in
the three conditions listed in Table 9 it is shown that the cooling duty of cooling water
systems increases with the decrease of dry-bulb temperature wet-bulb temperature and
humidity when the operation of cooling water systems did not change with the variation
of ambient air conditions
Table 9 Comparison of outlet temperature of processes from individual coolers between
before and after optimization for individual conditions
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
1
Case 1 458 800 510 604 555 603 455 1006 654
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -08 -05 -10 -09 -10 -08 -10 -06 -09
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
33
Outlet temperature of processes (
degC)
C1 C2 C3 C4 C5 C6 C7 C8 C9
Condition
2
Case 1 439 787 485 582 530 584 430 991 631
Optimisation 450 766 500 595 545 592 441 982 644
Difference 10 -23 14 12 14 07 10 05 -01
Condition
3
Case 1 454 798 505 599 550 599 450 1003 650
Optimisation 450 795 500 595 545 595 445 1000 645
Difference -04 -03 -05 -04 -05 -04 -05 -03 -05
As shown above a fixed operation of cooling water systems under different ambient air
conditions results in that either the cooling demand is not satisfied or the excessive heat
is removed from processes Therefore the operating variables of cooling water systems
are supposed to be adjusted for individual ambient air conditions to complete the
cooling demand and to reduce the operating cost at the same time With the model
developed in this work the operation of the cooling water system is optimised for
individual conditions with the objective of minimising the operating cost The optimal
operations of the cooling water system for individual conditions are displayed in Figure
6 The resulting power consumption make-up water consumption and operating cost are
listed in Table 10 The outlet temperature of processes from coolers is presented in
Table 9
Through optimisation the process streams are cooled to the specified temperature in the
three conditions In the conditions 1 and 3 both the cooling water flowrate and dry air
flowrate into individual cooling towers are increased to reduce the process outlet
temperature of coolers to the upper bound of the temperature requirement In the
condition 2 the cooling water flowrate in individual cooling towers is increased while
the air flowrate in individual cooling towers is decreased The process outlet
temperature of most coolers is increased which reduces the cooling duty of the cooling
water system From the economic perspective the total operating cost of the cooling
water system in the conditions 1 and 3 is increased after optimisation That is mainly
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
34
because the cooling duty of the cooling water system is increased after optimisation
which results in the increase of cooling water flowrate and air flowrate in individual
cooling towers The total operating cost of the cooling water caused by the optimal
operation in the condition 2 is about 2 less than that caused by the operation obtained
in Case 1 as the cooling duty of the cooling water system decreases
From the comparison of the optimisation results of the three conditions it is noted that
both the optimal power consumption and make-up water consumption reduce with the
decrease of dry-bulb temperature wet-bulb temperature and humidity As a result the
optimal operating cost of the cooling water system reduces with the decrease of dry-
bulb temperature wet-bulb temperature and humidity As the dry-bulb temperature
wet-bulb temperature and humidity in the condition 1 are higher than those in the
condition 3 the driving force for water evaporation and heat convection in the condition
1 is smaller than that in the condition 3 Therefore the cooling water flowrate and the
air flowrate into cooling towers in the condition 1 are larger than those in the condition
3 to achieve the same cooling requirement Therefore the power consumption by
pumping cooling water and blowing air in the condition 1 is more than that in the
condition 3 In the time condition 2 the driving force for water evaporation and heat
convection is larger than that in the condition 3 However the optimal cooling water
flowrate of the cooling water system in the condition 2 is slightly higher than that in the
condition 3 which results in that the optimal air flowrate of individual cooling towers in
the condition 2 is reduced to almost half of that in the condition 3 Although the cooling
duty of individual cooling towers in the three conditions is no big difference after
optimisation water evaporation reduces with the decrease of dry-bulb temperature That
is because heat convection rate increases with the decrease of dry-bulb temperature and
as a result the cooling duty of water evaporation reduces Therefore water evaporation
reduces with the decrease of dry-bulb temperature which results in the reduction of
make-up water consumption with the decrease of dry-bulb temperature
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
35
In summary a fixed operation of cooling water systems either fails to complete the
cooling requirement of processes or fulfils the cooling requirement with the processes
excessively cooled when the ambient air conditions change Operational optimisation
for individual air conditions allows the cooling requirement of all the processes to be
satisfied and improves the economic performance of cooling water systems under the
ambient air conditions that are more favourable to water evaporation and heat
convection
Figure 6 Optimal operation of the cooling water system under different ambient air
conditions
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
36
Table 10 Comparison of results between before and after optimization for individual condtions
Condition 1 Condition 2 Condition 3
Case 1 Optimisation Difference Case 1 Optimisation Difference Case 1 Optimisation Difference
Cooling
towers
Make-up water
flowrate (th)
1 231 241 10 217 207 -10 220 226 06
2 189 195 06 176 168 -08 180 183 03
Total 420 436 16 393 375 -18 400 409 09 Cooling duty (MW) 2302 2363 061 2395 2337 -058 2313 2342 029
Convective heat transfer
(MW) 097 071 -026 352 385 033 217 201 -016
Latent heat (MW) 2205 2292 087 2043 1952 -091 2096 2141 045
Pumps Power
consumption (kW)
1 2173 2469 296 2173 2307 134 2173 2197 24
2 1657 1951 294 1657 1769 112 1657 1723 66
Total 3830 4420 590 3830 4076 246 3830 3920 90
Fans Power
consumption (kW)
1 460 639 179 444 305 -139 452 597 145
2 419 538 119 405 239 -166 412 496 84
Total 879 1177 298 849 544 -305 864 1093 229
Total power consumption (kW) 4709 5597 888 4679 4620 -59 4694 5013 319
Cost (poundh)
Make-up water 1260 1308 048 1179 1125 -054 1200 1227 027
Power 4709 5597 888 4679 4620 -059 4694 5013 319
Total 5969 6905 936 5858 5745 -113 5894 6240 346
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
37
5 Conclusions
The economic performance of cooling water systems can be improved by the
integration of key components in cooling water systems Although some integration
models were developed for the cooling water system operation in the literature [1] [2]
[3] there are some limitations in those models only one cooling tower and cooler
networks in a parallel configuration are considered either detailed heat transfer or
pressure drop in coolers is ignored To overcome those limitations a nonlinear model
is developed for the operational optimisation of cooling water systems with the
integration of cooling towers cooler networks and piping networks In cooling tower
modelling the regression model of mechanical draft wet cooling towers developed by
Song et al [4] is employed to predict the thermal performance of cooling towers The
cooler network model includes detailed heat transfer equations for coolers and the
mass and energy balance for the interactions between coolers and cooling towers The
model takes multiple cooling towers and cooler networks in a series and parallel
arrangement into consideration The mechanical energy balance is carried out for
piping networks to distribute cooling water in individual coolers and to predict the
power consumption by pumps The pressure drop in both pipes pipe fittings valves
and cooling water side of coolers are considered For the optimisation the model is
solved by the solver CONOPT in GAMS With the model of cooling water systems
and the solution method the optimal cooling water mass flowrate entering individual
towers and coolers and air mass flowrate entering individual coolers are determined to
satisfy the process cooling demand with the minimum operating cost of cooling water
systems The model is proven to be effective to improve the economic performance
by integration of cooling water systems by a case study In the case study through
optimisation the operating cost of the cooling water system is about 6 less than that
in the base case
Due to the effect of ambient air conditions on the thermal performance of cooling
towers a fixed operation of cooling water systems may cause problems that the
specified process cooling demand cannot be achieved when ambient air become hot
and wet or that the cooling of processes is excessive which results in the unnecessary
operating cost when ambient air become cold and dry The optimisation of cooling
water systems under different ambient air conditions not only allows the process
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
38
cooling demand to be completed but also minimises the operating cost of cooling
water systems under different ambient air conditions With the increase of ambient
dry-bulb temperature wet-bulb temperature and humidity the optimal power
consumption and make-up water consumption increase and the resulting operating
cost increases
The operational optimisation of cooling water systems is implemented to minimise
the operating cost of cooling water systems for a specified process cooling demand
The specification for the process outlet temperature from coolers is considered in this
paper In fact the outlet temperature has an effect on the performance of some
processes such as condensing turbines pre-cooling of compression refrigeration
inter-cooling of compressors condensation of light components for distillation and so
on However the effect of the outlet temperature on the performance of processes is
not considered in this work and thereby it should be considered in future work
Nomenclature
Sets
j set of cooling towers
k set of coolers
q set of coolers
Parameters
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) tube inside diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) tube outside diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
g gravitational constant 981m2s
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
39
ii enthalpy of inlet air into cooling towers (Jkg dry air)
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(q) tube length of cooler q (m)
np(q) number of passes of cooler q
nt(q) number of tubes of cooler q
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
tdbi dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
zs1(q) elevation at node s1 of cooler q (m)
zs2(k) elevation at node s2 of cooler k (m)
zs2(q) elevation at node s2 of cooler q (m)
zs3(j) elevation of splitter j (m)
zs4(j) elevation of mixer j (m)
zs5(j) elevation at node s5 of cooling tower j (m)
zs6(j) elevation at node s6 of cooling tower j (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hfs2s1(kq) friction loss between node s2 of cooler k and node s1 of cooler q (m3s)
