analysis and optimisation of total site utility systems.pdf
TRANSCRIPT
ANALYSIS AND OPTIMISATION OF TOTAL SITE UTILITY SYSTEMS
A thesis submitted to the
University of Manchester Institute of Science and Technology
for the degree of
Doctor of Philosophy
by
Zhigang Shang
under the supervision of
Professor Antonis Kokossis
Department of Process Integration
University of Manchester Institute of Science and Technology
Manchester M60 1 QD
August 2000
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.
Zhigang Shang
Acknowledgements
I would like to express my sincere gratitude to Professor Antonis Kokossis for his
guidance and encouragement throughout the course of this study. His patience and
understanding have been tremendous. I would like to thank him for spending long hours
on reviewing this thesis.
I would also like to thank Professor Robin Smith, as the head of the department, gave
me the opportunity to do my doctoral degree in the department.
Many thanks to all the staff and students in the department for their support and for
creating a pleasant atmosphere. I consider myself very lucky indeed for having been
able to work in such a friendly and dynamic environment. Big thanks to you for making
my stay in Manchester so wonderful.
I wish to thank member companies of the Process Integration Research Consortium for
funding the research.
I would like to thank my wonderful parents for their love and support throughout my
life. In spite of being thousands of miles away, they have been so close to me with their
prayers and support.
No words can express my gratitude to my beloved wife, Jun. I thank her for her love
and encouragement during this very demanding time.
ii
Abstract
This thesis provides systematic methodologies for the analysis and optimisation of total
site utility systems under operational variations. The methodologies address three major
problems: (i) the optimal design of total site utility systems, (ii) the debottlenecking and
planning optimisation of an existing site, (iii) the optimisation of total site maintenance
scheduling.
A set of new models is developed for boilers, condensing turbines and gas turbines.
These models are used for the analysis and optimisation of site utility systems in view
of operational variations. They enable for an accurate prediction of unit efficiencies and
embody the efficiency trends of realistic units in terms of their variation with capacity,
load and operating conditions.
In the design of site utility systems, it is often the case that strong interactions exist
between the site utility systems and site processes. A novel approach is proposed for the
synthesis and design of site utility systems integrated with site processes. The design
decisions are mainly concerned with the selection of the optimal steam levels, and the
determination of the layout of the utility system. The approach combines the benefits of
pinch analysis, thermodynamic analysis and mathematical optimisation techniques. It
easily identifies the interactions between the utility system and site processes and
greatly reduces the size and complexity of the optimisation problem.
A systematic optimisation methodology is proposed for the debottlenecking and
planning of site utility systems. Given forecasts for the prices and demands of utilities,
the approach determines the best investment scheme for an existing system and the
optimal operational strategies to adopt.
iii
Finally, a multi-period MILP model is presented for the maintenance scheduling
optimisation of total sites. The optimisation method simultaneously considers the
maintenance and operation of the site processes and the utility system. Practical
maintenance constraints of industrial plants are also considered.
iv
Table of Contents
CHAYfER 1. INTRODUCTION .................................................................................. 1
1.1 PROBLEM DESCRIPTION ........................................................................................ 1
1.2 SCOPE OF TIfE TIlESIS ............................................................................................ 2
1.2.1 Design of Total Site Utility Systems ................................................................. 2
1.2.2 Debottlenecking and Planning Optimisation of an Existing Site ..................... 3
1.2.3 Total Site Maintenance Scheduling .................................................................. 3
1.3 OBJECTIVE OF TIfE TIlESIS .................................................................................... 3
1.4 OUTLINE OF TIfE THESIS ........................................................................................ 4
CHAPTER 2. REVIEW OF PREVIOUS WORK ....................................................... 5
2.1 INTRODUCTION ..................................................................................................... 5
2.2 PREVIOUS ApPROACHES TO THE SYNTHESIS AND DESIGN OF SITE UTILITY
SySTEMS ......................................................................................................................... 5
2.3 PREVIOUS APPROACHES TO TIfE DEBOTTLENECKING, PLANNING AND SCHEDULING
OF SITE UTILITY SySTEMS ............................................................................................... 8
2.4 TOTAL SITE ANALySIS .......................................................................................... 9
CHAPTER 3. HARDWARE MODELS ...................................................................... 13
3.1 INTRODUCTION ................................................................................................... 13
3.2 TIlE BOILER HARDWARE MODEL ........................................................................ 14
3.2.1 Model Development ........................................................................................ 14
3.2.2 Summary ......................................................................................................... 19
3.3 TIlE CONDENSING TuRBINE HARDWARE MODEL. ............................................... 20
3.3.1 The Turbine Hardware Model ........................................................................ 20
3.3.2 The Condensing Turbine Hardware Model .................................................... 21
3.3.3 Summary ......................................................................................................... 23
3.4 THE GAS TuRBINE HARDWARE MODEL. ............................................................. 23
v
3.4.1 Model Development ........................................................................................ 24
3.4.2 Summary ......................................................................................................... 29
3.5 CONCLUSIONS ..................................................................................................... 29
CHAPTER 4. STEAM LEVEL OPTIMISA TION .................................................... 31
4.1 INTRODUCTION ................................................................................................... 31
4.2 THE STRATEGY ................................................................................................... 33
4.3 THE TRANSHIPMENT NETWORK OF A TOTAL SITE ............................................... 33
4.4 OPTIMISATION MODEL ........................................................................................ 38
4.4.1 Model Formulation ......................................................................................... 41
4.4.2 Remarks on the Optimisation Model ............................................................. .47
4.5 CASE STUDIES ..................................................................................................... 48
4.5.1 Case 1: Steam Level Optimisation under a Single Scenario .......................... 48
4.5.2 Case 2: Steam Level Optimisation under Four Scenarios .............................. 53
4.5.3 Summary ......................................................................................................... 56
4.6 CONCLUSIONS ..................................................................................................... 58
CHAPTER 5. LAYOUT SCREENING AND OPTIMISATION ............................. 59
5.1 INTRODUCTION .................................................................................................... 59
5.2 THE STRATEGY ................................................................................................... 61
5.3 TOTAL SITE ANALySIS ........................................................................................ 63
5.4 THERMODYNAMIC ANALySIS .............................................................................. 64
5.4.1 Thermodynamic Efficiencies and Utility Structures ..................... .................. 65
5.4.2 The Thermodynamic Efficiency Curve ............................................................ 72
5.5 THE GENERATION OF THE SUPERSTRUCTURE ...................................................... 73
5.5.1 Superset of Back-pressure Steam Turbines .................................................... 74
5.5.2 Superset of Gas Turbines ................................................................................ 76
5.5.3 Superset of Boilers ............................................................... ........................... 78
5.5.4 Superset of VHP Condensing Steam Turbines ................................................ 79
5.5.5 Superset of Surplus Steam Condensing Turbines ........................................... 80
5.5.6 Reheat Cycles .................................................................................................. 81
5.6 OPTIMISATION MODEL ........................................................................................ 81
vi
5.6.1 Model Formulation ......................................................................................... B4
5.6.2 Remarks and Discussion ................................................................................. 90
5.7 SYNTIIESIS OF COMPLEX STEAM TuRBINES ........................................................ 90
5.8 CASE STUDIES ..................................................................................................... 91
5.B.1 Case Study 1 ................................................................................................... 92
5.B.2 Case Study 2 ................................................................................................... 99
5.B.3 Discussion .................................................................................................. ... 101
5.9 CONCLUSIONS ................................................................................................... 102
CHAPTER 6. DEBOTTLENECKING AND PLANNING OPTIMISATION OF
AN EXISTING SITE .................................................................................................. 103
6.1 INTRODUCTION ................................................................................................. 103
6.2 OPTIMISATION SlRATEGY ................................................................................. 105
6.3 STAGE I: OPTIMISATION OF THE EXISTING SYSTEM .......................................... 106
6.4 STAGE II: TOTAL SITE ANALYSIS ...................................................................... 106
6.5 STAGE III: THERMODYNAMIC ANALYSIS .......................................................... 108
6.5.1 The Thermodynamic Efficiency Curve/or Debottlenecking ......................... 10B
6.5.2 Identification o/the Promising Debottlenecking Options ............................ 109
6.5.3 The Debottlenecking Superstructure ............................................................ 112
6.6 STAGE IV: OPTIMISATION ................................................................................. 113
6.6.1 Mathematical Formulation ........................................................................... 116
6.6.2 Solution Methods .......................................................................................... 121
6.7 CASE STUDIES ................................................................................................... 122
6.7.1 Case Study 1 ................................................................................................. 122
6.7.2 An Industrial Case Study .............................................................................. 131
6.8 CONCLUSIONS ................................................................................................... 139
CHAPTER 7. TOTAL SITE MAINTENANCE SCHEDULING ..•..•............•........ 140
7.1 INTRODUCTION ................................................................................................. 140
7.2 MATHEMATICAL MODEL .................................................................................. 141
7.2.1 Objective Function ........................................................................................ 144
7.2.2 Peiformance Models ..................................................................................... 144
vii
7.2.3 Steam Mass Balances ............................................. ...................................... 147
7.2.4 Power Balance ................ .............................................................................. 147
7.2.5 Maintenance Constraints ............................ .................. "."."." .. "."."""""." 148
7.3 MAINTENANCE CASE STUDY ............................................................................ 151
7.4 CONCLUSIONS ................................................................................................... 154
CHAPTER 8. CONCLUSIONS AND FUTURE WORK ........................................ lS8
8.1 INTRODUCTION ................................................................ """ .. """" .. "."."."." .158
8.2 CONCLUSIONS ................................................................................................... 158
8.2.1 Design o/Total Site Utility Systems ............................................................. 158
8.2.2 Debottlenecking and Planning Optimisation o/the Existing Site ................ 160
8.2.3 Total Site Maintenance Scheduling .............................................................. 161
8.3 FuTURE WORK .................................................................................................. 161
REFE REN CES ............................................................................................................ 163
APPENDIX A. CORRELATIONS OF THE THM ..••..•••....•.......•........................... 168
APPENDIX B. REGRESSION OF CONDENSING TURBINE EFFICIENCY
DATA ............................................................................................................................ 170
APPENDIX C. REGRESSION OF GAS TURBINE EFFICIENCY DATA ......... 173
viii
List of Figures
Figure 1-1: Schematic of a total site under operational variations 2
Figure 2-1: Total Site Profiles (TSP) 10
Figure 2-2: The construction of the Site Composite Curves 10
Figure 2-3: The Site Composite Curves for Minimum Fuel Requirement (MFR) and
Minimum Utilities Cost (MUC) 11
Figure 2-4: The construction of the Site Utility Grand Composite Curve 12
Figure 3-1: Boiler specification on T-H diagram 15
Figure 3-2: The T-H diagram of steam 15
Figure 3-3: Typical heat loss plot for boilers (Pattison and Sharma. 1980) 16
Figure 3-4: The BHM accounts for the effect of boiler size, load and operating
conditions on efficiency
Figure 3-5: The THM of steam turbines
Figure 3-6: Typical data on the efficiency of condensing turbines
Figure 3-7: Simple gas turbine cycle
19
21
22
24
Figure 3-8: Typical data on the electrical efficiency of gas turbines as a function of size
(Marechal and Kalitventzeff, 1998) 26
Figure 3-9: The GTHM accounts for the effect of gas turbine size and load on
efficiency 28
Figure 4-1: Different operation scenarios can be represented by sets of total site profiles
32
Figure 4-2: Schematic showing the steam level optimisation strategy 33
Figure 4-3: Transhipment network representation of the total site heat flow 35
Figure 4-4: Heat flow pattern of the temperature intervals for steam level i 36
Figure 4-5: Heat flow pattern in each temperature interval of the heat source cascade 41
Figure 4-6: Heat flow pattern in each temperature interval of the steam level cascade 42
ix
Figure 4·7: Heat flow pattern in each temperature interval of the heat sink cascade 42
Figure 4·8: Schematic representation of the optimisation procedure 47
Figure 4·9: The total site profiles for the site of Case 1 49
Figure 4·10: Potential steam levels of Case 1 50
Figure 4·11: Transhipment network representation of case 1 51
Figure 4·12: Optimal structure for MUC case of Case 1 52
Figure 4·13: Optimal structure for MFR case of Case 1 52
Figure 4·14: Four operation scenarios for Case 2 53
Figure 4·15: Transhipment network representation for Case 2 56
Figure 4·16: The resulting SUGCCs corresponding to the optimal steam levels of Case
2 57
Figure 5·1: Schematic showing the configuration design optimisation strategy 62
Figure 5·2: Identification of steam turbines of a site by using the SCC 63
Figure 5·3: Total site profiles of a plant 65
Figure 5·4: Integration of the BBPT cycle 66
Figure 5·5: Integration of the GTWB cycle 67
Figure 5·6: Integration of the BCT cycle 69
Figure 5·7: Integration of the GTWBCT cycle 70
Figure 5·8: Integration of the SCT 71