hfs2s4(qj) friction loss between node s2 of cooler q and mixer j (m3s)
hfs3s1(jq) friction loss between splitter j and s3 of cooler q (m3s)
hfs4s5(j) friction loss between mixer j and node s5 of cooling tower j (m3s)
hfs6s3(j) friction loss between node s6 of cooling tower j and splitter j (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm-2
degC
-1)
Hp(j) pressure head provided by pump j (m)
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
40
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
ps1(q) pressure at node s1 of cooler q (Pa)
ps2(k) pressure at node s2 of cooler k (Pa)
ps2(q) pressure at node s2 of cooler q (Pa)
ps3(j) pressure at splitter j (Pa)
ps4(j) pressure at mixer j (Pa)
ps5(j) pressure at node s5 of cooling tower j (Pa)
ps6(j) pressure at node s6 of cooling tower j (Pa)
Pf(j) power consumption by fan j (kW)
Pp(j) power consumed by pump j (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(degC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
tdbo(j) air outlet dry-bulb temperature of cooling tower j (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
twbo(j) air outlet wet-bulb temperature of cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
TOC total operating cost (poundh)
us1(q) cooling water velocity at node s1 of cooler q (ms)
us2(k) cooling water velocity at node s2 of cooler k (ms)
us2(q) cooling water velocity at node s2 of cooler q (ms)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
41
us3(j) cooling water velocity at splitter j (ms)
us4(j) cooling water velocity at mixer j (ms)
us5(j) cooling water velocity at node s5 of cooling tower j (ms)
us6(j) cooling water velocity at node s6 of cooling tower j (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
W(j) energy provided by pump j (m3s)
wo(j) humidity of the air from cooling towers (kgkg dry air)
Greek Symbols
α coefficients
β coefficients
γ coefficients
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
( ) efficiency of pump j
density of air (kgm3)
(j) density of cooling water in cooling tower j (kgm3)
(k) density of cooling water in cooler k (kgm3)
(q) density of cooling water in cooler q (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
minimum temperature difference (degC)
Subscripts
a air
db dry bulb
f fans
i insideinlet
o outsideoutlet
p pumps
s1-s6 nodes
w cooling water
wb wet bulb
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
42
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 Integrated Analysis of
Cooling Water Systems Modeling and Experimental Validation Applied Thermal
Engineering 29 pp 3124-3131
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Song F Zhang N and Smith R 2016 Operational Optimisation of Mechanical Draft Wet
Cooling Towers
[5] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[6] Jaber H and Webb RL 1989 Design of Cooling Towers by the Effectiveness-NTU
Method ASME J Heat Transfer 111(4) pp 837ndash843
[7] Kloppers JC and Krӧger DG 2005 A Critical Investigation into the Heat and Mass
Transfer Analysis of Counterflow Wet-Cooling Towers International Journal of Heat and
Mass Transfer 48 pp 765ndash777
[8] Khan JR and Zubair SM 2001 An Improved Design and Rating Analyses of Counter
Flow Wet Cooling Towers ASME J Heat Transf 123 pp 770ndash778
[9] Qureshi BA and Zubair SM 2006 A Complete Model of Wet Cooling Towers with
Fouling in Fills Applied Thermal Engineering 26 pp 1982ndash1989
[10] Khan JR Qureshi BA and Zubair SM 2004 A Comprehensive Design and
Performance Evaluation Study of Counter Flow Wet Cooling Towers Int J Refrig 27 pp
914-923
[11] Kloppers JC and Krӧger DG 2005 Cooling Tower Performance Evaluation Merkel
Poppe and e-NTU Methods Analysis Trans ASME J Engrg GasTurbines and Power 127
pp 1-7
[12] Soumlylemez MS 2001 On the Optimum Sizing of Cooling Towers Energy Conversion and
Management 42(7) pp 783-789
[13] Soumlylemez MS 2004 On the Optimum Performance of Forced Draft Counter Flow
Cooling Towers Energy Conversion and Management 45 pp 2335-2341
[14] Serna-Gonzaacutelez M Ponce-Ortega JM and Jimeacutenez-Gutieacuterrez A 2010 MINLP
Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Chemical
Engineering Research and Design 88 (5-6) pp 614-625
[15] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
43
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[16] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2007 MINLP
Synthesis of Optimal Cooling Networks Chemical Engineering Science 62 pp 5728-5735
[17] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2009 A Disjunctive
Programming Model for Simultaneous Synthesis and Detailed Design of Cooling Networks
Ind Eng Chem Res 48 2991ndash3003
[18] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems Considering
Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39 pp 49-54
[19] Sun J Feng X Wang YF Deng C and Chu KH 2014 Pump Network Optimization
for A Cooling Water System Energy 1-7
[20] Shenoy AU and Shenoy UV 2013 Targeting and Design of CWNs Energy 55 pp
1033-1043
[21] Picon-Nunez M Canizalez-Daacutevalos L and Polley GT 2011 Modelling the Thermo-
Hydraulic Performance of Cooling Networks and Its Implications on Design Operation and
Retrofit Chapter 9 Evaporation Condensation and Heat transfer Dr Amimul Ahsan (Ed)
InTech
[22] Picon-Nunez M Nila-Gasca C and Morales-Fuentes A 2007 Simplified Model for the
Determination of the Steady State Response of Cooling Systems Applied Thermal
Engineering 27 pp1173ndash1181
[23] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[24] Kim JK and Smith R 2003 Automated Retrofit Design of Cooling-Water Systems
Process Systems Engineering 49(7) pp 1712-1730
[25] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[26] Majozi T and Moodley A 2008 Simultaneous Targeting and Design for Cooling Water
Systems with Multiple Cooling Water Supplies Computers and Chemical Engineering 32
pp 540ndash551
[27] Gololo KV and Majozi T 2011 On Synthesis and Optimization of Cooling Water
Systems with Multiple Cooling Towers Ind Eng Chem Res 50 3775ndash3787
[28] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[29] Kroumlger D G 2004 Air-Cooled Heat Exchangers and Cooling Towers Mass Transfer and
Evaporative Cooling PennWell Corporation Oklahoma USA
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
44
[30] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[31] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[32] Ulanicki B Kahler J and Coulbeck B 2008 Modelling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[33] Li KW and Priddy AP 1985 Power Plant System Design John Wiley amp Sons New
York USA
[34] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
Appendix
Appendix A Models
(A) Cooling tower modelling
A correlation of the NTU of cooling tower j is represented as
( ) ( ) ( )
( ) (A1)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate and ( ) is cooling water
inlet temperature of tower j
A correlation of air outlet humidity is expressed as
( ) ( ( ) ( )) ( ) ( ( ) ) ( )
( ) (A2)
where ( ) is cooling water inlet mass flowrate of tower j ( ) is dry air mass
flowrate is ambient air humidity ratio based on dry air mass flowrate ( ) is air
outlet humidity ratio based on dry air mass flowrate of tower j respectively ( ) and
( ) are cooling water inlet and outlet temperature of tower j respectively and
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
45
and are ambient dry-bulb temperature and ambient wet bulb temperature
respectively
A correlation of cooling water outlet temperature is expressed as
( ) ( ) ( ) ( ) ( )
( ( ) ) (A3)
where NTU is the number of transfer units of tower j ( ) is cooling water inlet
mass flowrate of tower j ( ) is dry air mass flowrate ( ) and ( ) are cooling
water inlet and outlet temperature of tower j respectively and is ambient wet
bulb temperature
The coefficients ( - and - ) in equations (2) and (3) are determined by
the characteristics of cooling towers which can be regressed by the least square
method
Mass balance of cooling tower j
( ) ( ) ( ) ( ( ) ) (A4)
Energy balance of cooling tower j
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A5)
where ( ) and ( ) are cooling water inlet and outlet mass flowrate of tower j
respectively is dry air mass flowrate ( ) is the specific heat capacity of
cooling water in tower j ( ) and ( ) are cooling water inlet and outlet
temperature of tower j respectively is specific enthalpy of ambient air and ( ) is
specific enthalpy of air leaving cooling tower j based on the dry air mass flowrate
respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
46
Water evaporation rate in a cooling tower j is expressed as equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water is calculated by equation (A7)
( ) ( )
(A7)
where ( ) is make-up water flowrate of tower j ( ) is evaporation rate of tower
j and cc is the cycles of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
Characteristic of fans j is represented as [34]
( ) 0 ( ) ( )
1 (A8)
where ( ) is power consumption of fan j ( ) is dry air mass flowerate of tower j
is density of ambient air and is air inlet humidity ratio based on dry air mass
flowrate
(B) Heat exchanger modelling
Energy balance of cooler q is expressed as equation (B1)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (B1)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
mass flowrate of cooling water in cooler q ( ) is specific heat of cooling water
of cooler q and ( ) and ( ) are temperature of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
47
Heat transfer in cooler q is expressed as equation (B2)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (B2)
where ( ) is heat capacity flowrate of process q ( ) and ( ) are
temperature of process fluids entering and leaving cooler q respectively ( ) is
overall heat transfer coefficients in cooler q ( ) is area of cooler q Δ ( ) is
logarithmic mean temperature of cooler q and ( ) is correction factor of cooler q
The overall heat transfer coefficient based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (B3)
where ( ) is overall heat transfer coefficient of cooler q ( )and ( ) are heat
transfer coefficient in tube side and shell side of cooler q respectively ( ) and
( ) are tube inside and outside diameters of cooler q respectively ( ) and ( )
are fouling factor of tube side and shell side in cooler q respectively and ( ) is
thermal conductivity of tube wall of cooler q
The correction factor is expressed as
( ) ( ) ( )
h ( ) ( ) (B4)
S( ) h ( ) h ( )
( ) ( ) (B5)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (B6)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (B7)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
48
The logarithmic mean temperature difference is written as equation (B8)
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(B8)
where Δ ( ) is logarithmic mean temperature difference in cooler q ( ) and
( ) are temperature of process fluids entering and leaving cooler q respectively
and ( ) and ( ) are temperature of cooling water entering and leaving cooler q
respectively
The heat transfer coefficient of the stream in the tube side is written as
( ) w( )
( ) ( )
w ( ) μw( )
w( )
(B9)
where ( ) is heat transfer coefficient in tube side of cooler q ( ) is tube inside
diameters of cooler q ( ) is thermal conductivity of cooling water in cooler q
( ) is specific heat of cooling water of cooler q ( ) is Reynolds number of
tube side in cooler q and ( ) is viscosity of cooling water in cooler q
The pressure drop of the tube side is written as
( ) 7 ( ) R ( ) 8 ( ) w( ) w( )
( ) ( ( ) ) ( ) ( )
( ) ( ( ) ( )
) (B10)
where ( ) is pressure drop in tube side of cooler q ( ) is number of tube passes
in cooler q ( ) is Reynolds number of tube side in cooler q ( ) is tube length of
cooler q ( ) is density of cooling water in cooler q ( ) is velocity of cooling
water in cooler q and ( ) and ( ) are velocity of cooling water entering and
leaving cooler q respectively
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
49
The fluid velocity in the tube side is written as
( ) ( ) ( )
w( ) ( ) ( ) (B11)
where ( ) is velocity of cooling water in cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is number of tube pass in cooler q ( ) is density
of cooling water in cooler q ( ) is number of tubes in cooler q and ( ) is tube
inside diameter in cooler q
The inlet fluid velocity of cooler q is written as
( ) ( )
w( ) n( ) (B12)
where ( ) is velocity of cooling water entering cooler q ( ) is mass flowrate of
cooling water in cooler q ( ) is density of cooling water in cooler q and ( ) is
pipe diameter connected with cooler q inlet
The outlet fluid velocity of cooler q is written as
( ) ( )
w( ) ut( ) (B13)
where ( ) is velocity of cooling water leaving cooler q ( ) is mass flowrate
of cooling water in cooler q ( ) is density of cooling water in cooler q and
( ) is pipe diameter connected with cooler q outlet
The models of heat transfer coefficient and pressure drop in tube side developed by
Wang et al [30] are validated by some heat exchangers provided in [30] The Stream
data and geometry of heat exchangers are presented in Appendix B The results of
heat transfer coefficients and pressure drop for those heat exchangers are listed in
Table A1 The results obtained by equations proposed by Wang et al [30] are
compared with the results calculated by the software HTRI From Table A1 it is seen
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
50
that heat transfer coefficients and pressure drops calculated from the model proposed
by Wang et al [30] are similar to the values obtained by HTRI
Table A1 Modelling results
No 1 2 3 4 5
ht
(W(m2 K))
Wang 12072 57689 14026 15846 75662
HTRI 12993 56440 14700 16169 73632
Relative error () -709 221 -459 -200 276
∆Pt
(kPa)
Wang 688 287 886 693 261
HTRI 712 297 868 735 268
Relative error () -337 -337 207 -571 -261
(C) Characteristics of pumps [32]
The efficiency of pump j is expressed as equation (C1)
( ) ( ) ( ) ( ) (C1)
where ( ) is efficiency of pump j and ( ) is volumetric flowrate of cooling water
going through pump j
The pressure head of pump j is written as equation (C2)
( ) ( ( ) ) (C2)
where ( ) is pressure head of pump j
The power consumed by pump j is calculated by the following equation
( ) ( ) w ( )
( ) (C3)
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
51
where ( ) is power consumption by pump j and ( ) is mass flowrate of cooling
water going through pump j
Appendix B Data information
The stream data and heat exchanger geometry used to validate the equations of heat
transfer coefficient and pressure drop in tube side provided by Wang et al [30] are
presented in Table A2 and Table A3 respectively
Table A2 Stream data [30]
No 1 2 3 4 5
Streams Tube Shell Tube Shell Tube Shell Tube Shell Tube Shell
Specific heat
(JkgK) 2470 2052 4179 4179 2135 2428 2512 2240 2430 4223
Thermal
conductivity
(WmK)
0137 0133 0633 0623 0123 0106 0089 0091 0087 0675
Viscosity
(mPa s) 040 360 062 071 289 120 033 110 180 030
Density
(kgm3) 785 850 991 994 820 790 702 801 786 957
Flow rate
(kgs) 568 1892 19272 38540 7522 1915 7692 40510 6023 2390
Inlet
temperature
(degC)
2000 380 480 330 517 2100 2270 1120 1700 770
Fouling
resistance (10-4
m2KW)
35 53 70 40 35 35 53 53 88 53
Chapter 3 Operational Optimisation of Recirculating Cooling Water Systems
52
Table A3 Heat exchanger geometry [30]
No 1 2 3 4 5
Tube pitch (m) 003175 002500 002540 003125 002500
Number of tubes 124 3983 528 1532 582
Number of tube passes 4 2 6 2 4
Tube length L (m) 4270 9000 5422 9000 7100
Tube effective length (m) 4170 8821 5219 8850 7062
Tube conductivity (WmK) 5191 5191 5191 5191 5191
Tube pattern
(tube layout angle) 90deg 90deg 90deg 90deg 90deg
Tube inner diameter (m) 00212 00150 00148 00200 00150
Tube outer diameter (m) 00254 00190 00191 00250 00190
Inner diameter of tube-side inlet
nozzle (m) 01023 04380 01280 03370 01540
Inner diameter of tube-side outlet
nozzle (m) 01023 04380 01280 03370 01540
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
Chapter 4
Publication 3 Operational Optimisation of
Recirculating Cooling Water Systems for Improving
the Performance of Condensing Turbines
(Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating
Cooling Water Systems for Improving the Performance of Condensing Turbines)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
1
Operational Optimisation of Recirculating Cooling
Water Systems for Improving the Performance of
Condensing Turbines
Fei Song Nan Zhang Robin Smith
Centre of Process Integration the University of Manchester Manchester M13 9PL UK
Abstract
The overall economic performance of cooling water systems and processes with
cooling demand can be improved by the integration of cooling water systems and
processes Condensing turbines with surface condensers using cooling water are
typical users of cooling water systems Therefore condensing turbines are taken as
examples of processes with cooling demand to illustrate the requirement of the
integration The increase of power generation in condensing turbines is at the cost of
the increase of operating cost of cooling water systems Therefore there is a trade-off
between power generation in condensing turbines and the operating cost of cooling
water systems to improve the overall economic performance of cooling water systems
and condensing turbines To solve this problem an equation-based integration model
of condensing turbines and cooling water systems is developed It includes
recirculating cooling water system modelling developed by Song et al [1] turbine
modelling based on mass and energy balance and condenser modelling Both
superheated steam and saturated steam leaving condensing turbines are considered
Detailed heat transfer in condensers is expressed for both the cooling of superheated
steam and that of saturated steam The model is optimised by the solver CONOPT in
GAMS A case study proves that the model is effective to improve the economic
performance In the case study the simultaneous optimisation increases the total
profit by 337 kpoundyr compared with focusing only on maximising the power
generation of condensing turbines
Key words recirculating cooling water systems condensing turbines integration
model operational optimisation
Corresponding author Tel +44 1613064384 Fax+44 1612367439
Email nanzhangmanchesteracuk
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
2
Highlights
bull An equation-based integration model of cooling water systems and condensing
turbines is established
bull In condenser modeling the cooling of superheated steam and saturated steam is
considered
bull The integration model is proven to be effective to improve the economic
performance
1 Introduction
Recirculating cooling water systems are widely used to reject process heat to the
environment in the process industry in order to keep processes working efficiently or
safely The operation of cooling water systems determines the outlet temperature of
processes from coolers The operating variables of cooling water systems include
cooling water flowrate entering individual cooling towers and coolers and air inlet
flowrate entering individual coolers For some processes their performance is
sensitive to the temperature obtained by cooling Condensing turbines with surface
condensers using cooling water are examples of those processes Condensing turbines
are devices that generate power by expanding steam to vacuum pressure The vacuum
pressure is created by condensing the steam out of turbines by cooling water in
condensers The power generation rate is influenced by the vacuum pressure that is
determined by the outlet temperature of condensate from condensers
It is noted that power generation rate by turbines is promoted by the increase of
vacuum in corresponding condensers when the other operating conditions of the
condensing turbine is fixed The increase of the vacuum in the condenser requires
lower cooling water temperature andor higher cooling water flowrate provided by
cooling water systems However the higher cooling water flowrate and the lower
cooling water temperature increase the operating cost of cooling water systems as the
higher cooling water flowrate increases the power consumption by pumps and a lower
cooling water temperature increases air flowrate and thereby increases the power
consumption by fans Although the operating cost of cooling water systems is
increased the profit of condensing turbines is also increased If the operation of
cooling water systems is determined by minimising the operating cost of cooling
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
3
water systems there will be an economic loss from condensing turbines If the
operation of cooling water systems is determined by maximising the profit of
condensing turbines there will be an increase in the operating cost of cooling water
systems Therefore both the economic performance of cooling water systems and that
of condensing turbines should be considered simultaneously to determine the optimal
operation of cooling water systems The optimal operation of cooling water systems is
determined by the trade-off between the revenue of power generation and the
operating cost of cooling water systems to maximise the total profit of cooling water
systems and condensing turbines In addition there is a trade-off between cooling
water flowrate and air flowrate to determine the optimal operation of cooling water
systems A cooling requirement of processes can be achieved by either increase of
cooling water flowrate with decrease of air flowrate or decrease of cooling water
flowrate with increase of air flowrate No matter how the operation is altered the
effect of the variation of cooling water flowrate is contrary to that of air flowrate on
power consumption Therefore there is a trade-off between cooling water flowrate
and air flowrate to determine the cost-effective operation of cooling water systems
Cooling water systems consist of three major components which are wet cooling
towers piping networks and cooler networks Wet cooling towers are used to produce
cold cooling water for process heat removal Mechanical draft wet cooling towers are
very common in recirculating cooling water systems as they can produce cooling
water with different temperature by adjusting air flowrate into cooling towers Piping
networks distribute cooling water to individual coolers Cooler networks are where
processes reject heat to cooling water Condensers are part of cooler networks The
cooling water flowrate into condensers is determined by the characteristics of pumps
and piping networks The cooling water inlet temperature of condensers is determined
by the cooling water outlet temperature of cooling towers The cooling water outlet
temperature of cooling towers is affected by the cooling water inlet temperature of
cooling towers However the cooling water inlet temperature of cooling towers is
determined by the cooling water outlet temperature of both condensers and coolers
The cooling water outlet temperature of condensers and coolers is dependent on the