Figure 5·9: The thermodynamic efficiency curve 72
Figure 5·10: Complex turbines are considered as a cascade of simple turbines 74
Figure 5·11: Decomposition of complex steam turbines 75
Figure 5·12: The candidate BP steam turbines for the case of two scenarios 75
Figure 5·13: The regenerative gas turbine 76
Figure 5·14: The effect of part load operation prevails over the increase of efficiency
with gas turbine size 77
Figure 5·15: Candidate gas turbines for the case of two scenarios 78
Figure 5·16: Superset of boilers 79
Figure 5·17: Candidate VHP condensing turbines for the case of two scenarios 80
Figure 5·18: Candidate surplus steam condensing turbines for the case of two scenarios
81
x
Figure 5·19: The SUGCC of a site 92
Figure 5·20: TECs for Case 1 94
Figure 5·21: Superstructure of Case 1 96
Figure 5·22: Optimal structure of Case 1 97
Figure 5·23: Superstructure of Case 2 99
Figure 5·24: Optimal structure of Case 2 100
Figure 6·1: Outline of debottlenecking and planning strategy 105
Figure 6·2: Identification of debottlenecking turbines of a site by using the SCC 107
Figure 6·3: Decomposing a complex turbine into different sizes of cylinders in each
expansion zone 107
Figure 6·4: Typical TEC for debottlenecking 108
Figure 6·5: The boiler and back-pressure turbine cycle for debottlenecking 109
Figure 6·6: The gas turbine and waste heat boiler cycle for debottlenecking 110
Figure 6·7: The gas turbine and waste heat boiler and condensing turbine cycle for
debottlenecking 110
Figure 6·8: The boiler and condensing turbine cycle for debottlenecking 111
Figure 6·9: Surplus condensing turbines for debottlenecking 111
Figure 6·10: Debottlenecking superstructure 112
Figure 6·11: Decomposition strategy 121
Figure 6·12: The existing utility system of Case 1 122
Figure 6·13: TECs for different operation periods for Case 1 126
Figure 6·14: Debottlenecking superstructure of Case 1 128
Figure 6·15: Optimal structure of Case 1 129
Figure 6·16: The existing utility system of the industrial case 131
Figure 6·17: Thermodynamic Efficiency Curves for the industrial case 135
Figure 6·18: Debottlenecking superstructure of the industrial case 136
Figure 6·19: Optimal structure of the industrial case 137
Figure 7·1: Total site optimisation 141
Figure 7·2: The configuration of a total site 152
Figure 7·3: Optimal maintenance and operation schedule of all units 155
xi
Figure 7·4: Optimal profile of steam consumed by processes 156
Figure 7·5: Optimal power consumption profile of processes 156
Figure 7·6: Optimal boiler operation 156
Figure 7·7: Optimal turbine operation 157
Figure 7·8: Optimal power export profile 157
Figure Bl: Regression parameter AC as a function of inlet saturation temperature 171
Figure B2: Regression parameter BC as a function of inlet saturation temperature 172
xii
List of Tables
Table 4·1: Cost data of utilities 48
Table 4·2: Candidate saturation temperatures for each steam level of Case 1 49
Table 4·3: Heat provided by the process heat sources in each temperature interval of
C~1 ~
Table 4·4: Heat required by the process heat sinks in each temperature interval of Case
1 50
Table 4·5: Candidate temperatures for each steam level of Case 2
Table 4·6: Heat enthalpy changes of processes of Case 2 (Scenario A)
Table 4·7: Heat enthalpy changes of processes of Case 2 (Scenario B)
Table 4·8: Heat enthalpy changes of processes of Case 2 (Scenario C)
Table 4·9: Heat enthalpy changes of processes of Case 2 (Scenario D)
53
54
54
55
55
Table 4·10: Heat required of process sinks above temperature interval (1,1) for Case 2
55
Table 4·11: Surplus heat of process sources below temperature interval (I,J) for Case 2
55
Table 4·12: Optimal steam levels for single and mUltiple scenarios
Table 5·1: PIH Characteristics of gas turbine cycles
Table 5·2: Capital cost data (Bruno et al., 1998)
Table 5·3: Summary of operating conditions
Table 5·4: Utility data
Table 5·5: Power demands of Case 1
Table 5·6: Steam amount across each expansion zone of Case 1 (t/h)
Table 5·7: Power outputs of possible SCT and BBPT cycles of Case 1
Table 5·8: PIH characteristics of Case 1
Table 5·9: Power outputs of the OTWB cycles of Case 1
Table 5·10: Candidate sizes of BP turbines of Case 1 (t/h)
Table 5·11: Candidate sizes of condensing turbines of Case 1 (t/h)
xiii
57
76
89
91
91
92
93
93
94
94
95
95
Table 5-12: Candidate sizes of gas turbines of Case 1 (MW) 95
Table 5-13: Optimal loads of the units of Case 1 98
Table 5-14: Power demands of Case 2 99
Table 5-15: Optimal loads of the units of Case 2 101
Table 6-1: Summary of Operating Conditions of Case 1 123
Table 6-2: Utility demands of Case 1 123
Table 6-3: Utility data of Case 1 123
Table 6-4: Maximum power generation of the existing system of Case 1 (MW) 124
Table 6-5: Steam amount across each expansion of Case l(tIh) 124
Table 6-6: Capacities of simple turbines in every expansion zone of Case l(tIh) 125
Table 6-7: Capacities of potential steam turbines of Case l(tIh) 125
Table 6-8: The capacities of potential GTWB cycles (MW) of Case 1 127
Table 6-9: Capacities of candidate steam turbines of Case 1 (tIh) 127
Table 6-10: Capacities of candidate GTWB cycles of Case l(MW) 127
Table 6- 11: Summary of the problem size 128
Table 6-12: Optimal capacities of the new units of Case 1 130
Table 6-13: Optimal operation of all units of Case 1 130
Table 6-14: Summary of operating conditions of the industrial case 132
Table 6-15: Utility demands of the industrial case 132
Table 6-16: Power demands of the allocated turbines of the industrial case 133
Table 6-17: Utility cost data in different periods for the industrial case 133
Table 6-18: Maximum power generation of the existing system of the industrial case
(MW) 133
Table 6-19: Total steam flowrates across expansion zones for the industrial case (tIh)
134
Table 6-20: Capacities of existing turbines in every expansion zone for the industrial
case (tlh) 134
Table 6-21: Capacities of potential steam turbines for each period for the industrial case
(tlh) 135
Table 6-22: Capacities of GTWB cycles for different periods for the industrial case 136
Table 6-23: Optimal operation of all turbines of the industrial case (MW) 138
xiv
Table 6-24: Optimal operation of all boilers of the industrial case (tlh) 138
Table 6-25: Optimal operation of all gas turbines of the industrial case (MW) 138
Table 7-1: Summary of operating conditions of the utility system 152
Table 7-2: Utility demands of process units in nonnal operating conditions 153
Table 7-3: Utility cost data 153
Table 7-4: Maintenance times of all units (days) 153
xv
Chapter 1 Introduction
Chapter 1
Introduction
1.1 Problem Description
A typical chemical plant usually consists of several chemical production processes,
which consume heat and power to make products in order to obtain maximum profit
(Figure 1-1). The heat and power are supplied by a site utility system. The site utility
system consumes fuel in boilers and gas turbines, supplies the necessary steam to
chemical processes via several steam mains and produces power via steam turbines and
gas turbines. The processes may also generate steam at various levels. The steam
generated by the processes can be supplied to the steam mains, and eventually
consumed in other processes.
It is often the case that considerable changes exist in the chemical processes as a result
of fluctuating demand and prices of products, feed compositions, ambient temperatures
and so on. The changes in the operation of chemical processes result in fluctuating heat
and power demands between the site utility system and chemical processes.
Most of the research conducted on the analysis and optimisation of total site utility
systems has given little attention to the operational variations and strong interactions
between the site utility system and site processes. Above all, no systematic methodology
for the analysis and optimisation of total site utility systems under operational variations
has been suggested.
1
Chapter i introduction
p;:;o~
c:> I Process 11 Demand and prices I Process 21 TIme c:> ~ I Process 31 Feed specifications
c:> I Process n 1
~ TIme
TIme
UHeat U Power Utility demands
b:: TIme
Figure 1-1: Schematic of a total site under operational variations
1.2 Scope of the Thesis
In this thesis, three types of issues are addressed for total site utility systems:
1.2.1 Design of Total Site Utility Systems
In design situations the objective is to design the site utility system that will meet
fluctuating utility demands of site processes. The main decisions involved are the
selection of the steam levels with respect to their temperatures and pressures and the
determination of the configuration of the operating units with respect to type, number,
capacity and connections among the units. The best practical site utility system design
will feature a minimum total cost.
2
Chapter 1 Introduction
1.2.2 Debottlenecking and Planning Optimisation of an Existing Site
In debottlenecking and planning situations, the objective is to make sure the site utility
system satisfies the changing utility demands of site processes in a long-term horizon in
order to minimise the total cost. It involves the following two tasks: the selection of the
new units to be added to the current system, and the determination of the optimal
operational strategies of all units with respect to operating conditions and on/off status.
1.2.3 Total Site Maintenance Scheduling
As both site process units and site utility units have to go through shutdown and start-up
changes, steam and power demands gradually increase or decrease. Strong interactions
exist between the site processes and the site utility system. In maintenance scheduling
situations the objective is to determine the optimal operation and maintenance schedules
of the total site. The total site maintenance scheduling approach simultaneously
considers the maintenance and operation of the site utility system and site processes so
that the total operating cost is minimised.
1.3 Objective of the Thesis
The objective of the thesis is to propose systematic analysis and optimisation
methodologies to tackle total site utility system problems under operational variations.
Grassroots design, debottlenecking and planning of site utility systems, as well as
maintenance scheduling of a total site are addressed.
The procedures use total site analysis, thermodynamic analysis and mathematical
optimisation techniques. The work aims at using previous total site analysis tools and
developing new thermodynamic tools which can help engineers to scope and screen
promising design options. Mathematical optimisation techniques are then proposed to
find the optimum solution.
3
Chapter 1 Introduction
1.4 Outline of the Thesis
The next chapter presents a review of previous techniques for the analysis and
optimisation of total site utility systems. The hardware models for steam turbines, gas
turbines and boilers are introduced in chapter 3. A systematic methodology for the
design of total site utility systems is proposed in chapter 4 and chapter 5. Chapter 4
introduces the method for steam level optimisation and chapter 5 introduces the method
for configuration optimisation of site utility systems. A systematic methodology for
debottlenecking and planning optimisation of an existing site is presented in chapter 6.
Chapter 7 deals with maintenance scheduling problem for a total site. The last chapter
presents major conclusions of the work, along with the possible future research on the
topic.
4
Chapter 2 Review of Previous Work
Chapter 2
Review of Previous Work
2.1 Introduction
Previous approaches to the synthesis and design of site utility systems will be
introduced first. This will be followed by a discussion on the available techniques for
the debottlenecking, and planning and scheduling of site utility systems. Finally, due to
their relevance to the concepts that will be developed in the following chapters, a
description of total site analysis approaches is provided.
2.2 Previous Approaches to the Synthesis and Design of Site Utility
Systems
A well-designed site utility system should be able to match the plant heat and power
variations and keep its total costs to a minimum. Design decisions are mainly concerned
with the selection of the optimum steam levels and the determination of the
configuration of the site utility system.
Several methods have been presented previously to address the problem of synthesis
and design of utility systems. These methods generally follow three basic approaches:
those based on thermodynamic targets, those based on pinch analysis targets, and those
based on optimisation techniques. Examples of the first group are papers presented by
Nishio et ai. (1980), EI-Masri and Magnusson (1984) and Chou and Shih (1987). The
traditional way of designing utility systems using thermodynamic methods is to
maximise the thermal efficiency of the system. Thermodynamic analysis reveals the
5
Chapter 2 Review of Previous Work
thermal inefficiencies of the various subsystems. Once the inefficiencies have been
identified, heuristic rules are applied to obtain the design structure. Although there is no
question that thermodynamic targets and heuristics provide a good understanding of the
processes, they do not take into account the complex interactions that take place
between the subsystems, nor do they guarantee optimality. Furthermore, the capital cost
hasn't been taken into account.
Townsend and Linhoff (1983) explained the concept of "appropriate" heat engine and
heat pump placement in process networks. They also introduced procedures for
preliminary design, involving heat engine, and heat pump equipment selection and
performance assessment. Dhole and Linnhoff (1992) introduced the concept of "Total
Site Profiles" for the analysis of an entire total site. They used thermodynamic insights
to graphically represent a total site on a Carnot factor-enthalpy diagram. In order to
target the Minimum Cost of Energy Requirements (MCER), Marechal and Kalitventzeff
(1996) proposed a concept of integrated composite curves for the integration of utility
systems.
In order to address the problem of selecting the pressures of the steam mains, Morton
and Linnhoff (1984) proposed the use of Grand Composite Curves. By using total site
analysis method, Raissi (1994) studied the optimum placement of steam levels and
identified the two extreme cases of the Minimum Fuel Requirement (MFR) and the
Minimum Utilities Cost (MUC) for single operation scenarios. The target model of
steam turbines in this work cannot account for the efficiency variation with load,
operating conditions and capacity, and the exhaustive enumeration algorithm was used
to find the optimal solution. Mavromatis and Kokossis (1998a) proposed a new Turbine
Hardware Model (THM) for steam turbines and an exhaustive enumeration method to
search for the optimal levels. The cases they studied were only based on the shaft-work
target. However, it is very difficult to get the optimal levels in large problems by using
exhaustive enumeration methods because of the huge computation requirement. In
addition, neither Raissi nor Mavromatis has taken into account the boiler target model to
calculate the fuel cost in order to determine the minimum utility cost. Finally,
systematic methods for generating potential steam levels have not been accounted for.
6
Chapter 2 Review of Previous Work
It is also possible to use mathematical optimisation techniques to synthesise and design
site utility systems. Most of the publications dealing with the synthesis and design of
utility systems have focused on fixed utility demands or specified header pressure
levels. Nishio (1977) appears to be the first to consider the problem of selecting optimal
header pressure levels and presented a direct search approach coupled with
simultaneous solution of the balance equations. Papoulias and Grossmann (1983a)
proposed an MILP method for the structural and parametrical optimisation of utility
systems under fixed steam and power demands. The work was subsequently extended to
account for the synthesis and design of chemical processes (Papoulias and Grossmann
1983c). Iyer and Grossmann (1998) have presented a multi-period MILP approach for
the synthesis of utility systems operating under multiple periods. However, steam level
optimisation is not considered in this work. Petroulas and Reklaitis (1984) used a
dynamic programming method to optimise the steam conditions as continuous variables
and a linear programming method for the optimum allocation of drivers with the
common objective of minimising the real work loss. A non-linear programming strategy
was applied by Colmenares and Seider (1989) for the design of utility systems
integrated with the chemical process. The interaction of steam level selection and steam
demand for each level is not accounted for in this work, and the steam raised by
chemical processes is not considered. A simulated annealing algorithm has been used by
Maia and Qassim (1997) for the synthesis of utility systems with variable utility
demands. Most recently, Mavromatis and Kokossis (1998b) have presented an MILP
approach for the optimal design of steam turbine networks. This approach is only
limited to the back-pressure steam turbine network design. An MINLP model for the
synthesis and design of utility plants has been presented by Bruno et al. (1998).
Wilkendorf et al. (1998) also proposed an MINLP model for the synthesis of complete
utility systems. In practice, however, there are several drawbacks in the approach. If all
the candidate options are included in the superstructure, the number of candidate
structures should be enormous and the size of the problem would become too large to be
handled even for moderate problems. The consideration of multiple operation scenarios
results in a further increase of the design options to an extent. Secondly, the formulation
of utility systems is inherently non-linear with respect to the efficiencies for the units,
which gives rise to complex models. Therefore it is essential to find a systematic
7
Chapter 2 Review of Previous Work
methodology which can build a superstructure including all the promising alternatives
without being too large, and to develop new modelling methods for the units.
Above all, we need a systematic methodology for the synthesis and design of site utility
systems, capable of considering the realistic efficiency trends of units, operational
variations and the interaction between the site utility system and site processes. One of
the objectives of this thesis is to present a systematic optimisation approach for the
synthesis and design of total site utility systems under operational variations.
2.3 Previous approaches to the debottlenecking, planning and
scheduling of site utility systems
A number of approaches have been reported for the debottlenecking and planning of site
utility systems. Iyer and Grossmann (1998) recently addressed the synthesis and
operational planning problem for utility systems that they formulated as an MILP
problem. A recent survey can be found in Iyer and Grossmann (1997) in which the
operational planning problem for utility systems is formulated as an MILP program.
The optimisation of steam production network under uncertainty has been reported by
Papalexandri and Pistikopoulos (1996). Nath and Holliday (1985) have proposed an
MILP model which can be used for the long term planning of plant utility systems. A
multi-period utility system model has been presented by Hui and Natori (1996) in which
an MILP model has been used to find out the best combination of new equipment to be
added. Yokoyama and Ito (1996) have proposed an MILP model for an operational
planning problem for a cogeneration system under a complex utility rate structure. A
planning method can be found in Ito et al. (1990) in which the operational policy of
each piece of constituent equipment has been decided so as to minimise the operational
cost. Makwana (1997) proposed a debottlenecking method for utility systems by using
top level analysis. The trend of assuming constant efficiencies for the gas turbines,
steam turbines and boilers appears to be a limiting assumption in these developments.
Furthermore, no systematic methodology has been addressed to target and scope for the
debottlenecking options for the utility systems under operational variations. An
alternative approach is reported by Yokoyama et al. (1994) in which an NLP+MILP
8
Chapter 2 Review of Previous Work
model is used. The shortcoming is that it can only optimise the fixed structure and there
is only one steam header in the approach. The approach is often limited in the size of
problems that they can handle. Olsbu et ai. (1988) proposed an MINLP model for the
design and planning of power systems which accounts for variable production profiles
and the availability of the system over a given time horizon.
Various maintenance-scheduling methods have been proposed. Dopazo and Merrill
(1975) described an integer programming approach that minimises the unit maintenance
costs. An MILP model has been proposed by AI-Khamis et al. (1992) to determine unit
maintenance schedules with fuel constraints. Chattopadhyay et ai. (1995) also proposed
an MILP model for least-cost generating unit maintenance scheduling for
interconnected power systems. Most recently, Moro and Ramos (1999) have presented a
mixed integer approach to maintenance scheduling of generating units in large scale
power systems. A simulated annealing method has been presented by Satoh and Nara
(1990) for the maintenance scheduling problem. Chen and Toyoda (1990) have
proposed a method to levelize the incremental risks, which results in a minimum Loss
of Load Probability (LOLP) maintenance schedule. Recently, an application of a
generic evolved fuzzy (GEF) system for the maintenance scheduling of generating units
can be found in Huang (1998), in which the fuzzy system was formulated with respect
to multiple objectives and soft constraints. Above all, all these approaches do not
consider the interactions between the site utility system and site processes. It results in a
local optimum maintenance schedule for the site utility system instead of an optimum
maintenance schedule for the total site.
2.4 Total Site AnalysiS
Dhole and Linhoff (1993) introduced a graphical representation of all process heat
sources and heat sinks in the site, that need to be connected to the utility system, termed
the "Total Site Profiles" (TSP) shown in Figure 2-1. It is used in this paper to represent
the chemical processes and extract the information required for the analysis of site
utility systems. By integrating the utility system, especially the steam system with the
total site profiles, the optimal steam level operating conditions and loads can be
9
Chapter 2 Review of Previous Work
detennined to minimise the utility cost, or to minimise the fuel requirement. It should be
noted that in the total site profiles, the steam demand at each steam level is expressed as
heat load, namely, the amount of heat can be used for heating at the saturation
temperature. The Total Site Profiles provide site-wide targets for fuel and co-generation.
The targets can be used for screening possible design options of site utility systems.
HP site heat
H H
Figure 2-1: Total Site Profiles (TSP)
In order to understand the interactions between fuel demand, heat recovery and co
generation, Raissi (1994) proposed "Site Composite Curves" (SCC). These are
constructed by shifting the Total Site Profiles towards each other (Figure 2-2).
T
HP
H H cw H
Total Site Profiles Site CompOSite Curves
Figure 2-2: The construction of the Site Composite Curves
10
Chapter 2 Review of Previous Work
The Site Composite Curves provide targets for fuel and co-generation, in a similar way
to the original Total Site Profiles. More importantly, the Site Composite Curves can
visually represent the steam flow in the utility system in addition to heat flow between
processes and utilities.
Raissi (1994) discussed the trade-offs between the fuel requirement and the
cogeneration potential when the steam levels under selection for one operation scenario.
Two extreme cases of Minimum Fuel Requirement (MFR) as shown in Figure 2-3a and
Minimum Utilities Cost (MUC) as shown in Figure 2-3b were studied.
VHP
MP
CW
a. MFR
Increased fuel
Increased cooling utility
b.MUC
Cogeneration
Figure 2-3: The Site Composite Curves for Minimum Fuel Requirement (MFR) and Minimum
Utilities Cost (MUC)
The costs of fuel and power determine the optimal steam levels for the MUC case. The
work boiler efficiency and the steam turbine efficiency are assumed constant. For the
utility system operating under operational variations, the steam load raised by VHP
boilers and steam amount passing steam turbines should not be constant. As the steam
raised by boilers varies for different steam level selection, as well as for different
operation scenarios, it requires a model for the boiler that is able to account for the
variation of steam boiler efficiency with the load and the size, as well as the operating
conditions. The shaftwork-targeting model of steam turbine should account for
11
Chapter 2 Review of Previous Work
efficiency variation with load, capacity and operating conditions as well . If the models
that fail to address these effects are used to select the steam levels, the selection of
steam levels will not be the optimum.
T T VHP
HP
MP
IP
H H
Site Composite Curves Site Utility Grand Composite Curve
Figure 2-4: The construction of the Site Utility Grand Composite Curve
In order to provide the net steam balance for each steam header of site utility systems,
Raissi (1994) proposed a Site Utility Grand Composite Curve (SUGCC) (Figure 2-4) by
plotting the steam generation load towards the right and the steam use load towards to
the left for each steam level. The site-wide targets for fuel and co-generation can also be
identified by SUGCC in a similar way by TSP and SCC. Figure 2-4 illustrates steam
turbines placed on the Site Utility Grand Composite Curve. The characteristics of steam
turbines are easily identified.
12
Chapter 3 Hardware Models
Chapter 3
Hardware Models
3.1 Introduction
In the synthesis and design of the total site utility systems under operational variations,
the loads and operating conditions of the units vary for different operation scenarios.
Their efficiencies vary and the unit capacities influence the efficiencies. Most of the
publications dealing with the synthesis and design of site utility systems simplify the
problem with linear mass/energy balances whereby the units are assumed of constant
efficiencies. A new approach for the targeting models of the units is proposed in this
chapter. The targeting models account for the variation of efficiency with load and
capacity, as well as changes in the operating conditions.
In the first part of this chapter a new Boiler Hardware Model (BHM) is developed to
describe the performance of boilers. The BHM exploits the basic thermodynamic
principles relating to the operation of boilers. Next, the development of a new Gas
Turbine Hardware Model (GTHM) is proposed which is based on thermodynamic
principles, hardware data and engineering knowledge. The Turbine Hardware Model
(THM) proposed by Mavromatis and Kokossis (1998a) is introduced to describe the
performance of the back-pressure steam turbines. Finally, the THM is extended towards
a Condensing Turbine Hardware Model (CTHM) to describe the operation of
condensing turbines.
13
Chapter 3 Hardware Models
3.2 The Boiler Hardware ModeJ
Most of the conventional applications dealing with the synthesis and design of site
utility systems have either simply focused on the balance calculations associated with
boilers or assumed the constant boiler efficiency. In order to address the problems of the
optimisation of total site utility systems under operational variations, a new boiler
model is proposed, termed the Boiler Hardware Model (BRM). The model makes use of
basic thermodynamic principles related to the operation of steam boilers. As a result, the
model is capable of accounting for the efficiency trends of realistic steam boilers.
3.2.1 Model Development
The BRM relies on the principle of the calculation of boiler efficiency. Figure 3-1
shows us the relation between steam load (Qsteam), heat losses (Qloss) and fuel
requirement (Qfuel). The numerical expression for this relation is:
Q fuel = Qloss + Qsteam
The definition of steam load yields:
where:
hI : the enthalpy of boiler inlet water
h2 : the enthalpy of steam raised by boiler
M: the steam load raised by boiler
14
(3-1)
(3-2)
Chapter 3 Hardware Models
T T,
Steam
T.
H
~'
QIuoI
Figure 3·1: Boiler specification on T-H diagram
Figure 3·2: The T -H diagram of steam
In terms of the thermodynamic principle as shown in Figure 3-2, gives:
(3-3)
where:
Tin : the temperature of inlet water
Tout sat : the saturation temperature of outlet steam
15
Chapter 3 Hardware Models
Cp : the specific heat of saturation water between Tin and Tout sat
~Tsat : the temperature difference between Tin and Tout sat
q : the specific heat load of the steam, namely, the heat that can be used for
heating at saturation temperature
The efficiency is defined by:
It follows that:
Substituting Equations (3-2) and (3-3) into Equation (3-1) yields:
Qjue/ = (C p~Tsal + q)M + Q/oss
35~----------------------------~
30
Q[oss (%) 25 QSleam
20
15+-~--~--~~--~--~~--~--~~
o 10 20 30 40 50 60 70 80 90 100
Figure 3-3: Typical heat loss plot for boilers (Pattison and Sharma, 1980)
(3-4)
(3-5)
(3-6)
In order to define the boiler model, the Qloss needs to be known. The Qloss originates
mainly from two parts: the external boiler surface losses and the flue gas losses. Typical
16
Chapter 3 Hardware Models
data on the total heat loss can be found in the form of plot over a range of loads as
shown in Figure 3-3 (pattison and Sharma, 1980). The plot shows the heat loss percent
QIOSS versus steam load percent ~. Q Mmax
steam
where:
Qsteam : the steam heat load
M : the steam load
Mmax : the maximum steam load
On the basis of the data as shown in Figure 3-3 (Passison and Sharma, 1980), the
following equation is regressed within the range between 10% and =100% of~: M max
Qloss ~=a+b~, Q Mmax M max
steam
M 10% 5 -- 5100%
M max (3-7)
Where a and b are regression parameters. The regression over the data provided by
Pattison and Sharma (1980) yields a=0.0126 and b=0.2156 for the plot in Figure 3-3. It
should be noted that both ~ and Qloss vary within the above range of ~. The M~ Q M~
steam
expression estimates the heat loss within 2% throughout the operating range.
Substituting Equations (3-2) and (3-3) into Equation (3-7) gives:
(3-8)
As a result of this expression, the operation of a boiler can be fully defined, once its size
is known in terms of the maximum steam load Mmax. Substitution of Equation (3-8) into
Equation (3-6) gives:
(3-9)
17
Chapter 3 Hardware Models
The Equation (3-9) constitutes the core of the new boiler model. It relates the fuel
requirement of the boiler to the boiler size, the steam load and its operating conditions.
Given a set of expected conditions, the performance of the boiler is a function of its
size. Most notably, while the non-linear variation of the efficiency is accounted for, the
relation of the fuel requirement to the steam load is linear. The predicted boiler
efficiency from Equations (3-5) and (3-9) is:
M MOlaX
11 = ---=-=-----M
(1+b)--+a M max
(3-10)
Equation (3-10) accounts for the variation of efficiency with load and capacity. If we
define the efficiency 11b as the ratio of the heat load of steam (the heat that can be used
for heating at the saturation temperature) to the heat of fuel, gives:
M q MOlaX
11b=------=~----M-----
(CpllTsat +q)«1+b)--+a) MOlaX
(3-11)
By plotting the efficiency Tlb predicted by the above expression versus M~X for
different working conditions, the attributes of the new model are best revealed. As seen
in Figure 3-4, the new model accounts for the variation of efficiency Tlb with the effect
of load, capacity and operating conditions, as would be required by a realistic model. In
the remaining of the dissertation, the model will extensively be used for the
optimisation and analysis of total site utility systems in order to minimise the total
utility cost.