cooling load of processes Cooling water inlet flowrate and inlet temperature of
condensers have an influence on the vacuum created in condensers The vacuum
pressure of condensers determines the steam outlet state from condensing turbines and
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
4
thereby determines the power generation of condensing turbines In reverse the steam
outlet state from condensing turbines has an influence on the cooling duty of
condensers and thereby the cooling duty of cooling water systems Therefore there is
a complex thermal behaviour of cooling water systems and condensing turbines
In previous studies Castro et al [2] Cortinovis et al [3] Song et al [1] separately
implemented operational optimisation of cooling water systems with the integration of
the major components of cooling water systems Models of cooling water systems
were developed in their works including models of cooling towers cooler networks
and piping networks Castro et al [2] did not consider heat transfer model of coolers
Cortinovis et al [3] did not consider the pressure drop in coolers in the hydraulic
model Both Castro et al [2] and Cortinovis et al [3] developed a model for cooling
water systems with single cooling tower and cooler networks in a parallel
arrangement In the model developed by Song et al [1] water evaporation was related
to cooling water mass flowrate and dry air mass flowrate into cooling towers and
ambient air conditions while in [2] and [3] the effect of air flowrate and ambient air
conditions on water evaporation is not considered Both a heat transfer model and
pressure drop in coolers and pipes were included in the model by Song et al [1] In
addition cooler networks in series and parallel configurations as well as multiple
cooling towers were taken into consideration
Laskowski et al [4] analysed the effect of cooling water flowrate and temperature on
the performance of condensing turbines based on data from simulators and the actual
measurement Laković et al [5] investigated the effect of cooling water temperature
and flowrate on the performance of condensers and condensing turbines with a
thermodynamic model of condensers and turbines In the literature [6] [7] the
cooling water inlet flowrate and temperature into condensers were optimised to
maximise the power output by the trade-off between power generation of condensing
turbines and power consumption by pumping water in which correlation models of
condensers steam turbines and pumps were included In the literature [8] [9] the
effect of air flowrate into cooling towers and ambient air conditions on the energy
efficiency of power plants was analysed with the consideration of the performance of
cooling towers and condensing turbines The Merkel method [10] was applied to
estimate the cooling water outlet temperature of cooling towers in [8] [9]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
5
Condensers were simulated by heat transfer equations with the assumption that steam
into condenser was at the saturated state and the power generation was calculated by
mass and energy balance
Even though cooling water systems and condensing turbines were paid attention to
separately in the past few years there was few literature focusing on operational
optimisation of cooling water systems with the integration of cooling water systems
and condensing turbines In the literature [11] a modular-based optimisation method
was proposed for a waste-and-energy cogeneration plant to maximise the net power
output In the method an optimisation code compiled in Matlab interacted with a
commercial design and simulation software Thermoflex to determine the optimal
performance of the plant In this model power generation and power consumption
were considered while water consumption was ignored As the modular-based
optimisation has less advantage than the equation-based optimisation approach in
terms of robustness speed and power an equation-based optimisation method is
proposed to integrate cooling water systems and processes with cooling demand in
this paper In this method an integration model of cooling water systems and
condensing turbines will be developed to determine the optimal cooling water
flowrate entering individual towers coolers and condensers and air flowrate entering
individual towers The performance of the other processes is not considered in the
model but the cooling requirement of these processes is taken into account Except
cooling water temperature and cooling water flowrate the other elements that affect
the performance of condensing turbines are not considered in this paper
In the following sections a model for the operational optimisation of cooling water
systems is developed The model includes models of cooling water systems power
generation of condensing turbines and heat transfer of condensers The model of
cooling water systems developed by Song et al [1] is applied Then a case study is
used to illustrate the application of the model In the case study the optimal
operations of cooling water systems with different objectives are compared The
objectives include minimising the operating cost of cooling water systems
maximising the profit of power generation by condensing turbines and maximising
the total profit of cooling water systems and condensing turbines Conclusions and
future work are made in the last section
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
6
2 Model Development
In order to determine the operation of cooling water systems to improve the overall
economic performance of cooling water systems and condensing turbines models
power generation of condensing turbines and heat transfer rate of condensers are
included besides the model of cooling water systems
21 Recirculating cooling water system modelling
An optimisation model of recirculating cooling water systems developed by Song et al
[1] is applied in this paper The model includes models of cooling towers cooler
networks piping networks The cooling requirement of processes is taken into
account The detailed model is presented in Appendix A)
22 Turbine modelling
221 Steam outlet properties
Power generation of condensing turbines is dependent on the state of inlet steam and
outlet steam steam flowrate and turbine efficiency The state of inlet steam and the
flowrate of inlet steam are parameters As it changes with load the isentropic
efficiency is assumed to be constant when the load is constant
Isentropic efficiency of condensing turbine i is defined as equation (1)
( ) n( ) ut( )
n( ) ( ) (1)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively and ( ) is specific
enthalpy of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
The enthalpy of the outlet steam is calculated by equation (2) rearranged from
equation (1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
7
( ) ( ) ( ( ) ( )) ( ) (2)
The enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam is determined by the outlet pressure which is unknown when the inlet state
of steam is given
(1) Superheated steam
When the entropy of the inlet steam is greater than the entropy of the saturated steam
at the outlet pressure the temperature of the steam leaving turbine i that has the same
entropy as the inlet steam can be calculated by IAPWS-IF 97 [12] for the calculation
of entropy for superheated steam which is expressed as equation (B1) in Appendix B)
( ) is calculated by IAPWS-IF 97 [12] for the calculation of enthalpy for
superheated steam which is expressed as equation (B2) in Appendix B)
The steam outlet temperature of turbines is needed for the calculation of heat transfer
in condensers The steam outlet temperature of turbine i is determined by the
calculation of enthalpy for superheated steam presented in the IAPWS-IF 97 [12]
which is expressed as equation (B3) in Appendix B)
(2) Saturated steam
When the entropy of the inlet steam is less than the entropy of the saturated steam at
the outlet pressure the steam at the outlet pressure having the same entropy as the
inlet steam is saturated The dryness of the steam at the outlet pressure having the
same entropy as the inlet steam in condensing turbine i is calculated by equation (3)
S ( ) ( ) S ( ) ( ( )) S ( ) (3)
where S ( ) is the entropy of the saturated steam at the exhaust pressure of turbine i
S ( ) is the entropy of the saturated liquid and ( ) is dryness of steam at the outlet
pressure having the same entropy as the inlet steam in condensing turbine i S ( ) and
S ( ) are represented by equations (B4)and (B5) in Appendix B)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
8
When the steam at the outlet pressure having the same entropy as the inlet steam is
saturated the enthalpy is calculated by equation (4)
( ) ( ) ( ) ( ( )) ( ) (4)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
and ( ) is the enthalpy of the saturated liquid They are represented by equations (B
6) and (B7) in Appendix B)
The dryness of the steam leaving turbines is needed for the calculation of mass
flowrate of steam that is condensed in condensers The dryness of the steam is
calculated by equation (5)
( ) ut( ) ( )
( ) ( ) (5)
where ( ) is the enthalpy of the saturated steam at the exhaust pressure of turbine i
( ) is the enthalpy of the saturated and ( ) is specific enthalpy of steam leaving
condensing turbine i
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B) The equation represents the relationship between temperature and
pressure of saturated steam in the IAPWS-IF 97 [12]
222 Power generation
Power generation of condensing turbine i is calculated by equation (6)
( ) ( ) ( ) ( ( ) ( )) (6)
where ( ) and ( ) are specific enthalpy of steam entering condensing turbine i
and that of steam leaving condensing turbine i respectively ( ) is the mass flowrate
of steam entering turbine i and ( ) is mechanical efficiency of condensing turbine i
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
9
23 Condenser modelling
1) Superheated inlet steam of condensers
Cooling water systems and condensing turbines are connected by condensers The
cooling water flowrate in cooling water systems is distributed to condensers to
condense the steam from condensing turbines The cooling water flowrate and cooling
water temperature into condensers determine the temperature of condensate The
temperature of the condensate determines the pressure of steam out of condensing
turbines Therefore the condensate temperature is needed to be predicted to determine
the outlet pressure of steam from condensing turbines and the outlet temperature of
cooling water from condensers is needed for the determination of the operation of
cooling water systems
If the steam into the condenser i is superheated the mass flowrate of the steam to be
condensed in the condenser i is the same as the flowrate of the steam going through
turbine i which is expressed as equation (7)
( ) ( ) (7)
where ( ) is the mass flowrate of steam entering turbine i and ( ) is the mass
flowrate of steam entering condenser i
It is assumed that there are no heat and pressure loss in the pipes connecting
condensing turbines and condensers Therefore the properties of steam leaving
turbines are the same as those of steam entering condensers The properties of steam
and water in different conditions are calculated by IAPWS-IF 97 [12]
The condensate from condenser i is assumed to be saturated Therefore the condenser
i is divided into two zones which are desuperheating zone and condensing zone The
heat transfer equations for condensers presented in Smith [13] are employed which
are presented in Appendix C) The heat transfer in the desuperheating zone is
expressed by equations (C2) and (C4) The inlet steam temperature of the
desuperheating zone in condenser i is the same as the outlet steam temperature of
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
10
condensing turbine i which is ( ) calculated by equation (B3) The outlet steam
temperature of the desuperheating zone in condenser i is the saturated temperature of
the steam at the vacuum pressure which is ( ) calculated by equation (B8) The
inlet and outlet cooling water temperature of the desuperheating zone in condenser i is
represented by ( ) and ( ) The heat transfer in the condensing zone is
expressed by equations (C3) and (C5) In the condensing zone of condenser i the
temperature of the steam side is kept at ( ) The inlet and outlet cooling water
temperature of the condensing zone in condenser i is represented by ( ) and ( )
The logarithmic mean temperature of the desuperheating zone and the condensing
zone in condenser i is calculated by equations (8) and (9) respectively
( ) ( ut( ) ( )) ( ( ) ( ))
ut( ) t ( )
( ) t ( )
(8)
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(9)
2) Saturated inlet steam of condensers
If the outlet steam from the turbine i is saturated the mass flowrate of the steam to be
condensed in the condenser i is calculated by equation (10)
( ) ( ) ( ) (10)
where ( ) is the mass flowrate of steam entering turbine i ( ) is the mass
flowrate of steam entering condenser i and ( ) is dryness of the steam leaving
turbine i
There is only the condensing zone in condenser i The heat transfer in the condensing
zone is expressed by equations (C3) and (C5) The temperature of the steam side is
kept at ( ) The inlet and outlet cooling water temperature of condenser i is
represented by ( ) and ( ) The logarithmic mean temperature of the condensing
zone in condenser i is calculated by equations (11)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
11
( ) ( ( ) ( )) ( ( ) ( ))
( ) t ( )
( ) t ( )
(11)
Because condensers are part of cooler networks in cooling water systems the
interactions between condensers coolers and cooling towers are represented by the
model of cooler networks
24 Objective functions
The objective function is to maximise the total profit of cooling water systems and
condensing turbines which is represented by equation (12)
Max (12)
The total profit (TNP) of cooling water systems and condensing turbines includes the
revenue of power generation (PR) by condensing turbines and the operating cost of
cooling water systems (TOC)
The revenue of condensing turbines is expressed as equation (13)
sum ( ) (13)
where ( ) is power generated by turbine i is unit cost of power
The operating cost of cooling water systems consists of the cost of make-up water and
the cost of power consumed by pump j and fan j which is presented as equation (14)
sum ( ) sum ( ( ) ( )) (14)
where ( ) is make-up water consumption of tower j ( ) is power consumption
by pump j and ( ) is power consumption by fan j
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
12
3 Solution Method
The regression of coefficients in the models for cooling towers pumps and fans is
implemented according to the measured data or the operating data of individual
equipment before models of cooling towers pumps and fans are used to determine
the operation of cooling water systems The regression of coefficients is realised by
the least square method
With the input data consisting of ambient air conditions process specifications steam
inlet conditions of condensing turbines cooler configurations condenser
configurations and pipe specifications the objective function is maximised subject to
the constraints composed of models of cooling water systems condensers and
condensing turbines as well as the practical constraints to determine the optimal
operating conditions of cooling water systems and the resulting economic
performance of cooling water systems and condensing turbines When the cooler
network is in a parallel configuration equations (A29) - (A34) are excluded When
the outlet steam of condensing turbines is superheated equations (3) - (5) (10) (11)
(B4) and (B5) are excluded When the outlet steam of condensing turbines is saturated
equations (7) - (9) (B1) - (B3) (C1) (C2) and (C4) are excluded As the model
contains nonlinear equations the solver CONOPT is selected to solve the model in the
software GAMS CONOPT is appropriate to solve highly nonlinear problems
4 Case Studies
A simplified subset of a cooling water system in a refinery is employed in the case
study which consists of a forced draft wet cooling tower 12 coolers and a condenser
in a series and parallel arrangement a pump a fan 12 process streams and a
condensing turbine Some processes can reuse the cooling water from the condenser
while the other processes and the steam condensation in the condenser use the cooling
water from the cooling tower as the only source The flowrate of cooling water into
individual coolers and the condenser can be changed by the adjustment of valves
The specifications of processes are listed in Table 1 including heat capacity flowrate
temperature specifications heat transfer coefficient and fouling resistance
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
13
Table 1 Process specifications
Processes Temperature
entering coolers
degC
Temperature leaving
coolers degC
Heat capacity
flowrate
kWdegC
Heat transfer
coefficient
W(m2degC)
Fouling
resistance
msup2degC W Upper Lower
C1 998 650 600 735 1864 000035
C2 847 600 550 1167 2375 000035
C3 781 650 600 4367 3625 000035
C4 787 600 550 3356 4747 000035
C5 951 600 550 669 2106 000035
C6 952 600 550 2159 4747 000035
C7 637 450 400 2492 7036 000018
C8 676 450 400 1612 7347 000018
C9 642 500 450 3050 4686 000018
C10 742 500 450 2198 3903 000018
C11 635 450 400 2955 8277 000018
C12 696 500 450 2201 4820 000018
The geometry of coolers is presented in Table 2
Table 2 Geometry of coolers
Coolers Number of
tubes
Tube
passes
Tube
diameter
(mm)
Tube
length
(m)
Cross sectional
area (m2)
Heat transfer
area (m2)
C1 1234 2 19times2 6 01090 4346
C2 742 2 25times2 9 01285 5184
C3 1452 2 19times2 9 01290 7642
C4 1452 2 19times2 9 01290 7642
C5 588 2 25times2 9 01018 4108
C6 1452 2 19times2 9 01290 7642
C7 1424 4 19times2 9 00745 7495
C8 988 2 19times2 9 00873 5249
C9 1234 2 19times2 9 01090 6556
C10 1452 2 19times2 9 01290 7642
C11 1452 2 19times2 9 01290 7642
C12 860 4 25times2 9 00745 5956
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
14
The specifications for the condensing turbine and the condenser are listed in Table 3
The inlet steam conditions the turbine efficiency and the condenser configuration are
provided
Table 3 Specifications of the condensing turbine and the condenser
Inlet steam
Mass flowrate (th) 666
Pressure (bara) 40
Temperature (degC) 360
Turbine
Isentropic efficiency 075
Mechanical efficiency 096
Minimum power generation
requirement (kW) 13190
Condenser
Area (m2) 1984
Number of tubes 3023
Tube passes 1
Tube diameter (mm) 25times25
Tube length (m) 836
Tube pitch (m) 0032
Shell diameter (m) 149
The ambient air conditions unit cost of make-up water and power and the other
information are shown in Table 4
Table 4 Other information for optimisation
Ambient air
conditions
Dry-bulb temperature (degC) 350
Wet-bulb temperature (degC) 285
Humidity (kgkg dry air) 00222
Cooling towers Cycles of concentration 4
Make-up water temperature (degC) 350
Unit cost Water(poundt) 03
Power(poundkWh) 01
Working hours (hyr) 8000
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
15
Some practical constraints are listed in Table 5
Table 5 Practical constraints
Cooling towers
Water mass flowrate
(th)
Upper bound 9000
Lower bound 5000
Air mass flowrate
(th)
Upper bound 12600
Lower bound 5000
Ratio of water mass flowrate
and air mass flowrate
Upper bound 15
Lower bound 07
Inlet water temperature(degC) Upper bound 480
Approach temperature(degC) Lower bound 28
Coolers
Minimum temperature difference(degC) 100
Water velocity (ms) Upper bound 20
Lower bound 05
Condensers Vapor fraction of outlet steam Lower bound 088
With the information provided above the system is optimised with the aim of
minimising the operating cost of the cooling water system maximising the power
generation of the condensing turbine and maximising of the overall profit of the
cooling water system and the condensing turbine in Case 1 Case 2 and Case 3
respectively
41 Base case
The operation of the cooling water system is presented in Figure 2 The thermal and
economic performance of the cooling water system and the condensing turbine caused
by the operation are recorded in Table 6 and Table 7 which include make-up water
and power consumption of the cooling water system the power generation of the
condensing turbine the operating cost of the cooling water system the total profit of
the cooling water system and the condensing turbine and the outlet temperature of
individual processes from coolers
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
16
Figure 2 Operation in base case
Table 6 Comparison of results
Units Results Base case Case
1
Case
2
Case
3
Cooling
water system
Operation
Circulating water
flowrate (th) 7560 6047 9000 6414
Air flowrate (th) 8237 7267 12053 7258
Inlet temperature of
cooling water into
the cooling tower
(degC)
430 456 405 449
Outlet temperature
of cooling water
from the cooling
tower (degC)
320 319 313 321
Water
consumption
Make-up water
(th) 183 181 187 181
Power
consumption
Fans (kW) 398 351 582 350
Pumps (kW) 1568 1372 1877 1411
Total (kW) 1966 1723 2459 1762
Operating cost (poundyr) 2012k 1813k 2416k 1844k
Condensing
turbine
Inlet cooling water mass flowrate (th) 5287 3908 6796 4246
Power generation (kW) 13360 13190 13528 13234
Profit from power generation (poundyr) 10688k 10552k 10822k 10587k
Total profit (poundyr) 8676k 8739k 8406k 8743k
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
17
Table 7 Outlet temperature of processes from coolers or condensers
Base
case
Case
1
Case
2
Case
3
C1 640 650 648 650
C2 592 600 600 600
C3 643 650 650 650
C4 592 600 600 600
C5 590 600 600 600
C6 592 600 600 600
C7 450 450 450 450
C8 440 450 450 450
C9 500 500 500 500
C10 500 500 500 500
C11 445 450 450 450
C12 500 500 500 500
Condensate from the condenser 488 509 467 504
42 Case study 1
Before optimisation the coefficients in the models of the cooling tower the pump and
the fan are regressed and presented in Table 8
Table 8 Models of the cooling tower pump and fan
Unit Models
Cooling tower
( times times ( ) times
( ) times ( ))
7
7
( )
Pump
( )
Fan
( )
Processes
Outlet temperature (⁰C)
Cases
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
18
In Case 1 the system that includes the cooling water system and the condensing
turbine is optimised for minimising the operating cost of the cooling water system
with the method proposed in the previous section The optimal operating conditions
are described in Figure 3 and the consequent operating cost power generation total
profit of the overall system and the outlet temperature of processes from coolers or the
condenser are listed in Table 6 and Table 7
Figure 3 Optimal operation for minimising the operating cost
Through operational optimisation the operating cost of the cooling water system is
minimised by reducing cooling water flowrate and air flowrate Due to the reduction
of cooling water flowrate and air flowrate the consequent power consumption is