18
Chapter 3
80
75
llb (%) 70
65
60
55
50
45
40
0
h 7f:-)( )(
20 40 60 80 100
M --(%) M max
Hardware Models
-+- Tin= 144, P=88bar, q=2005kj/kg
~ Tin=144, P=88bar, q=1383kj.kg
Tin=144, P=48bar, q=2005kj/kg
Tin: 144, P=48bar, q=1651kj/kg
Figure 3-4: The BHM accounts for the effect of boiler size, load and operating conditions on
efficiency
3.2.2 Summary
The Boiler Hardware Model is based on basic thermodynamic principles and the typical
heat loss plot proposed by Pattisson and Sharma (1980). The thermodynamic principles
describe the operation of boilers and the relation between fuel requirement and steam
generation. The plot of heat loss against load represents typical operation of boilers.
Againist the published data (Pattisson and Sharma (1980» , the BHM provides estimates
within 2% error. In addition to size, load and operating conditions, the heat loss of a
boiler depends on a series of other factors, such as its type, technology and age. Hence,
it is not realistic to expect all boilers to fit in the same curve. To get plots for the
particular classes of boilers , it is sensible one revises the regression parameters to
accurately reflect on the particular case.
19
Chapter 3 Hardware Models
3.3 The Condensing Turbine Hardware Model
The Turbine Hardware Model (THM) presented by Mavromatis and Kokossis (1998a)
is only valid for back-pressure steam turbines. In order to address the optimisation and
analysis problem of total site utility systems, the THM is extended towards a
generalised Condensing Turbine Hardware Model (CTHM).
3.3.1 The Turbine Hardware Model
The THM is based on the Willans Line which depicts steam turbine performance as
shown in Figure 3-5. Where Wmax is maximum power output and n is incremental shaft
work generation against a unit of steam change. The THM relies on the size of the
steam turbine and describes the operation of the unit over its entire range. The turbine
shaftwork is given by (Mavromatis and Kokossis, 1998a):
W 6 1 (A lJ A)( 1 max =-- UIIis - M --M ) 5B M max 6
(3-12)
The isentropic efficiency can be predicted by (Mavromatis and Kokossis, 1998a):
_6~(1_ A )1_1Mmax
llis - 5 B MlisM max ( 6 M ) (3-13)
where:
W : the shaft-work of the steam turbine
A, B : the regression parameters
Ml is : the isentropic enthalpy change
M : the steam flowrate
Mmax : the steam turbine capacity
llis : the isentropic efficiency
20
Chapter 3
Throttle Flow (M)
M Willans line
wmax Shaftwork (W)
Figure 3·5: The THM of steam turbines
Hardware Models
W
The THM accounts for a maximum steam flowrate through a simple turbine, an
isentropic enthalpy change between the turbine inlet and outlet, and a set of regression
parameters. The isentropic enthalpy change and the regression parameters can be
calculated using saturated temperatures of the steam at the turbine inlet and outlet (see
Appendix A). The maximum steam flowrate is derived from the heat demands and
specific heat load at the turbine exhaust. The THM takes into account changes in
isentropic efficiency with the turbine load and working conditions.
3.3.2 The Condensing Turbine Hardware Model
It is assumed that the Willans Line applies to condensing turbines (Church, 1950). The
Condensing Turbine Hardware Model (CTHM) pursues similar calculations for the
shaftwork:
(3-14)
where:
W : the shaft-work of the condensing turbine
AC, BC
: the regression parameters
Mi i., : the isentropic enthalpy change
21
Chapter 3 Hardware Models
M : the steam f10wrate
Mm3x : the steam turbine capacity
The isentropic efficiency is similarly predicted by:
c =~_1 (1 1]/.1 5 Be
Ae 1 M max =:----)(1----) ~isMmax 6 M
(3-15)
The differences between the CTHM and theTHM relate to the regression parameters AC
and BC• Typical data on the efficiency of condensing turbines are found from plots of
the maximum efficiency, as shown in Figure 3-6 (Peterson and Mann, 1985). The
regression parameters are derived from the data on Figure 3-6. By definition, the
maximum efficiency is:
hence:
E max
rh·.max = MI . M max /.1
E max ~i.\· Mmax = __
77 ;s ,max
0.85 ..,.-------------------
0.75
11 is , max 0.65 ____ 28bar
41bar
0.55 62bar
X 83bar
0.45 +---------,,-------,------~
0.1 10 100
Emax(MW)
Figure 3-6: Typical data on the efficiency of condensing turbines
22
(3-16)
(3-17)
Chapter 3 Hardware Models
The curves in Figure 3-6 are represented by an expression of the following equation for
each inlet pressure:
E max
Ml isM max = __ = A C + B C E max (3-18) l]is.max
The regression parameters AC and Be are derived as functions of the inlet pressure or the
respective saturation temperature Tsat (see Appendix B):
(3-19)
Be = be +be Tsar 1 2 (3-20)
3.3.3 Summary
The Condensing Turbine Hardware Model follows similar principles with the THM. It
has the capacity to accurately consider the effect of turbine size, load and operating
conditions on the efficiency of typical condensing turbines.
The plots of maximum efficiency represent typical condensing turbines. Compared to
such plots, the CTHM provides estimates within 3% error by conducting two segments'
regression (see Appendix B). More accurate estimates can be obtained by applying
more segments' regression analysis.
3.4 The Gas Turbine Hardware Model
Most of the previous applications dealing with the synthesis and design of site utility
systems assume constant efficiency for the gas turbine and disregard the effect of
capacity and partial loading. With a purpose to address the problems of the synthesis
23
Chapter 3 Hardware Models
and design of total utility systems under operational variations, a Gas Turbine Hardware
Model (GTHM) is proposed here. The GTHM makes use of the basic thermodynamic
principles, exploits available information for gas turbine equipment, and accounts for a
realistic model to use in synthesis and conceptual calculations.
3.4.1 Model Development
Figure 3-7 illustrates us the basic structure of a gas turbine cycle. The power output
(W), the total power loss of the gas turbine cycle (WIOSS), the fuel flowrate (F\ the fuel
temperature (Tf) , the air flowrate ~), the air temperature (Ta) and the outlet
temperature rout are related by:
(3-21)
where,
Cpa : the specific heat of air
Cpf : the specific heat of fuel
cpg : the specific heat of flue gas
MIf : the specific enthalpy of fuel reaction
W10ss : mechanical losses, heat loss and so on.
Ft, Tt
r6 Combustor
Compressor Turbine
Figure 3-7: Simple gas turbine cycle
24
Chapter 3 Hardware Models
If we define f = Ff ,Equation (3-21) becomes: Fa
(3-22)
Let us define
(3-23)
Then, Equation (3-22) yields:
(3-24)
The parameters .1h and W10ss generally depend on the size of the gas turbine. For a gas
turbine, the overall electrical efficiency increases with size. Typical data on the
electrical efficiency against the turbine size are shown in Figure 3-8 (Marechal and
Kalitventzeff, 1998). The curve explores the impact of the turbine size on the basis of a
full-load efficiency; It does not provide information on the resulting efficiency from a
partly loaded unit. The curve is regressed in the form:
(3-25)
Where Ag and Bg are regression parameters (see Appendix C).
25
Chapter 3 Hardware Models
o.~~----------------------------------------~
0.4
0.35 l1e•max
0.3
0.25
0.2 +-----..,.------r-----.----r-----.---~--____"
o 10 20 30 40 50 60 70
Figure 3-8: Typical data on the electrical efficiency of gas turbines as a function of size
(Marechal and Kalitventzeff, 1998)
From the definition of the electrical efficiency:
It follows that:
It is assumed that:
Where n is a constant parameter.
w 11e = Ml Ff
f
wmax
11e.max = Ml F f .rnax f
26
(3-26)
. (3-27)
(3-28)
Chapter 3 Hardware Models
According to Equations (3-24) and (3-28) the maximum power output is equal to:
(3-29)
Substituting Equation (3-27) into Equation (3-25) yields:
(3-30)
By combining Equations (3-28), (3-29) and (3-30), the following expressions for the
parameters of the model are derived:
1 A g
ilh = (1+n)-(Ml j - f ) Bg F ,max (3-31)
and
(3-32)
Substituting Equations (3-31) and (3-32) into the Equation (3-24) gives:
(3-33)
According to Equation (3-23) and Equation (3-31), the outlet temperature Tout is given
by:
27
Chapter 3 Hardware Models
Equations (3-30) and (3-33) relate the power output of the gas turbine to the size and the
load of the turbine, as well as its operating conditions. Equation (3-34) relates the outlet
temperature of the gas turbine to the size of the turbine and its operating conditions,
expressed through r, Tf, f, .MIf. Given the expected operating conditions, the
performance of the turbine can be estimated merely on the basis of its size. While the
non-linear variation of the efficiency is accounted for, the relation of the power output
to the load is linear. The predicted electrical efficiency can be deri ved from Equations
(3-26) and (3-33):
1 A8 Ff.max
rtl' =-(1- f )«1+n)-n f) (3-35) B8 Ml fF ,max F
0.5
0.4 40MW 60MW
l1e 0.3
0.2
0.1
0 0 10 20 30 40 50 60
W(MW)
Figure 3·9: The GTHM accounts for the effect of gas turbine size and load on efficiency
By plotting the predicted efficiency against the fuel load Ff at various turbine size Ff,max,
Figure 3-9 shows the variation of the electrical efficiency with load and the effect of the
turbine size on the turbine efficiency as it would be expected by a reliable and realistic
model.
28
Chapter 3 Hardware Models
3.4.2 Summary
The GTHM is based on basic thermodynamic principles of gas turbine operations. It
considers a maximum efficiency plot and the assumption of fixed percentage of Wloss to
maximum power output. The thermodynamic principles ensure heat and mass balances
and the maximum efficiency plot accounts for a standard performance of a gas turbine.
The GTHM accounts for only 2% errors by conducting a two segments' regression (see
Appendix C). In addition to capacity, load and operating conditions, the efficiency of
gas turbine depends on a series of other factors, such as it's type, technology and age.
Consequently, it is not realistic to expect all gas turbines to fit in the same set of curves.
It is sensible to obtain plots for the particular class of turbines that are under
consideration and extract the corresponding regression parameters that will more
accurately describe the specific class.
3.5 Conclusions
A set of hardware models CTHM, BHM and GTHM are proposed. The use of the
models for the analysis and optimisation of site utility systems will be explained in the
following sections. The models combine thermodynamic principles, engineering
knowledge and performance data for condensing turbines, boilers and gas turbines.
They enable for an accurate prediction of unit efficiencies and embody the efficiency
trends of realistic units in terms of their variation with capacity, load and operating
conditions. These effects are accounted for in a simple and linear fashion, the
importance of which will be illustrated in the subsequent chapters.
The hardware models CTHM, BHM and GTHM provide results of good accuracy, by
considering the dependence of the efficiency on the capacity and operating conditions.
In view of operational variations, the effect of the part-load operation is well accounted
for all these models.
29
Chapter 3 Hardware Models
With respect to the analysis and optimisation problem, the CTHM, BHM and the
GTHM models provide the basis for modelling the condensing turbines, boilers and gas
turbines respectively in a manner that the efficiency trade-offs of the various design
alternatives can be considered. The linear relations of the power output to the steam
load of condensing turbines, the steam load to the fuel requirement of boilers and the
power output to the fuel requirement of gas turbines are essential for simple
formulations for the optimisation of site utility systems.
30
Chapter 4 Steam Level Optimisation
Chapter 4
Steam Level Optimisation
4.1 Introduction
In the design of process plants, the perfonnance of site utility systems directly
influences the operation of the plants, hence, the optimal design of site utility systems
often leads to significant savings. As there are strong interactions between the site
utility system and site processes, the design problem needs to consider the integration of
the site processes with the site utility system. The design usually involves two major
tasks:
1. the selection of steam levels with respect to their pressure or saturation
temperatures;
2. the development of a configuration for the operating units (ie, boilers, steam
turbines, gas turbines and the auxiliary units).
This chapter introduces a systematic optimisation methodology for the selection of
steam levels. In the next chapter a systematic methodology will be presented for the
optimal configuration of the utility system.
The placement of steam levels has a significant bearing on the utility demands, the
cogeneration potential of the processes and the operating conditions of the steam
turbines. The specific problem addressed in this approach assumes a given structure for
the chemical processes. Different operation scenarios are also given for the chemical
processes along with forecasts for prices of utilities over a finite number of time
periods. The different operation scenarios of the total site are described by the sets of
Total Site Profiles (TSP) shown in Figure 4-1. The process heat sources reject heat by
31
Chapter 4 Steam Level Optimisation
raising steam at different levels; the process heat sinks absorb heat also at different
levels. The total amount of steam raised by the process heat sources doesn't usually
match the amount required by the process heat sinks. Because of thermodynamic
constraints and heat transfer constraints, auxiliary cooling and heating are required.
These are available by the cold utility and the VHP steam raised by the boiler. The
timing of demands changes the profiles of heat sources and sinks over time and the
duration of each time period is usually different.
The objective of this chapter is to find the optimum locations for the steam levels
considering the total site. Single operations will be discussed first and subsequently be
generalised for multiple operation scenarios. As discussed by Petroulas and Reklaitis
(1984), if auxiliary fuel-boilers are required, they should operate at the highest-pressure
level. The optimisation problem then needs to determine the temperature of the VHP
steam, the saturation temperature (or pressure) of each steam level, the auxiliary boiler
duty, the cooling utility demand and the shaft-work produced by the steam turbine
network for each expansion zone. By using the THM and BHM models, one is able to
target the overall fuel requirement, the cooling utility demand and the co-generation
potential. In order to obtain the optimal solution for minimum utility cost, we need to
identify the correct compromise between heat recovery and co-generation.