reduced by 243 kW The cooling water into the condenser is reduced to reduce the
overall cooling water flowrate in the cooling water system As a result of the decrease
of cooling water flowrate the temperature of the condensate from the condenser is
increased by about 2 degC and the corresponding power generation rate of the
condensing turbine is decreased by 170 kW to the minimum requirement As the
decrease of power consumption is greater than the decrease of power generation the
total profit of the cooling water systems and the condensing turbine increases by 63
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
19
kpoundyr For the other processes their outlet temperature from coolers satisfies the
cooling requirement
43 Case study 2
In Case 2 the operational optimisation of the cooling water system is performed for
maximising the power generation of the condensing turbine with the proposed method
The optimal operation is presented in Figure 4 and the corresponding thermal and
economic performance of the overall system is presented in Table 6 and Table 7
Figure 4 Optimal operation for maximising power generation
The power generation of the condensing turbine is increased by 168 kW through
optimisation In order to maximise the power generation by the condensing turbine
the cooling water used by the condenser is increased as much as possible to reduce the
temperature of the condensate from the condenser Air flowrate is increased as well to
reduce the outlet temperature of cooling water from the cooling tower in order to
reduce the temperature of the condensate However the increase of cooling water and
air flowrate increase power consumption of the cooling water system by 493 kW
Although the power generation of the condensing turbine is increased the total profit
of the cooling water system and the condensing turbine is decreased by 270 kpoundyr
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
20
That is because the increase of the operating cost of the cooling water system is
greater than the increase of the profit from the power generation of the condensing
turbine The outlet temperature of all the processes from coolers is within the required
temperature range The operation of cooling water systems for the maximum power
generation of condensing turbines reduces the outlet temperature of process 1 by
02 degC
44 Case study 3
In Case 3 the optimal operating conditions of the cooling water system are
determined for maximising the total profit of the cooling water system and the
condensing turbine by the method proposed in the previous section The optimal
operating conditions are shown in Figure 5 The resulting thermal and economic
performance of the cooling water system and the condensing turbine is recorded in
Table 6 and Table 7
Figure 5 Optimal operation for maximising the total profit
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
21
Through operational optimisation for maximisation of the total profit of the cooling
water system and the condensing turbine the total profit is 67 kpoundyr more than that in
base case by decreasing cooling water and air flowrate Cooling water flowrate into
the condenser is decreased resulting in the decrease of power consumption by the
pump Cooling water temperature into the condensers is increased which leads to a
drop of air flowrate The decrease of air flowrate reduces the power consumption of
the fan The power consumption in the cooling water system is reduced by about 200
kW The reduction of power consumption lowers the operating cost of cooling water
systems However due to the reduction of the cooling water flowrate and the increase
of the cooling water temperature into condensers the power generation of the
condensing turbine is reduced by around 100 kW As the saving of power
consumption in the cooling water system is more than the power generation reduction
of the condensing turbine the total profit of the condensing turbine and the cooling
water system is increased The outlet temperature of processes from coolers presented
in Table 7 illustrates that the cooling requirement of processes is fulfilled by the
operation determined in Case 3
45 Discussion
Both the operating cost of the cooling water system and the power generation of the
condensing turbine obtained by minimising the operating cost of cooling water
systems are the least in the three cases Both the operating cost of the cooling water
system and the power generation of the condensing turbine obtained by maximising
the power generation of the condensing turbine are the most in the three cases
However none of those two cases obtains the optimal total profit of the cooling water
system and the condensing turbine In the case of minimising the operating cost of
cooling water systems the operating cost is reduced but opportunities to improve the
power generation of the condensing turbine are lost In the case of maximising the
power generation of the condensing turbine the power generation of the condensing
turbine is improved but the increase of the resulting power consumption is greater
than the increase of the power generation which decreases the total profit When the
performance of the cooling water system and the performance of the condensing
turbine are considered simultaneously as in Case 3 the profit from the power
generation of the condensing turbine and the operating cost of the cooling water
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
22
system are traded off to improve the total profit of the cooling water system and the
condensing turbine The total profit obtained by optimising the overall economic
performance of the cooling water system and the condensing turbine is improved by
337 kpoundyr compared with that obtained by maximising the power output of the
condensing turbine The circulating water flowrate determined by optimising the
overall economic performance of the cooling water system and the condensing turbine
is increased by about 370 th compared with that determined by minimising the
operating cost of the cooling water system
5 Conclusions
The integration of cooling water systems and processes with cooling demand provides
opportunities to improve the overall economic performance In the literature [11] a
modular-based optimisation method was developed for a waste-to-energy
cogeneration plant to maximise the net power output In this paper an equation-based
optimisation method is proposed for the integration of cooling water systems and
processes with cooling demand Condensing turbines are taken as examples of
processes An equation-based model is developed for the integration of cooling water
systems and condensing turbines In the proposed model the detailed model of
cooling water systems developed by Song et al [1] is employed a turbine model
based on the mass and energy balance is established to calculate the power generation
of turbines and the state of the exhaust steam from turbines and a detailed heat
transfer equation for condensers is used to calculate the pressure of exhaust steam
leaving turbines and the cooling water temperature leaving condensers The model
can be used for cooler networks in either parallel arrangements or series and parallel
arrangements and for either the cooling of superheated steam or the cooling of
saturated steam in condensers The model is optimised by the solver CONOPT in
GAMS to determine the optimal cooling water flowrate entering individual towers
coolers and condensers and air flowrate entering individual towers A case study
proves that the proposed method is effective to improve the economic performance by
the integration of cooling water systems and processes In the case study the
simultaneous optimisation increases the total profit by 337 kpoundyr compared with
focusing only on maximising the power generation of condensing turbines
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
23
In this work the cooling requirement of the other processes except condensing
turbines is considered instead of the performance of processes If the operation of
cooling water systems has an influence on the economic performance of processes
the performance of the processes is preferred to be taken into account with the
performance of cooling water systems The method developed in this work can be
extended to cooling water systems with other processes such as compressor inter-
cooling condensation of light components for distillation pre-cooling for
compression refrigeration and so on In future work therefore the integration of
cooling water systems with processes whose performance is affected by the operation
of cooling water systems is performed to determine the optimal operation of cooling
water systems and the outlet temperature of processes from coolers
Nomenclature
Sets
i set of condensing turbines
j set of cooling towers pumps fans
k q set of coolers
Parameters
Ac(i) area of condenser i (m2)
Ao(q) area of cooler q (m2)
C1 unit cost of makeup water (poundt)
C2 unit cost of power (poundkWh)
cc cycles of concentration
CPh(q) heat capacity flowrate of process q (WdegC)
Cpwm specific heat of makeup water (JkgdegC)
di(q) inside tube diameters of cooler q (m)
din(q) pipe diameter connected with cooler q inlet (m)
do(q) outside tube diameters of cooler q (m)
dout(q) pipe diameter connected with cooler q outlet (m)
Ds(i) shell diameter of condenser i (m)
g gravitational constant (981m2s)
ho(q) heat transfer coefficient in shell side of cooler q (Wm2deg
C)
Hin(i) specific enthalpy of steam into condensing turbine i (kJkg)
ii enthalpy of inlet air into cooling towers (Jkg dry air)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
24
k(q) thermal conductivity of tube wall of cooler q (WmdegC)
Lt(i) tube length of condensing turbine i (m)
Lt(q) tube length of cooler q (m)
ms(i) mass flowrate of steam into condensing turbine i (kgs)
np(i) tube pass of condenser i
np(q) tube pass of cooler q
nt(i) number of tubes of condenser i
nt(q) number of tubes of cooler q
NR(i) number of tubes in a vertical row of condenser i
pt(i) vertical tube pitch in condenser i (m)
Ri(q) fouling factor of tube side in cooler q (m2 deg
C W)
Ro(q) fouling factor of shell side in cooler q (m2 deg
C W)
Sin(i) entropy of inlet steam of condensing turbine i (kJdegC)
tdbi inlet air dry-bulb temperature (degC)
tm temperature of makeup water (degC)
twbi inlet air wet-bulb temperature (degC)
thi(q) inlet temperature of process fluids into cooler q (degC)
wi humidity of the air into cooling towers (kgkg dry air)
z(m) elevation of node m (m)
z(n) elevation of node n (m)
a1-a3 coefficients
b1-b3 coefficients
Variables
Acn(i) area of the condensation zone in condenser i (m2)
Ads(i) area of the desuperheating zone in condenser i (m2)
Cpw(j) specific heat of cooling water of cooling tower j (JkgdegC)
Cpwc(q) specific heat of cooling water of cooler q (JkgdegC)
f(q) correction factor of cooler q
hc(i) heat transfer coefficient of condensation in condenser i (Wm2deg
C)
hf (mn) friction loss between node m and node n (m3s)
hi(q) heat transfer coefficient in tube side of cooler q (Wm2deg
C)
Hf(i) specific enthalpy of saturated liquid in condenser i (kJkg)
Hg(i) specific enthalpy of saturated vapor in condenser i (kJkg)
His(i) specific enthalpy of steam at the outlet pressure having the same entropy as the inlet
steam in condensing turbine i (kJkg)
Hout(i) specific enthalpy of steam out of condensing turbine i (kJkg)
Hp(j) head pressure provided by pump j (m)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