Scenario A Scenario B
T T HP
MP
IP
LP
H H H H
Figure 4-1: Different operation scenarios can be represented by sets of total site profiles
32
Chapter 4 Steam Level Optimisation
4.2 The Strategy
Considering the drawbacks of the conventional techniques (see section 2.2) for the
selection of steam levels, the following strategy is proposed to determine the optimal
steam levels. The new strategy is shown in Figure 4-2. The strategy comprises two
stages:
1. The total site analysis is used to postulate a new transhipment network that describes
the heat integration of the steam levels with the process heat sources and heat sinks.
2. An optimisation model is developed based on the transhipment network and the
THM and BHM models. The model optimises by minimising the total annual cost
and is formulated as a multi-period Mixed Integer Linear Programming (Mll..P)
model.
Gal Analy~)-----t~~ I Transhipment Network Development I
G; and BHM m~)-----1~ ~r
~ I Optimisation I ~
I Optimal Steam Levels I Figure 4·2: Schematic showing the steam level optimisation strategy
4.3 The Transhipment Network of a Total Site
The transportation model determines the optimum transfer of commodities from sources
to destinations. The transhipment model has been widely used in the Operation
Research (Garginkel and Nemhauser, 1972) that deals with the optimum allocation of
resources and represents a variation of the transportation problem. Papoulias and
Grossmann (l983b) proposed a transhipment model for the synthesis of heat exchanger
33
Chapter 4 Steam Level Optimisation
networks. In this work, a transhipment network representation is developed for the total
site in order to get the optimal steam levels.
The total site heat flows can be represented by total site profiles. As seen in Figure 4-3,
heat is regarded as a commodity to ship from process heat sources to steam levels and
from steam levels to process heat sinks through temperature intervals. These intervals
account for thermodynamic constraints in the transfer of heat. In particular the second
law of thermodynamics requires that heat flows only from higher to lower temperatures,
and therefore these thermodynamic constraints have to be accounted for in the network
model. This is accomplished by partitioning the entire temperature range into
temperature intervals. For the total site profiles the interval temperatures are the
temperatures of turning points (critical points) of each heat source and heat sink. These
are all candidate locations of the optimum steam levels. The selected temperatures are
listed in descending order. The optimal steam levels are selected from all potential
steam levels denoted by their saturation temperatures.
As shown in Figure 4-3, the points A,B,C,D,E,F... are the turning points. This
partitioning method guarantees the feasible heat transfer of heat in each interval, given
the minimum temperature approach L\ T min. In this way as shown in Figure 4-3, the total
site heat flows are represented by the transhipment network. The network comprises
three cascades of temperature intervals:
• Heat source cascade.
• Steam level cascade.
• Heat sink cascade.
The heat source cascade represents that heat flows from process heat sources to the
corresponding temperature interval, and then to the steam level in the same temperature
interval with residual going to the next lower temperature interval. For the heat sink
cascade, it can be considered that heat flows from steam level to the corresponding
temperature interval, and then to the process heat sinks in the same temperature interval
with residual going to the next lower temperature interval. The steam level cascade
represents that heat flows from process heat sources to the corresponding steam level,
34
Chapter 4 Steam LeveL Optimisation
and then to the process heat sinks in the same temperature interval with residual passing
a steam turbine to the next stearns level.
T Heat source Steam Levels Heat sink cascade cascade cascade
A
8 --
Cooling Utility
H
Figure 4-3: Transhipment network representation of the total site heat flow
It is assumed that the total number of stearn levels for the site is I. The levels are
labelled from the highest level (i=l) down to the lowest level (i=I). The temperature
range for each level is partitioned into J temperature intervals which are labelled from
the highest interval (j=I) down to the lowest interval (j=J). In this way, the entire
temperature range of the total site is partitioned into IxJ temperature intervals. The
intervals are labelled from the highest interval (i=l, j=l) down to the lowest interval
(i=I, j=J).
The heat flow pattern of the temperature intervals for stream level i can be illustrated as
shown in Figure 4-4. It is represented by the three heat cascades:
35
Chapter 4 Steam Level Optimisatioll
Heat souce Steam level Heat sink
Site heat cascade cascade cascade Site heat
source
~ n. sink
~ i, j=1 (]--.I H it II
i, j=2 0--.1 H n: ~ JJ ~ ~
~ --------.. ~ ~
---------------
i, j=J-1 <l
i, j=J
Figure 4-4: Heat flow pattern of the temperature intervals for steam level i
(a) Heat source cascade:
(1) Heat flows into a particular interval from the process heat sources
contributing to the temperature interval.
(2) Heat flows out of a particular interval to raise steam with a temperature at the
lower bound of the interval.
(3) Heat flows out of a particular interval to the next lower temperature interval
or the cooling utility. The heat is the residual heat that can't be utilised in the present
interval, and consequently has to flow to a lower temperature interval or the cooling
utility.
(4) Heat flows into a particular temperature interval from the previous interval
that is at higher temperature. This heat is the residual heat that can't be utilised in the
higher temperature interval.
36
Chapter 4 Steam Level Optimisation
(b) Steam level cascade:
(1) Heat flows into a particular level from the heat source cascade in the same
temperature interval and VHP steam.
(2) Heat flows out of a particular level to the heat sink cascade in the same
temperature interval.
(3) Heat flows out of a particular level passing a steam turbine to the next lower
temperature steam level.
(4) Heat flows into a particular level from the higher temperature steam level.
This heat is the residual heat out of steam turbines.
(c) Heat sink cascade:
(1) Heat flows into a particular interval from the steam level in the same
temperature interval and VHP steam.
(2) Heat flows out of a particular interval to the process heat sinks within the
temperature interval.
(3) Heat flows out of a particular interval to the next lower temperature interval.
This heat is the residual heat that can't be utilised in the present interval, and
consequently has to flow to a lower temperature interval.
(4) Heat flows into a particular temperature interval from the previous interval
that is at higher temperature. This heat is the residual heat that can't be utilised in the
higher temperature interval.
Different operations are favoured by different sets of steam levels. Since it is
impractical to vary the conditions of steam levels between different operation scenarios,
the optimisation is searching for the conclusions that minimise the total utility cost over
the entire set of scenarios. For mUltiple scenarios the temperature intervals are extracted
from each individual scenario following the previous analysis that is based on a single
scenario; a general model is constructed next whereby intervals are listed in descending
order. The selection of steam levels is made out of all possible cases.
37
Chapter 4 Steam Level Optimisation
4.4 Optimisation Model
In this section, the postulated transhipment representation is modelled as a multi-period
MILP model. The model minimises the utility cost for the total site utility system under
multiple operation scenarios and incorporates the BHM and THM models that predict
the reliable equipment performance against a wide range of operating conditions. In
order to develop the mUlti-period MILP model continuous and binary variables are
associated with the transhipment network presented in Figure 4-3. The binary variables
assigned to steam levels represent the existence or non-existence of the corresponding
steam level at a given condition. The binary variables associated to units define the
operating status of boilers and steam turbines for each scenario. The continuous
variables represent the heat flows across temperature intervals, the boiler duty, the fuel
requirement, the cooling utility demand, the power output of each steam turbine and so
on.
The optimisation problem involves the following sets, parameters and variables:
Sets
IS = { i=I,2 .. .11 steam level}
I is the total number of steam levels.
1S = (j =1,2 ... 1 or jm=1,2 ... 1 I temperature intervals}
1 is the total number of temperature intervals for each steam level.
K = { k=I,2 ... Nk I operation scenarios}
Nk is the total number of operation scenarios.
V = { v=1,2 ... Nv I operating conditions of VHP steam }
Ny is the total number of candidate operating conditions of VHP steam.
Parameters
a,b regression parameters of BHM
Ai,j, Bi,j: regression parameters of THM for the steam turbine using steam in interval
(i,j)
Ay,By regression parameters of THM for the VHP steam turbine
38
Chapter 4 Steam Level Optimisation
Ci,j,k : total heat required by all process heat sinks in temperature interval (i, j) under
scenario k
CHk : total heat required by all process heat sinks above temperature interval (1,1)
under scenario k
Cp specific heat of saturation water between Tin and Tout sat
E1Si,j,jm: isentropic enthalpy change between the steam level in intervals (i, j) and the
steam level in interval (i+ 1, jm)
EISV v,j: isentropic enthalpy change between the VHP steam level at condition v and
the steam level in interval (1, j)
H operating hours per year
Hi,j,k total heat provided by all process heat sources in temperature interval (i, j)
under scenario k
HLk : total heat provided by all process heat sources below temperature interval (I, J)
under scenario k
Mimax
: capacity of the steam turbine locating between the steam level i and the steam
level i+l
Mmax : capacity of the VHP steam turbine
MBmax: capacity of the boiler
qv specific heat load of the VHP steam at operating condition v
qi,j specific heat load of the steam level in interval (i, j)
Ti,j lower bound temperature of interval(i, j). The intervals are labelled from the
highest interval (Tl,I) down to the lowest interval (TJ,J). The saturation temperature of
the steam level in interval (i, j) equals Ti,j
TkS time fraction of scenario k
~Tsat temperature difference between Tin and Tout sat
TVH saturation temperature of the VHP steam
U/ unit cost of fuel under scenario k
Ukc unit cost of cooling utility under scenario k
UkP unit cost of electricity under scenario k
Wkd electricity demands of the site under scenario k
39
Chapter 4 Steam Level Optimisation
Binary variables
Yi,j variable to denote the steam level in interval (i,j) is selected (Yi,j=1) or not
(Yi,j=<»
ytij,k variable to denote the steam turbine using steam in interval (i,j) works under
scenario k (ytj,j,k=1) or not (ytij,k=<»
Xv : variable to denote the operating condition v of the VHP steam level is selected
(xv=!) or not (xv=<»
xbv,k : variable to denote the boiler works at operating condition v under scenario k
(xbv,k=1) or not (xbv,k=O)
Xtv,k : variable to denote the VHP steam turbine works at operating condition v under
scenario k (Xtv,k=!) or not (xtv,k=1)
Continuous variables
RHi,j,k : residual heat flowing out of interval (i,j) of the heat source cascade under
scenario k
RCij,k : residual heat flowing out of interval (i,j ) of the heat sink cascade under
scenario k
Di,j,k : heat flowing out of interval (i,j) of the heat source cascade to the steam level
cascade under scenario k
Sjj,k : heat flowing into the steam level in interval (i,j) from a steam turbine under
scenario k
QSTv,j,k: heat flowing into the steam level in interval (l,j) from the VHP steam level at
operating condition v under scenario k
QSv,k : heat flowing out of the VHP steam level at operating condition v to the VHP
steam turbine under scenario k
Fj,j,k : heat flowing out of the steam level in interval (i,j) passing a steam turbine to
next steam level under scenario k
Ei,j,k : heat flowing out of the steam level in interval (i,j) to the heat sink cascade
under scenario k
FTj,j,jm,k: heat flowing out of the steam level in interval (i,j) passing a steam turbine to
the steam level in interval (i+l,jm) under scenario k
40
Chapter 4 Steam Level Optimisation
Wj,k : power output of the steam turbine locating between steam levels i and i+ 1
under scenario k
WVHk: power output of the VHP steam turbine under scenario k
steam load raised by the boiler at operating condition v under scenario k
fuel required by the boiler under scenario k
heat flowing out of the VHP steam level at operating condition v to process
heat sinks under scenario k
QVk : heat flowing into interval (1,1) of the heat sink cascade from the VHP steam
level under scenario k
CC: total cost of cooling utility
Cf: total cost of fuel
cp,tot total cost of electricity
4.4.1 Model Formulation
The previous sections explained the transhipment representation of the total site (as
shown in Figure 4-3) and the temperature intervals of the system (Figure 4-4). The heat
flows across the intervals of the heat source cascade, the steam level cascade and the
heat sink cascade can then be represented by Figures 4-5, 4-6 and 4-7 respectively.
RH,j-l.k RHi-I.J.k
RH'j.k
i=I.2 •.. .I, j=2,3,,,.J, k=I,2,,,.K i=I,2,,,.I, j=l, k=I,2,,,.K
Figure 4-5: Heat flow pattern in each temperature interval of the heat source cascade
41
Chapter 4 Steam Level Optimisation
S'J.k
F'J.k
Figure 4·6: Heat flow pattern in each temperature interval of the steam level cascade
RC..I).k
E.J.k
i=1,2 .... 1. j=2.3 ... .J. k=I.2 .... K i=I.2 ... .I. j=l. k=I.2 .... K
Figure 4·7: Heat flow pattern in each temperature interval of the heat sink cascade
Given the sets, the parameters and the variables introduced above, the mathematical
model includes:
Heat balances for each temperature interval (i,j) in the process heat source cascade:
H. k + RH . . 1 k = D .. k + RH . . k' i E IS, J' ~ 2, k E K I.J. I.J- • I.J. I.J. (4-1)
Hi.J.k + RHH.J.k = Di.J.k + RHi.J,k' i :t 1, j = 1, k E K (4-2)
H. k = D . k + RH . k' i = 1, j = 1, k E K I.J. I.J. I.J. (4-3)
42
Chapter 4 Steam Level Optimisation
Heat balances for each temperature interval (i,j) in the steam level cascade:
D"k +S""k =E."k +F. Ok' iE IS,jE JS,kE K I,j, I,j, I,j, I,j,
Heat balances for each temperature interval (i,j) in the process heat sink cascade:
E;,j,k + RCi,j_I,k = Ci,j,k + RCi,j,k ' i E IS, j ~ 2, k E K
Ei,j,k + QV k= Ci,j,k + RCi,j,k ' i = 1, j = 1, k E K
Ei,j,k + RCH.J ,k = Ci,j,k + RCi,j,k' i::l: 1, j = 1, k E K
Heat balances of the process heat sink cascade above the temperature interval (1,1):
CRk +QVk = LQCV,k' kE K veV
For each steam level exactly one operating condition can be selected. Therefore,
~y" " = 1, iE IS ~ I,j
jeJS
VHP steam also works at a single condition. Therefore,
(4-4)
(4-5)
(4-6)
(4-7)
(4-8)
(4-9)
(4-10)
If a steam level in interval (i, j) is not selected, the steam turbine cannot use steam from
the steam level, the following logical models apply:
Lyti,j,k ~ Yi,j' iE IS,jE JS (4-11) keK
43
Chapter 4 Steam Level Optimisation
To ensure that the input and output flowrates of each level are eliminated if the
corresponding level doesn't exist, the following inequalities must be included:
Si,j,k -UYi,j ~ 0, ie IS, j e JS,ke K (4-12)
Ei,j,k ~UYi,j :SO, ie IS,je JS,ke K (4-13)
Dj,j,k -UYi,j ~ 0, i e IS,j e JS,k e K (4-14)
F;,j,k - UYi,j :S 0, i e IS, j e JS, k e K (4-15)
A single steam turbine is assumed for every expansion zone. The shaft-work of the
steam turbines employs the THM:
[6 1 ( A r FT k 1 J] = __ EIS ... __ ,_,j_ I,j,jm, __ M.max t ..
Wi,k LL 5 B . I,j,jm M max . . 6 I Y I,j,k ' JEJS "nEJS I,j I q',j
ie IS,k e K
(4-16)
~ FT .. k = F .. k' i E IS, J' E JS, k E K L.J I,j,jm, I,j, (4-17) jmeJS
~ IT 1 .. k = S. . k' i ~ 2, J'm E JS, k E K L.J 1- ,j,jm, I,jm, (4-18) jEJS
The fuel consumption employs the BHM:
Q! = L ((C pD.Tsa, + qv X(1 + b )MBv'k + aMBrnax
Xbv,k )~ k E K (4-19) veV
If no VHP steam is available at condition v, the operation of the boiler at condition v is
also excluded. Therefore, the following logical inequalities apply:
44
Chapter 4
Lxbv•k ~ Xv' VE V keK
MBv•k -Uxbv•k ~ 0, vE V,k E K
Steam Level Optimisation
(4-20)
(4-21)
The heat balance for the VHP steam level is fonnulated as follows:
The power output of the VHP steam turbine is gi ven by:
where:
LQSTv.j •k = QSv.k' VE V,kE K jeJS
Lxtv•k ~ xv' VE V keK
QSv.k -Uxv.k ~O, vE V,kE K
LQSTv•j.k = Sl.j,k. jE JS,kE K lEV
The annual cost of the fuel required by the boiler is:
c f = LU! Q!T/ H keK
(4-22)
(4-24)
(4-25)
(4-26)
(4-27)
(4-28)
As the heat of cooling utility required by the process heat sources is RI,J.k + HLk under
scenario k, the annual cost of cooling utility is:
45
Chapter 4 Steam Level Optimisation
CC = 'LU%(R1,J,k + HLk)TkS H (4-29)
kEK
The savings from the power cogeneration are:
ct = LU:Wi,kT/ H, iE IS (4-30) keK
CVH = 'LU!WVHkT/H (4-31) kEK
The annual cost of electricity is:
cp,tot = 'LU[W/T/ H - 'LC/-CVH (4-32) kEK iE/S
The objective function used minimises the annual utility cost that includes the cost of
fuel and cooling utilities, as well as the cost of power. It is given by:
(4-33)
It should be noted that the proposed MILP model can also be used to find the optimal
steam levels for total site utility systems in order to minimise the fuel requirement. This
can be accomplished by replacing the above objective function by:
minMFR=C f (4-34)
Normally, these two objectives define different steam levels and this can be illustrated
by Case Study 1 which will be introduced next.
46
Chapter 4 Steam LeveL Optimisation
4.4.2 Remarks on the Optimisation Model
The above fonnulation consists of linear constraints of continuous and integer variables.
It comprises a multi-period Mixed-Integer Linear Programming (MILP) model. The
problem of synthesising a total site utility system given by the objective function and
the proposed set of constraints in Section 4.4.1, corresponds to a model whose
development requiring the following infonnation:
(a) Data on the total site profiles for each operation scenario.
(b) Specific heat load of VHP steam for each working condition; it is assumed that the
specific heat load of steam expanded through a turbine remains approximately
constant for all exhaust pressure values. The assumption is based on the observation
by Mavromatis and Kokossis (1998a), Raissi (1994) and Salisbury (1942).
(c) Cost correlations for the available utilities.
Total site profiles generation
Temperature intervals partition
Transhipment superstructure
Optimisation
Optimal solution
Figure 4-8: Schematic representation of the optimisation procedure
The steps are presented in Figure 4-8. The total site profiles for each operation scenario
are generated from the procedure proposed by Dhole and Linhoff (1993). The
temperature range is partitioned following the propositions of Section 4.3. The
transhipment representation is developed as explained in Section 4.3. The optimisation
determines the optimal structure of the steam levels and the operating condition of the
47
Chapter 4 Steam Level Optimisation
VHP steam. It also provides the steam load and power output of each steam turbine, the
heat duty of the boiler and the cooling utility demand for each operation scenario.
4.5 Case Studies
The methodology is illustrated with two different cases. Case 1 is a steam level
optimisation problem under a single operation scenario. The second case considers
multiple scenarios. The cost data of the available utilities are given in Table 4-1.
Cooling Water Fuel (Natural Gas) Electricity
Tout-Tin=20°C LfrV: 13856kWhlTon
Cost: O.0185$ffon Cost: 223$ffon Cost: O.12$/kWh
Table 4-1: Cost data of utilities
4.5.1 Case 1: Steam Level Optimisation under a Single Scenario
The total site profiles are given in Figure 4-9. The steam system comprises a boiler, the
four steam levels shown on the TSPs, and a single cooling utility. It is assumed that a
single steam turbine is placed at each steam expansion zone. The very high-pressure
(VHP) steam is raised in the boiler house at 500°C and 90 bar (Tsat =302°C). The
temperature of inlet water is 245°C. The specific heat load of the VHP steam is
0.557MWhlt at 500°C and 90bar. The HP, MP and LP steam are raised against process
heat sources and consumed by process heat sinks. On the basis of the total site profiles,
the objective is to find the optimal placement of the intermediate steam levels HP, MP
and LP in order to minimise the utility cost and minimise the fuel requirement
respecti vel y.
48
Chapter 4 Steam Level Optimisation
ToCi
Fuel __ ~
300 ----~--------~~ VHP
HP
MP
LP
Cooling Utility
---' ___ l •
. H(MW) H(MW)
Figure 4-9: The total site profiles for the site of Case 1
Based on the total site profiles and the temperature partition rule, the candidate
saturation temperatures for each level are obtained as shown in Table 4-2.
HPCOC) MPeC) LPCOC)
275 210 130
260 200 120
250 190 110
Table 4-2: Candidate saturation temperatures for each steam level of Case 1
The total heat provided by the process heat sources and total heat required by the
process heat sinks for each temperature interval (i,j) are obtained by targeting the heat
loads with the help of Figure 4-10 as shown in Table 4-3 and Table 4-4. The heat
requirement of the process sinks above the temperature interval (1,1) is 3MW. The
surplus heat of the process heat sources below the temperature interval (3,3) is 9MW.
49
Chapter 4 Steam Level Optimisation
=-::_ .. ===_--=~~~~_:_= ___ =-::=:: _____ :-__ -_-=--__ -_fC-__
H(MW)
-+ =====;::.;;.:;:::::====-==-=--t~. -fic>==-------.-.-.. --.---=----... --.... -...
Figure 4·10: Potential steam levels of Case 1
I.
H(MW)
H(I,j) MW 1 sl interval 2na interval 3r<1 interval
1 sl level 18 2 3
2D<1level 9 3 10
3r<1 level 9 5 2
Table 4·3: Heat provided by the process heat sources in each temperature interval of Case 1
C(I,j) MW 1 sl interval 2Da interval 3r<1 interval
1 sl level 1 2 3
2nd level 2 37 9
3rd level 3 3 6
Table 4·4: Heat required by the process heat sinks in each temperature interval of Case I
After the partition of the temperature intervals, the transhipment representation is set up
on the basis of Figure 4-11.
The proposed MILP model is applied to minimise the total utility cost. The model is
developed using the general algebraic modelling system (GAMS) (Brooke, etc., 1992)
and the optimisation has been conducted by employing the OSL solver. The
50
Chapter 4 Steam Level Optimisation
corresponding MILP model involves 92 continuous variables, 24 binary variables and
125 constraints.
302
270 260 250
210 200 190
130 120 110
Fue:..:..I_~ VHP
. . .-.~:-~:~~:~.~ ::~!~. f==5::::::+:;tl=~~ HP .... ..
- - - +- L-··=:·····:;:·· ~+:t~::::;;~ ... :~ .... + .~ .... -=: +- I . ....... ....... -=<.:........-. ................. ,...... -........ _ . ., .... _ .. _._ ..... _._ ... _ ..... ~----- MP
--+-
LP
Cooling Water
Figure 4-11: Transhipment network representation of case 1
The optimal steam levels for the Minimum Utility Cost (MUC) case are shown in
Figure 4-12. The optimisation determines the saturation temperature of each steam
level, the heat load balance of each steam level, the heat load of each steam turbine, the
power output of each steam turbine, the heat duty and fuel requirement of the boiler and
the cooling utility requirement. The optimal temperature levels are 260°C for HP, 200°C
for MP and 110°C for LP. The total utility cost is 68.5 k$/year, out of which the fuel
cost is 6618.7 k$/year, the cooling utility cost is 63.1 k$/year and the power saving is
6613.3 k$/year. The site pinch is located at the MP level.
The same MILP model can be used to minimise the fuel requirement. The optimal
steam levels for the Minimum Fuel Requirement (MFR) case are shown in Figure 4-13.
The optimal steam levels are 270°C for HP, 200°C for MP and 130°C for LP. Even
though the MFR case has the same total site profiles as the MUC case, their optimal
steam levels are apparently different. The fuel cost for the MFR case is 4280 k$/year
51
Chapter 4 Steam Level Optimisation
which is less than the MUC case. However, the power output is zero and there IS no
power saving.
302
270 260
250
Fuel 47_2MW
210 ------/--200 190
130 120 110
302
270 260
250
210 200 190
130 120 110
Cooling Water
Figure 4-12: Optimal structure for MUC case of Case 1
~ 22~ Fuel 30MW l5-~----r"
19MW _ --------------------------------- ------~ --------- ------....I.----'r:::--- ----. ---- -:=;------.--.-.--.. -.--... -.--.. --.-.--.... -.--...... -- -.... . ==:===:==~~=:==::::::::::=~:_==~ :====: =~==:====:::::::::::::::::====~M:W ----.- -=+-.------ ----.---.. --------- .--
- -14MW 17MW
:=~==:=:===::::===-....:-~===:==~ ~i~~: =:=~-.-.--.-.-.----.. ---.-.-.==:= J~~ ~:=::::========::::==~-.-~===: ---.. -.--..... ------.------.- ... -.--. -·_--·---··-·--·--··---i7MW -.---.. - -.-.. --.. --.-.-. --.-----.--.--.---... --.----.-.-
19MW OMW -.... ,,-..•.. -~.- ---..... -.--.----... ---.---.---.-.-.. -.------.-.. ----.
-- ... _------------_ .. _----------:=+ ---- -··---·-·1:2MW ---- .=+.- --.. -... -.. --.--... -------.-... ---.---.. --.-.-.-
16~
Cooling Water 7~
Figure 4-13: Optimal structure for MFR case of Case 1
52
VHP
HP
MP
LP
VHP
HP
MP
LP
Chapter 4 Steam Level Optimisation
4.5.2 Case 2: Steam Level Optimisation under Four Scenarios
The site of Case 1 is now considered with three additional scenarios, scenarios B, C and
D. The total site profiles for each scenario are shown in Figure 4-14. Each scenario
spans for a period equal to one-fourth of the year.
L '. -=r-= '.
H(MW)
T oe
--
T oe
:: =--=- ---:: -------
:: ::::::-:. =-==---
H (MW)
T oe Scenario A Scenario B
/ LP
H(MW) H(MW) H(MW)
Scenario C Scenario D
H(MW ) H(MW) H(MW)
Figure 4-14: Four operation scenarios for Case 2
Based on the total site profiles and the temperature partition, four candidate saturation
temperatures are obtained for each level as shown in Table 4-5.
HP(OC) MP(OC) LPeC)
280 210 140
270 200 130
260 190 120
250 180 110
Table 4-5: Candidate temperatures for each steam level of Case 2
53
Chapter 4 Steam Level Optimisation
For each temperature interval, the total heat provided by the process heat sources and
the total heat required by the process heat sinks are obtained by targeting the heat loads
and using Figure 4-14. Results are summarised in Tables 4-6, 4-7, 4-8 and 4-9, where
H(i,j) represents the heat provided by the heat sources and C(i,j) represents the heat
required by the heat sinks. The heat requirement of process heat sinks above
temperature interval (1,1) for each scenario is shown in Table 4-10. The surplus heat of
the process heat sources below temperature interval (3,3) for each scenario is shown in
Table 4-11.