25
io(j) enthalpy of outlet air from cooling tower j (Jkg dry air)
kw(q) thermal conductivity of cooling water in cooler q (WmdegC)
kl(i) thermal conductivity of condensate in condenser i (WmdegC)
L(i) tube length in condensing zone in condenser i (m)
m(jq) mass flowrate from cooling tower j to cooler q (kgs)
m(qj) mass flowrate from cooler q to cooling tower j (kgs)
m(kq) mass flowrate from cooler k to cooler q (kgs)
m(qk) mass flowrate from cooler q to cooler k (kgs)
ma(j) mass flowrate of dry air through cooling tower j (kgs)
mc(q) mass flowrate of cooling water in cooler q (kgs)
mcs(i) mass flowrate of steam condensed in condenser i (kgs)
me(j) evaporation rate of cooling tower j (kgs)
mm(j) mass flowrate of makeup water of cooling tower j (kgs)
mwi(j) mass flowrate of cooling water into cooling tower j (kgs)
mwo(j) mass flowrate of cooling water from cooling tower j (kgs)
NTU(j) the number of transfer units of cooling tower j
p(m) pressure at node m (Pa)
p(n) pressure at node n (Pa)
Pf(j) power consumption by fan j (kW)
Pout(i) pressure of steam out of turbine i (MPa)
Pp(j) power consumed by pump j (kW)
PR profit of power generation (poundyr)
Qcn(i) heat transfer duty for the condensing zone in condenser i (kW)
Qds(i) heat transfer duty for the desuperheating zone in condenser i (kW)
Qw(j) volumetric flowrate of cooling water through pump j (m3s)
Re(q) Reynolds number of tube side in cooler q
Sg(i) entropy of saturated steam at outlet pressure of condensing turbine i (kJdegC)
Sf(i) entropy of saturated liquid at outlet pressure of condensing turbine i (kJdegC)
t(j) temperature of mixture of cooling water from cooling tower j and make-up water
(oC)
tci(q) inlet temperature of cooling water into cooler q (degC)
tco(q) outlet temperature of cooling water from cooler q (degC)
tho(q) outlet temperature of process fluids from cooler q (degC)
twi(j) inlet temperature of cooling water into cooling tower j (degC)
two(j) outlet temperature of cooling water from cooling tower j (degC)
Tcc(i) saturated steam temperature of condenser i (degC)
Trsquocc(i) saturated steam temperature of condenser i (K)
Tis(i) temperature of steam at the outlet pressure having the same entropy as the inlet
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
26
steam of condensing turbine i (K)
Tout(i) temperature of steam from turbine i (degC)
Trsquoout(i) temperature of steam from turbine i (K)
TNP total net profit (poundyr)
TOC total operating cost (poundyr)
u(m) cooling water velocity at node m (ms)
u(n) cooling water velocity at node n (ms)
uw(q) velocity of cooling water in tubes of cooler q (ms)
uin(q) velocity of cooling water into cooler q (ms)
uout(q) velocity of cooling water out of cooler q (ms)
Ucn(i) overall heat transfer coefficient of the condensing zone in condenser i (Wm2deg
C)
Uds(i) overall heat transfer coefficient of the desuperheating zone in condenser i (Wm2deg
C)
Uo(q) overall heat transfer coefficient of cooler q (Wm2deg
C)
vf(i) dryness of outlet steam from condensing turbine i
vfis(i) dryness of steam at the outlet pressure having the same entropy as the inlet steam in
condensing turbine i
wo(j) humidity of the air from cooling tower j (kgkg dry air)
W(j) energy provided by pump j (m3s)
Wt(i) power generation by condensing turbine i (kW)
Greek Symbols
α β γ coefficients
(i) viscosity of the condensate in condenser i (kgm-1
s-1
)
(q) viscosity of cooling water in cooler q (kgm-1
s-1
)
ηis(i) isentropic efficiency of condensing turbine i
ηm(i) mechanical efficiency of condensing turbine i
( ) efficiency of pump j
density of air (kgm3)
(q) density of cooling water in cooler q (kgm3)
(m) density of cooling water at node m (kgm3)
(n) density of cooling water at node n (kgm3)
( ) pressure drop of tube side in cooler q (Pa)
( ) logarithmic mean temperature of cooler q (degC)
Δtcnm(i) logarithmic mean temperature for the condensing zone in condenser i (degC)
Δtdsm(i) logarithmic mean temperature for the desuperheating zone in condenser i (degC)
Subscripts
a air
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
27
db dry bulb
f fans
i insideinlet
m n nodes
o outsideoutlet
p pumps
w cooling water
wb wet bulb
m mean value
cn condensing zone
ds Desuperheating zone
References
[1] Song F Zhang N and Smith R 2016 Operational Optimisation of Recirculating Cooling
Water Systems
[2] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[3] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[4] Laskowski R Smyk A Lewandowski J and Rusowicz A 2015 Cooperation of A
Steam Condenser with A Low-Pressure Part of a Steam Turbine in Off-Design Conditions
American Journal of Energy Research 3 (1) pp 13-18
[5] Laković MS Stojiljković MM Laković SV Stefanović VP and Mitrović DD
2010 Impact of the Cold End Operating Conditions on Energy Efficiency of The Steam
Power Plantsrdquo Thermal Science 14 pp S53-S66
[6] Wang YM and Zhang LZ 2011 Optimal Operation of Cold End System for Steam
Turbine in Coal-Fired Power Plant 2011 International Conference on Materials for
Renewable Energy amp Environment pp 1645-1649
[7] Zheng L Chen C Xie D and Zhang H 2013 Optimisation of the Cold-End System of
the 1000 MW Ultra-Supercritical Units by VB Trans Tech Publications 694-697 pp 778-
781
[8] Laković MS Laković SV and BANJAC MJ 2012 Analysis of the Evaporative Towers
Cooling System of a Coal-Fired Power Plant Thermal Science 16 pp S375-S385
[9] Laković M Banjac M and Jovic M 2015 Improving the Energy Efficiency of the Coal
Fired Power Plant by Adjusting the Hydraulic Load of the Cooling Tower System Sci-Afric
J Sci Issues Res Essays 3(12) pp 873-880
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
28
[10] Merkel F 1925 Verdunstungshuhlung Zeitschrift des Vereines Deutscher 70 pp 123ndash
128
[11] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74
[12] IAPWS 2007 Revised Release on the IAPWS Industrial Formulation 1997 for the
Thermodynamic Properties of Water and Steam Available from httpwwwiapwsorg
[13] Smith R 2005 Chemical Process Design and Integration John Wiley amp Sons Ltd
[14] Evans FL 1980 Cooling Towers Equipment Design Handbook for Refineries and
Chemical Plants Gulf Publishing Houston vol 2
[15] Wang YF Pan M Bulatov I Smith R and Kim JK 2012 Application of Intensified
Heat Transfer for the Retrofit of Heat Exchanger Network Applied Energy 89 pp45ndash59
[16] Colebrook CF and White CM 1937 Experiments with Fluid Friction in Roughened
Pipes ProcRSocA Math Phys Eng Sci 161(906) pp 367-381
[17] Ulanicki B Kahler J and Coulbeck B 2008 Modeling the Efficiency and Power
Characteristics of a Pump Group Journal of Water Resources Planning and Management
134 pp 88-93
[18] Mueller AC in Hewitt GF 1992 Handbook of Heat Exchanger Design Begell House Inc
Appendix
A) Recirculating cooling water system modelling
The model of cooling water systems developed by Song et al [1] includes models of
wet cooling towers cooler networks and piping networks which are presented as
follows
A1) Mechanical draft wet cooling tower modelling
There are some basic assumptions listed as follows
bull The system is at steady state
bull Negligible heat and mass transfer through the tower walls to the environment
bull Negligible heat transfer from the tower fans to air or water streams
bull Constant water water vapour and dry air specific heats throughout the tower
bull Uniform temperature throughout the water stream at any cross section
bull Uniform cross-sectional area of the tower
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
29
Mass and energy balance of cooling tower j are represented as equation (A1) - (A2)
( ) ( ) ( ) ( ( ) ) (A1)
( ) ( ( ) ) ( ) ( ) ( ) ( ) ( ) ( ) (A2)
The regression model of wet cooling tower j includes equation (A3) - (A5)
( ) ( ) ( )
( ) (A3)
( ) ( ( ) ( )) ( ) ( ( ) )
( ) ( )
(A4)
( ) ( ) ( ) ( ) ( )
( ( ) ) (A5)
Water evaporation rate in a cooling tower j is calculated by equation (A6)
( ) ( ) ( ( ) ) (A6)
The flowrate of make-up water for cooling tower j is calculated by equation (A7)
( ) ( )
(A7)
where cc is the cycle of concentration defined as the ratio between the concentration
of dissolved solids in the circulating water and in makeup water
The characteristic of fans j is represented by equation (A8) [14]
( ) 0 ( ) ( )
1 (A8)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
30
A2) Cooler network modelling
A21 Cooler modeling
The model of cooler networks includes models of coolers and cooler networks The
cooler model is given as equations (A9) - (A21)
There are some assumptions made in cooler modelling
bull The properties of streams are constant
bull Heat transfer coefficient of hot streams is assumed to be constant
bull The properties of streams which are related to temperature are calculated at
the average of inlet and outlet temperature in individual coolers
bull Heat losses to the environment are negligible
bull Streams in both tube and shell are in turbulent flow
bull Cooling water is set to flow in the tube and hot streams are set to flow in the
shell
Energy balance of cooler q is expressed as equation (A9)
( ) ( ( ) ( )) ( ) ( ) ( ( ) ( )) (A9)
Heat transfer in cooler q is expressed as equation (A10)
( ) ( ( ) ( )) ( ) ( ) Δ ( ) ( ) (A10)
The overall heat transfer coefficient of cooler q based on the outside area is written as
( )
( )
h ( ) ( )
R ( ) ( )
( )
h ( ) ( )
( )
( )
( )
( ) (A11)
The correction factor of cooler q is written as equations (A12) - (A15)
( ) ( ) ( )
h ( ) ( ) (A12)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
31
S( ) h ( ) h ( )
( ) ( ) (A13)
For S( )
( ) radic ( ) (( ( )) ( ( ) ( ))frasl )
( ( ) ) ( ( ) ( ) radic ( ) ) ( ( ) ( ) radic ( ) )frasl (A14)
For S( )
( ) radic (q)
(q)
( ) ( radic ) ( ) ( radic )frasl (A15)
The logarithmic mean temperature difference
Δ ( ) ( h ( ) ( )) ( h ( ) ( ))
th (q) t (q)
th (q) t (q)
(A16)
The heat transfer coefficient of the stream q in the tube side is written as equation
(A17) [15]
( ) w( )
( ) ( )
w( ) μw( )
w( )
(A17)
The pressure drop of the tube side is calculated by equation (A18) [15]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( ( ) ) ( )
( ) ( ) ( ( ) ( )
)
(A18)
The fluid velocity is written as
( ) ( ) ( )
w( ) ( ) ( ) (A19)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
32
( ) ( )
w( ) n( ) (A20)
( ) ( )
w( ) ut( ) (A21)
A22 Network modelling
In cooler network modelling mass balance and energy balance are carried out for
cooler networks in parallel arrangements and in series and parallel arrangements
(1) Mass and energy balance of cooler networks in parallel arrangements are
expressed as equations (A22) ndash (A27)
( ) sum ( ) (A22)
( ) sum ( ) (A23)
( ) sum ( ) (A24)
( ) sum ( ) (A25)
( ( ) ( )) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) (A26)
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A27)
If the jth cooling tower provides cooling water for the qth coolers then the inlet
temperature of cooling water into the qth cooler is calculated by the following
equation
( ) ( ) ( ) sum ( ( ) ( ) ( )) (A28)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
33
(2) Mass and energy balance of cooler networks in series and parallel arrangements
( ) sum ( ) ( ) (A29)
( ) sum ( ) sum ( ) ( ) (A30)
( ) sum ( ) ( ) (A31)
( ) sum ( ) sum ( ) ( ) (A32)
( ) ( ) ( ) sum ( ( ) ( ) ( )) ( ) (A33)
( ) ( ) ( ) sum ( ( ) ( ) ( )) sum ( ( ) ( )
( )) ( ) (A34)
A3) Piping network modelling
There are some assumptions made in piping network modelling
bull There is no heat loss from the piping