H(i,j) MW 1 st interval 2na interval 3ra interval 4tn interval
1 st level 3 15 2 3
2nd level 9 3 10 1.5
r d level 6 1.5 5 2
C(i,j) MW 1 st interval 2na interval 3ra interval 4 tn interval
1 st level 3 1 2 3
2nd level 2 37 1.5 6
3rd level 1.5 3 3 6
Table 4-6: Heat enthalpy changes of processes of Case 2 (Scenario A)
H(i,j)MW 1 st interval 2nd interval 3rd interval 4tn interval
1 st level 3 15 2 3
2nd level 9 3 10 1.5
3rd level 6 1.5 5 2
C(i,j) MW 1 st interval 2nd interval 3rd interval 4tn interval
1 st level 3 1 2 3
2nd level 2 12 1.5 6
3rd level 1.5 3 3 31
Table 4-7: Heat enthalpy changes of processes of Case 2 (Scenario B)
54
Chapter 4 Steam Level Optimisation
H(i,j)MW 1 st interval 2nd interval 3rd interval 4th interval
1 st level 3 10 6 3
2ha level 9 3 5 3
3rd level 6 3 5 2
C(i,j) MW 1 st interval 2nd interval 3rd interval 4th interval
1 st level 6 8 8 3
2nd level 2 15 4 6
3ra level 13 5 3 6
Table 4-8: Heat enthalpy changes of processes of Case 2 (Scenario C)
H(i,j) MW 1 st interval 2na interval 3ra interval 4th interval
1 st level 5 4 2 3
2na level 9 3 10 1
3ra level 6 8 5 2
C(i,j) MW 1 st interval 2nd interval 3ra interval 4th interval
1 st level 3 1 2 3
2nd level 2 10 9 6
3ra level 6 3 9 10
Table 4-9: Heat enthalpy changes of processes of Case 2 (Scenario D)
Scenario A Scenario B Scenario C Scenario D
O(MW) O(MW) 3(MW) 2MW
Table 4-10: Heat required of process sinks above temperature interval (1,1) for Case 2
Scenario A Scenario B Scenario C Scenario D
9(MW) 9(MW) 5(MW) 7MW
Table 4-11: Surplus heat of process sources below temperature interval (1,1) for Case 2
55
Chapter 4 Steam Level Optimisatioll
The transhipment network is set up on the basis of Figure 4-15.
302 Fuel '----_.
280-------- -. 27()---- .-+---= 260-'·-- '0
250 - -- - -.------ -.~-- -- ... -.-.. - .. ·+· .. I-~----I~-+-~
U
., ~
5 _OJ
VHP
HP
MP
==t~±==t:::::=:::I==5t:::t:t:~:::::;;;:::::~::::-:. :::::;=:= .=: : :==::=:::::=:::::::~ ... -. :=:~~==::::==== ....L.--+-L--_~-- - + -.---- . ~-.-. - .... --- .. - ... - LP
..... ,. ........................... _ .. _ ... :g .... _ ............ _ ...... __ ............ _ .......... .
Cooling Water
Figure 4·15: Transhipment network representation for Case 2
The Mll...P model is applied to minimise the total annual utility cost. The mathematical
model in GAMS involves 513 continuous variables, 88 binary variables and 628
constraints. The model employs the OSL solver.
The optimal saturation temperatures are 260°C for HP, 200°C for MP and 140°C for
LP. Figure 4-16 shows the Site Utility Grand Composite Curves for the four scenarios.
The total utility cost is 150.6 k$/year, out of which the fuel cost is 5252.8 k$/year, the
cooling utility cost is 126.1 k$/year and the power saving is 5228.3 k$/year.
4.5.3 Summary
The results of Table 4-12 illustrate different optimal steam levels between single and
multiple scenarios. Figure 4-16 shows that the site pinch of scenario A is at the MP. The
site pinches of the other three scenarios are at the LP. The illustration explains that:
• The optimal levels in considering isolated scenarios are generally different from the
case more scenarios are considered simultaneously
56
Chapter 4 Steam Level Optimisation
• Each scenario favours a different set of steam levels.
• Results may yield not only different levels but also different location of the site
pinch.
Scenario A 47,3MW
T VHPF===~~~~~~
HP 7MW
15MW MP ~--------~------~-------
58MW
17,5MW LP J------,
VLP 17,5MW
cw
H
Scenario C
2,2MW
15MW
CW H
Scenario B
Q,5MW
2,5MW
15MW MP ----
19,5MW
17,5MW LP J-----"---'-----
38,5MW
17,5MW
cw
Scenario D
T Q,86MW
HP
MP 15MW
'----r-r---_ 1, lMW
LP
22MW
CW
2,2MW
H
H
Figure 4-16: The resulting SUGCCs corresponding to the optimal steam levels of Case 2
Optima steam levels Single scenario (Case 1) Multiple scenarios (Case2)
lIP (OC) 260 260
MP (OC) 200 200
LP (OC) 110 140
Table 4-12: Optimal steam levels for single and multiple scenarios
57
Chapter 4 Steam Level Optimisation
4.6 Conclusions
As shown with the presented case studies, the proposed optimisation methodology is
powerful to address the needs of the preliminary steam levels design for the total site
system under operational variations. By exploiting engineering knowledge, the BHM
and THM models are capable of predicting the real efficiency trends of units, by
considering the dependency of the efficiency on load and operating conditions. The
application of the two models are particularly important in the case of multiple
operation scenarios, where the steam loads and the respective efficiencies may vary
significantly. By exploiting total site analysis techniques, a new transhipment network
is developed to represent the total site system. It can be used to describe the interaction
between the placement of steam levels and steam loads of site processes. Based on the
transhipment representation and combined with the BHM and THM models, a multi
period MILP model is applied to minimise the total utility cost for the total site under
multiple operation scenarios. Major decision variables include the overall fuel
requirement, the cogeneration potential and the cooling utility demand. The MILP
model is a general model which can not only be used for the Minimum Utility Cost
(MUC) case but also for the Minimum Fuel Requirement (MFR) case.
58
Chapter 5 Layout Screening and Optimisation
Chapter 5
Layout Screening and Optimisation
5.1 introduction
A typical chemical plant consists of several chemical production processes, which
consume heat and power to make products. The chemical processes usually operate in
different scenarios. Heat and power are supplied by a central site utility system and the
design should be able to adjust efficiently to variations in demand for heat and power.
The design decisions include the selection of the optimum steam levels and the layout
of the site utility system. The system consists of available steam turbines, gas turbines,
boilers and other auxiliary units. The optimal selection of steam levels has been
discussed in chapter 4.
Once the steam levels are determined, the design can proceed with the development of
the best structure to produce utilities. This task comprises a large combinatorial
problem. Candidate systems involve layouts of the following units:
1. simple and/or complex back-pressure turbines.
2. simple and/or complex condensing turbines.
3. reheat cycles.
4. simple and/or regenerative gas turbine cycles.
5. boiler networks.
Each alternative configuration results in a different overall efficiency and a different
capital cost. The consideration of multiple operation scenarios results in a further
increase of the design options to an extent that is difficult to handle even for moderate
problems. As the utility demands vary with time, it is important the utility system
59
ChapterS Layout Screening and Optimisation
maintain high efficiency over the entire variation range. On the other hand, the optimum
trade-off between flexibility and capital cost needs to be identified. In order to evaluate
the alternative design options and distinguish amongst the associated efficiencies, the
effects of the unit size, as well as load and operating conditions on the unit efficiencies
need to be taken into account. These effects generally involve non-linear relations that
give rise to complex models and formulations.
The problem addressed in this chapter assumes given structures of existing chemical
processes and fixed steam levels whose optimisation has been separately addressed in
chapter 4. Also given are the power and steam demands at each level. The time
associated with each operation scenario can be different. Then the design problem is to
determine the structure of the site utility system to minimise the total cost, subject to the
satisfactory of the utility demands over the available operation horizon.
The following boilers are considered in the analysis:
1. Very High Pressure (VHP) boilers fired by fuel.
2. Heat Recovery Steam Generators (HRSG) which recover heat contained in the gas
turbine or the furnace exhaust gases. Supplementary firing is allowed for these units.
3. Waste heat boilers recovering heat from chemical processes.
4. Medium pressure boilers fired by fuel, which reheat steam in reheat cycle.
The capacities of the boilers should be determined, and the boiler efficiencies are
variable and depend on the boiler capacity, heat load and the operating conditions.
Steam is collected and distributed to chemical processes, steam turbines, reheat cycles
or to the next low pressure steam level through letdown valves.
Power can be generated by gas turbines, steam turbines and diesel engines or by
importing electricity from the utility grid.
For gas turbines, the following configurations are considered:
1. Simple gas turbine cycles.
2. Regenerative gas turbine cycles.
60
Chapter 5 Layout Screening and Optimisation
The gas turbine efficiencies are variable and depend on the gas turbine size, load and the
operating conditions. The exhaust gas may be used by a HRSG to generate steam.
For steam turbines, the following configurations are considered:
1. Back-pressure (BP) steam turbines.
2. Extraction BP steam turbines.
3. Condensing turbines.
Steam turbine efficiencies vary with the turbine capacity, type of exhaust, i.e.,
condensing or non-condensing, load, and the operating conditions. If a condensing
turbine is selected a condenser and a vacuum header have to be selected.
Steam can be returned as condensate. The return of condensate is collected in a
condensate header at a given pressure and saturated condition. Auxiliary units include
deaerator and pumps.
5.2 The Strategy
Systematic techniques are required to address the optimal configuration design of total
site utility systems under operational variations. The strategy that is proposed in this
work is schematically shown in Figure 5-1.
The approach combines the benefits of total site analysis, thermodynamic analysis and
optimisation techniques. The total site analysis technology is used to screen and identify
all possible design options. The thermodynamic analysis is applied to reduce the size of
the optimisation problem. Since the energy cost of a utility system is an overwhelming
factor in the analysis of each year's cost, the thermodynamic efficiency is used to guide
the selection of the main utility structures. This strategy has been applied successfully in
utility system design (Chou and Shih, 1987) and heat exchanger network design
(Linnhoff and Turner, 1981). The proposed strategy comprises the following five
stages:
61
Chapter 5 Layout Screening and Optimisation
1. The total site analysis is used to screen and identify all possible design options
2. The thermodynamic analysis is employed to screen among various design
alternatives and identifies the most promising design options that are passed on to
the next stage.
3. Based on the promising design options, this stage is to develop the detailed design
components for the superstructure that is much smaller than the conventional
superstructures. The components will be concerned with back-pressure steam
turbine network, condensing steam turbine network, reheat cycles, gas turbine
network, boiler network and auxiliary units.
4. The superstructure is optimised so as to minimise the total cost. The optimum model
is a result of the BHM, THM, CTHM and the GTHM applications and is formulated
as a multi-period MILP model.
5. The component back-pressure and condensing turbines are synthesised into practical
and complex turbines.
c;; site ana~)-----I.~ Possible design options
G;;odynamiC a~r----i.~ Promising design options
Superstructure generation (reduced size)
Synthesis of complex turbines
Figure 5-1: Schematic showing the configuration design optimisation strategy
62
Chapter 5 Layout Screening and Optimisation
5.3 Total Site Analysis
There are enormous number of candidate structures which include steam turbine cycles,
condensing turbine cycles, simple gas turbine cycles, regenerative gas turbine cycles,
combined steam and gas turbine cycles with or without condensing turbine, diesel
drivers, and all of their djfferent combinations.
The synthesis and design problem is to find a site utility system that satisfies the
chemical processes ' varying heat and power requirements, subject to minimum energy
consumption and capital investment. The method discussed in this work proposes that
the process heat requirements are satisfied first and the heat and power requirements are
matched exactly. This is particularly desirable for those industties that use a very large
amount of thermal energy such as the petrochemkal , food processing and the paper &
pulp (Chou and Shih, 1987).
VHP
HP
CW
Figure 5-2: Identification of steam turbines of a site by using the SCC
The Site Composite Curves (SCC) reflect on the integration opportunities between
chemjcal production processes and the site utjlity system. The curves can represent the
steam flow in the utility system as well as the heat exchange between site processes and
utilities (Figure 5-2). The enclosed shaded area between the steam levels is proportional
to the potential for power cogeneration . The curves also reveal the heat recovery, fuel
63
ChapterS Layout Screening and Optimisation
requirement and cooling utility demands of the site. Therefore, the see can be used as a
conceptual tool to screen and target the possible design options for the site utility
system. Figure 5-2 illustrates a possible allocation of back-pressure turbines with the
use of the see. The sizes and positions of the turbines can be identified using the
curves.
5.4 Thermodynamic Analysis
The objective of the thermodynamic analysis is to screen out the infeasible and
inefficient options. As it will be shown later in the chapter, The size and complexity of
the optimisation problem is reduced dramatically.
Heat and power represent energy of different quality. The thermodynamic efficiency is
defined by a relationship that determines the ratio of the useful part of the energy to the
total fuel input. The thermodynamic efficiency of a typical utility unit is defined by:
(5-1)
W is the shaft-work generated. L Qt is the sum of the steam heat loads required by the
chemical processes at different levels. Qfuel is the net fuel heat input. The
thermodynamic efficiency indicates fuel utilisation efficiency.
In the proposed work, the thermodynamic analysis is used to calculate the
thermodynamic efficiency of each potential utility structure and lead to the construction
of an overall efficiency curve. The curve accounts for all possible structures, assuming
that heat demands of the processes are satisfied first. The efficiency curve explains the
most appropriate combinations of the utility structures to be selected as the candidate
structures.
64
Chapter 5 Layout Screenillg alld Opti/'/'lisation
5.4.1 Thermodynamic Efficiencies and Utility Structures
Figure 5-3 illustrates the total site profiles of a pl ant. The possi ble utility structures
which satisfy the heat and power demands of the site processes are identified. T he
thermodynamic efficiencies of the corresponding utility structures are provided.
VHP
cw
Figure 5-3: Total site profiles of a plant
5.4.1.1 Integration of the Boiler and Back-Pressure steam Turbine (BBPT) cycle
The stearn crossing each expansion zone can be used by bac k-pressure steam turbines to
generate power (Figure 5-4). The VHF steam is raised by the VHF boiler. The
thermodynamjc efficiency is defined by the ratio of the useful energy (power outputs
and steam heat loads to processes) over the fuel consumption :
I wi + IQ/ I Q;" eI, i
(5-2)
where Wi is the shaft-work generated by the stearn turbine, Q/ is the steam heat load of
the steam turbine to processes and Q;',el,i is the net fuel heat input in boiler i.