bull There are one splitter corresponding to each cooling tower which provides
cooling water to individual coolers and one mixer corresponding to each
cooling tower that collect hot water from individual coolers
bull Equivalent length is used in friction loss calculation
1) Mechanical energy balance between two connected nodes m and n is performed
by the Bernoulli Equation as equation (A35)
( ) ( )
( )
w( ) ( )
( )
( )
w( ) ( ) (A35)
The Darcy-Weisbash equation is used for friction loss prediction The Colebrook-
White equation is used for friction factor calculation [16]
2) Pump modelling [17]
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
34
( ) ( ) ( ) ( ) (A36)
( ) ( ( ) ) (A37)
( ) ( ) w ( )
( ) (A38)
B) Thermal properties of steam and water
The temperature of the steam leaving turbine i that has the same entropy as the inlet
steam is calculated equation (B1)
S ( ) (
( ) ((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B1)
Where ( ) is temperature of steam at the outlet pressure having the same entropy as
the inlet steam of turbine i and ( ) is pressure of steam leaving turbine i
( ) is calculated by equation (B2)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B2)
The steam outlet temperature of turbine i is determined by equation (B3)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
35
( ) ((sum
ut ( )
) (sum ( ( ))
ut ( )
)) (B3)
where ( ) is temperature of steam leaving turbine i
The entropy of the saturated steam at the exhaust pressure of turbine i and the entropy
of the saturated liquid are represented by equations (B4) and (B5) respectively
S ( ) (
( )
((sum
( )
) (sum ( ( ))
( )
)) (( ( ) sum
( )
) (sum ( ( ))
( )
))) (B4)
where ( ) is saturated temperature of steam at the outlet pressure from turbine i
S ( ) (
( )
(sum ut( )
( )
)
sum ut( )
( )
) (B5)
The enthalpy of the saturated steam at the exhaust pressure of turbine i and that of the
saturated liquid are represented by equations (B6) and (B7)
( ) ((sum
( )
) (sum ( ( ))
( )
)) (B6)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
36
( ) (sum ut( )
( )
) (B7)
The saturated temperature of the steam leaving turbine i is calculated by equation (B8)
in Appendix B)
( ) ( ( )
( ) ( ( ) ( ) ( )) )
(B8)
( ) ( )
( )
( )
( )
(B9)
( ) ( )
( )
( )
( )
(B10)
( ) ( )
( )
7 ( )
( )
(B11)
Where
are coefficients whose value is presented in [12]
C) Condenser modelling
Assumptions
bull Steam is condensed in the shell side of condensers and cooling water is in the
tube side of condensers
bull No pressure drop is in the shell side of condensers
bull Condensate is at the saturated state
When heat exchange involves desuperheating and condensation condensers can be
divided into two zones When desuperheating and condensation is on the shell side of
a horizontal condenser the model of condensers can be expressed by the following
equations [13]
The total heat transfer area of condenser i is the sum of the area for each zone
( ) ( ) ( ) (C1)
Chapter 4 Operational Optimisation of RCWS for Improving the Performance of Condensing Turbines
37
The area of each zone can be calculated by equations (C2) and (C3) respectively
( ) ( )
( ) ( ) (C2)
( ) n( )
( ) n ( ) (C3)
( ) ( ) ( ) ( ) (C4)
( ) ( ) ( ) ( ) (C5)
Uds and Ucn are calculated by equation (A11)
The condensing film coefficient for condensation in shell side of condenser i is
expressed as equation (C6) [18]
( ) ( ) ( )
( ) ( )
μ ( ) ( )
( )
(C6)
( ) ( )
( ) (C7)
( ) n( )
( ) ( ) (C8)
The heat transfer coefficient of cooling water is calculated by equation (A17) The
heat transfer coefficient of superheated steam can be calculated by heat transfer
coefficient equation for shell side developed by Wang et al [15]
Chapter 5 Conclusions and Future Work
20
Chapter 5 Conclusions and Future Work
51 Conclusions
For the operational optimisation of industrial cooling water systems there are two
main areas of investigation in this project
bull Standalone optimisation of overall cooling water systems including
mechanical wet cooling towers cooler networks and piping networks
bull Simultaneous optimisation of cooling water systems and processes with
cooling requirement
To address the first area some literature [1] [2] [3] proposed models of cooling
water systems that integrate cooling towers cooler networks and piping networks
However they have some limitations all of them are limited to one cooling tower and
cooler networks in parallel configurations detailed heat transfer in coolers is not
considered in the literature [1] the pressure drop in coolers is ignored for the
hydraulic modelling in the literature [2] and [3] To overcome those limitations
therefore a nonlinear model of recirculating cooling water systems is developed for
operational optimisation of cooling water systems in this work In this model
mechanical draft wet cooling tower modelling cooler network modelling and piping
network modelling are all included Multiple cooling towers and cooler networks in
both a parallel configuration and a series and parallel configuration are taken into
consideration In cooling tower modelling a regression model of mechanical draft wet
cooling towers is developed to predict the water evaporation rate and the cooling
water outlet temperature The regression model is validated by some published data
In cooler network modelling detailed heat transfer equations for individual coolers
are included to predict the thermal performance of coolers and mass and energy
balance are carried out to represent the interactions between cooling towers and
coolers Hydraulic calculation of networks takes pressure drop in pipes pipe fittings
and coolers into account The model is optimised by the solver CONOPT in GAMS to
determine the optimal cooling water flowrate entering individual coolers and towers
and air flowrate entering individual towers In a case study through optimisation the
total operating cost of a cooling water system with specified process cooling demand
is reduced by about 6 compared with that in the base case
Chapter 5 Conclusions and Future Work
21
To exploit the interactions between processes and cooling water systems in the second
area condensing turbines are taken as examples of cooling water using processes
whose performance is affected by the conditions of cooling water In the literature
[13] a modular-based optimisation method was proposed to integrate condensing
turbines with cooling towers for maximising the net power output In this thesis an
equation-based model is developed to combine cooling water systems and condensing
turbines The model is optimised by the solver CONOPT in the software GAMS to
determine the optimal cooling water flowrate entering individual coolers condensers
and towers and air flowrate entering individual towers In a case study it is shown
that the simultaneous optimisation of a cooling water system and a condensing turbine
increases the profit by 337 kpoundyr compared with focusing only on maximising the
power generation of condensing turbines
In summary it is shown from this research that there is a clear need to optimise the
operation of industrial cooling water systems both on a standalone basis and on a
combined basis with processes in cooling demands The developed methodologies
have been validated and proven to be effective in dealing with the two challenges as
shown in corresponding case studies
52 Future work
As shown in the literature the research on operational management of overall cooling
water systems has been very limited Even though some progress has been made in
this project there is still much room of improvement to be made including a few
areas listed below
Model improvement of cooling water systems in the current method the
operating cost does not include cost of chemicals used to treat cooling water
and cost of blowdown treatment The cooling water treatment and blowdown
treatment could be incorporated in the model
Improvement of the solution algorithms as the model is nonconvex the
obtained optimisation results are possibly global optimum which could be
investigated in the future
Chapter 5 Conclusions and Future Work
22
Extended integration between cooling water systems and processes with
cooling demands in this research only condensing turbines are integrated
with cooling water systems However there are many processes that require
cooling water such as compressor inter-cooling condensation of light
components for distillation and pre-cooling for compression refrigeration The
improvement of the performance of those processes increases the operating
cost of cooling water systems Therefore the method proposed to improve the
overall performance of cooling water systems and condensing turbines can be
extended to the other processes
Online optimisation as the thermal performance of cooling water system
changes frequently with the continuous change of ambient air conditions the
online optimisation combined with control systems allows the operation to be
adjusted with the variation of ambient air conditions to reduce the operating
cost
Cooling water system design and retrofit various options could be available to
improve the configuration of cooling water systems such as adding a
connection between coolers to allow cooling water to be reused if possible
and better load distribution of cooling water pumping systems etc Such
options typically require systematic consideration at the design and retrofit
stage the methodology of which could be developed in the future
23
References
[1] Castro MM Song TW and Pinto JM 2000 Minimisation of Operational Cost in
Cooling Water Systems Trans IChemE 78 (part A) pp 192-201
[2] Cortinovis GF Paiva JL Song TW and Pinto JM 2009 A Systemic Approach for
Optimal Cooling Tower Operation Energy Conversion and Management 50 pp 2200-
2209
[3] Cortinovis GF Ribeiro MT Paiva JL Song TW and Pinto JM 2009 Integrated
Analysis of Cooling Water Systems Modelling and Experimental Validation Applied
Thermal Engineering 29 pp 3124-3131
[4] httpjnyuhanggovcnnewsshowaspxartid=704ampclassid=5
[Accessed at 20 Dec 2016]
[5] Kelly NW and Swenson LK 1956 Comparative Performance of Cooling Tower
Packing Arrangements Chem Eng Prog 52(7) pp 263-268
[6] Cooling Tower chapter 7 Bureau of Energy Efficiency pp 135-151
[7] Improving the Energy Efficiency of Cooling Systems
httpwwwdhigroupcomuploadpublicationsscribd195443742-Improving-
the-energy-eff-iciency-of-cooling-systems-DHI-Solutionpdf
[Accessed at 15 Dec 2016]
[8] Kim JK and Smith R 2001 Cooling Water System Design Chemical Engineering
Science 56(12) pp 3641-3658
[9] Ponce-Ortega JM Serna-Gonzaacutelez M and Jimeacutenez-Gutieacuterrez A 2010 Optimization
Model for Re-circulating Cooling Water Systems Computers and Chemical Engineering 34
pp 117ndash195
[10] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega JM and El-Halwagi MM 2013
Synthesis of Cooling Water Systems with Multiple Cooling Towers Applied Thermal
Engineering 50 pp 957-974
[11] Sun J Feng X and Wang YF 2014 Optimisation of Cooling Water Systems
Considering Temperature-Rise and Pressure-Drop Chemical Engineering Transaction 39
pp 49-54
[12] Rubio-Castro E Serna-Gonzaacutelez M Ponce-Ortega J M and Morales-Cabrera M A
2011 Optimisation of Mechanical Draft Counter Flow Wet-Cooling Towers Using a
Rigorous Model Applied Thermal Engineering 31 pp 3615-3628
[13] Barigozzi G Perdichizzi A and Ravelli S 2014 Performance Prediction and
Optimization of a Waste-To-Energy Cogeneration Plant with Combined Wet and Dry
Cooling System Applied Energy 115 pp 65ndash74