65
Chapter 5 Layout Screening and Optimisation
Q ,
cw
Figure 5-4: Integration of the BBPT cycle
As shown in Figure 5-4, the exhaust heat of BP steam turbines can be used as process
heat, therefore the VHP steam load equals:
(5-3)
Substituting Equation (5-3) into Equation (5-2) gives:
(5-4)
where Tl rB is the thermodynamic efficiency of the boilers.
5.4.1.2 Integration of the Gas Turbine and Waste heat Boiler (GTWB) cycle
The GTWB cycle is shown in Figure 5-5.
66
Chapter 5 Layout Screening and Optimisation
F'
WB
GT
+ VHP
Figure 5-5: Integration of the GTWB cycle
The gas turbine is integrated with the waste heat boiler to generate power, and the waste
heat boiler is used to raise steam. It is assumed the gas turbine works at full load (i.e. ,
maximum efficiency load). The thermodynamic efficiency of the GTWB cycle is
defined as the ratio of the useful energy (the power output of gas turbine and the steam
load raised by the waste heat boiler) over the fuel consumption. It is calculated by:
(5-5)
where WG is the power output, QG is the steam load generated in the waste heat boiler
and pf is the fuel consumption . On the basis of the GTHM, the fuel consumption is
given by:
(5-6)
As presented by Cohen et al. (1987), the stack temperature is assumed as 170°C.
Therefore, the useful waste heat from the gas turbine to the boiler is:
67
Chapter 5 Layout Screening and Optimisation
(5-7)
T'ut can be calculated by using Equation (3-34).
The steam load of the boiler is given by:
G BQ Q = 11, waste (5-8)
where 1]/8 is the thermodynamic efficiency of the waste heat boiler.
5.4.1.3 Integration of the Boiler and Condensing Turbine (BCT) cycle
The BCT cycle is shown in Figure 5-6. As the exhaust heat of the condensing turbine is
lost to cooling water, the thermodynamic efficiency is defined by the ratio of the useful
energy (the power output of the condensing turbine) and the fuel requirement. It is
calculated by:
BCT We 11, =-QB
fuel
(5-9)
where We is the power output of the condensing turbine and Q~e1 is the fuel
consumption.
It is assumed that the condensing turbine works at full load. Hence, on the basis of the
CTHM, the relation between the power output and the steam load crossing the
condensing turbine is:
(5-10)
68
Chapter 5
The fuel requirement is given by:
a 1 Q juel =-a qM
'fit
Layout Screen.ing and Optimisation
(5-11)
where q is the specific heat load of the steam and 'fIta is the thermodynamic efficiency of
the boiler.
Combining Equations (5-9), (5-10) and (5-11), the thermodynamic efficiency of the
BCT cycle is given by:
(5-12)
Boiler
VHP VHP
+
VAC
Figure 5-6: Integration of the BeT cycle
5.4.1.4 Integration of the Gas Turbine, Waste heat Boiler and Condensing Turbine
(GTWBCT) cycle
The GTWBCT cycle is shown in Figure 5-7. When the gas turbine and waste heat boiler
cycle produces the amount of steam more than the steam requirements from the
processes, a condensing turbine can be integrated to the gas turbine and waste heat
boiler cycle to generate additional power by using the surplus heat. The thermodynamic
efficiency for the GTWBCT cycle is defined as the ratio of the useful energy (power
69
Chapter 5 Layout Screening and Optimisation
outputs of the condensing turbine and the gas turbine) over the fue l requirement. It is
calcul ated as follows:
GTWBCT We + W G
T] =----( F J t1H
J
(5-13)
where WC and WG are the power outputs of the condensing turbine and the gas turbine
respecti vely. WC is calculated by applying the CTHM and WG is calcul ated by the
GTHM.
F'
WB
Fa
GT VHP
+
VAC
Figure 5-7: Integration of the GTWBCT cyc le
5.4.1.5 Integration of the Surplus steam Condensing Turbine (SCT)
The SCT is defined as the condensing turbine using surplus steam from chemical
processes as shown in Figure 5-8. Condensing turbines can be integrated to the site
utility systems to generate power with the use of surplus heat.
As the SCT uses surplus heat, it should be considered as the first priority choice fo r
power generati on in the design problem provided that chemical processes have surplus
heat. In order to compare efficiencies of different SCT units, the thermodynamic
70
Chapter 5 Layout Screening and Optimisatioll
efficiency of the SCT is defined as the ratio of the power output to the surplus heat of
the processes. It is calculated as follows:
w surp surp _
llr - Q surp (5-14)
where Wsurp is the power output of the condensing turbine and Q surp is the surplus heat
of the chemical processes. The W urp can be calculated by using the CTHM.
VHP
ew~ VAC VAC
Figure 5-8: Integration of the SCT
5.4.1.6 Import of Power (lP)
There is always an option to import power from a utility grid. In order to compare the
efficiencies of the site utility systems with imported power, a thermodynamic efficiency
for importing power is included based on the principle of the Top Level Analysis
(Makwanna, 1997). It is assumed that the cost of Qrucl fuel can buy Wimp! power. The
imp0l1ed power efficiency is defined as:
. W impr C F
rJ"1Jpt = --= _ Q cP
fuel
(5-15)
where C F is the unit fuel price and cP is the unit power price.
71
Chapter 5 Layout Screening and Optimisation
The concept defined above provides us an efficiency for importing power, which can be
directly used for comparison with the thermodynamic efficiencies of utility structures.
5.4.2 The Thermodynamic Efficiency Curve
In order to identify the most efficient candidate structures, a Thermodynamic Efficiency
Curve (TEC) is constructed. The efficiency relates the utility structures of Section 5.4.1.
The efficiencies are computed following the discussions in Section 5.4.1. Given the
steam demand for each level, the calculations yield the thermodynamic efficiency and
the maximum power output for each possible design option. The TEC is presented
graphically in Figure 5-9. The vertical and horizontal axes respectively represent the
thermodynamic efficiency and the power requirement. The TEC is constructed by first
plotting the efficiency curve of units using surplus heat from chemical processes (SCT
in this case), whose length equals the maximum power capacity. The curve follows with
the other designs plotted one by one in a step downwards in terms of efficiency until
completion of options. In this case, the SCT and the BBPT cycles are the preferable
options, the GTWB cycle follows next and the GTWBCT cycle is itself followed by the
BCT cycle and the option to import power.
BBPT
GlWBCT I
I SCT I IP t-- [-~-' f~ ~-I(--J f[~~_~I ___ PB8PT~f'~~_}~_J _~~ __ Iuuu~
Ll ---------------�r-----~!--------+I----~I---------------~ ~ ~ Pc Po Power (MW)
Figure 5-9: The thermodynamic efficiency curve
The power requirement of the site determines the utility systems to consider. The
corresponding sizes of the units are identified and targeted with the use of the TEC; the
72
Chapter 5 Layout Screening and Optimisation
inefficient options are screened out. Superstructures are developed only using the
options enabled by the TEC. Figure 5-9 explains the case. Assuming a power
requirement P A, the SCT and the BBPT cycles are only allowed. The other inefficient
options are excluded. Assuming the power requirement from PA to PB, additional
considerations include a gas turbine and waste boiler cycle. The other options are
similarly screened out. The power capacity of the gas turbine is equal to the difference
between the power requirement and P A. Additional power requirement from PB to Pc
introduces the GTWBCT cycle. The power capacity of the cycle is equal to the
difference between the power demand and PB. Extending the power requirement from
Pc to PD includes the option for the BCT cycle. The capacity in power of the cycle is
equal to the difference between the power requirement and Pc. Beyond the power
requirement PD, the residual power has to be imported from the utility grid.
It should be understood the TEC is a screening tool based on thennodynamics and in
particular based on energy efficiency. Alternative tools can be designed to replace the
focus on energy efficiency by a focus on fuel to power ratios or other economic criteria.
In all cases, one should ensure the screening tool considers second and third-best
options. Alternatively, the TEC procedure can be relaxed by shifting the cut-off line of
the synthesis screening and let synthesis options with slightly lower efficiencies to also
become part of the superstructure.
So far, the TEC is discussed on the basis of a single operation scenario. Changes in the
steam and power demands will affect the TEC and suggest different utility structures.
For mUltiple operation scenarios, a systematic methodology is presented that makes use
of superstructure development.
5.5 The Generation of the Superstructure
The TEC is constructed for each operation scenario. The curves are applied to identify
candidate structures and capacities of the utility units. A systematic method is presented
to generate the superstructure for the site utility system and optimise for the best option.
73
Chapter 5 Layout Screening and Optimisation
5.5.1 Superset of Back-pressure Steam Turbines
The cogeneration potential available between the steam levels can be exploited through
a lot of combinations of turbine networks and layouts such as complex turbines,
multistage turbines, single turbines and so on. As discussed by Mavromatis and
Kokossis (1998b), both complex turbines and multistage turbines are equivalent to a
cascade of simple turbines, each taking up potential from a single expansion zone, as
shown in Figure 5-10. On the grounds of the equivalence, all possible combinations of
turbine layouts are reduced to a single superset of component cylinders as illustrated by
Figure 5-11. It is only this superset of design components that is required in order to
derive the optimum structure of back-pressure steam turbine network.
Figure 5-10: Complex turbines are considered as a cascade of simple turbines
The sizes of component turbines for each scenario are determined at the thermodynamic
analysis stage. For multiple operation scenarios the number and sizes of the simple
component cylinders for each expansion zone are identified by using the discretisation
method proposed by Mavromatis and Kokossis (1998b). The method suggests that the
turbines are sized to match the loads of every scenario as well as all their possible
combinations.
74
Chapter 5 Layout Screening and Optimisation
Figure 5-11: Decomposition of complex steam turbines
The case of two scenarios with the steam flows across an expansion zone is illustrated
in Figure 5-12. The first combination involves the select jon of turbine TI sized to the
scenario B, while operating at part load under scenario A. This option features the
lowest capital cost, but lower part load efficiency for scenario A. Alternatively, turbine
T2 can be installed to size scenario A. This option achieves the highest overal l
efficiency but requires the highest capital cost. In option 3, turbine T2 can be se lected,
along with turbine T3 sized to take up the remaining load for scenario B. The efficiency
for scenario B will be smaller than the first two options, but achieves the highe t
efficiency for scenario A and requires lower capital cost than the second option.
14--- Scenario B ScenarioA ~
HP E}gg § HP
Q MP MP
Superset of BP steam turbines
n 11 11 . .
""m'~"" ""'; " ""'~"""""" " ' '''''''''2?T~'''''''' '' ' :'' "" '[' "''' '''' '''' '' '' '' '''' '' 'Y'r''''''''' :·fi .. .. · .. ·j .. 1 : : T1 :: 2: T3:
· . . . . . · . . . . . · . . . . . · . . . . . l...-__ -'-. _---'-. -+ .. . .
Q Q Q
Option 1 Option 2 Option 3
Figure 5-12: The candidate BP steam turbines for the case of two scenarios
75
Chapter 5 Layout Screening and Optimisation
5.5.2 Superset of Gas Turbines
The capacity of the gas turbine for each scenario is determined by using the TEC. For
multiple operation scenarios the number, sizes and types of candidate gas turbines of the
superset depend on the specific problem, as explained in the following section.
5.5.2.1 Types of Gas Turbines in the Superset
The types of the gas turbine cycles are concerned with simple and regenerative gas
turbine cycles. The major difference between the simple and regenerative gas turbine
cycles is the addition of a recuperator for heat exchange between the turbine outlet and
the compressor outlet as shown in Figure 5-13. Following Chou and Shih (1987), the
types of the gas turbines are screened by the characteristic value of power to heat ratio,
PIH. Table 5-1 shows the ratio corresponding to each gas turbine cycle.
Heat -exchanger
Air
Compressor Turbine Power
Figure 5·13: The regenerative gas turbine
Gas turbine cycle PIH ratio
Simple gas turbine cycle 0.65
Regenerative gas turbine cycle 0.85
Table 5-1: P/H Characteristics of gas turbine cycles
76
Chapter 5 Layout Screening and Optimisation
5.5.2.2 Number and Sizes of Gas Turbines in the Superset
The GTHM relates the power output to the fuel load and the size of the gas turbine as
shown in Equation (3-33). As both the load and size of the unit need to be optimised,
straightforward modelling would result in an MINLP formulation. The discretisation
method follows next, however, reveals an MILP problem could be solved as the
economic analysis of the gas turbine operation suggests the discrete sizes and number of
the candidate gas turbines.
0.5
0.4 40MW 60MW
0.3 TJe
0.2
0.1
0 0 10 20 30 40 50 60
W(MW)
Figure 5·14: The effect of part load operation prevails over the increase of efficiency with gas
turbine size
As the electrical efficiency increases with size but decreases at part load, the highest
efficiency is obtained when a gas turbine is sized to operate at full load under the
specific power demands. This is shown in Figure 5-14. Hence, in terms of efficiency,
the optimum turbine size for each scenario is that which exactly matches the power
demand for each scenario. For multiple operation scenarios, the maximum efficient
sizes may not be the optimal sizes if capital cost is considered. Following the
discretisation scheme used for BP steam turbines, a discretisation method is proposed
whereby gas turbines are sized to match the power demand of every scenario as well as
all their possible combinations. The case of two scenarios with the power demands is
illustrated in Figure 5-15.
77
Chapter 5 Layout Screening and Optimisation
There are three combinations and three component gas turbines are identified. The first
option features the lowest capital cost, but lower part load efficiency for scenario A. The
second option achieves the highest overall efficiency but requires the highest capital
cost. In option 3, The efficiency for scenario B will be smaller than the first two
options, but achieves the highest efficiency for scenario A and requires lower capital
cost than the second option.
~ PB (MW) --+j t4- PA (MW) ~ I
DO PA D=cJo PB
G~
. . . . . . .
n .... j/ .................. ~ ... ~ ......... nr~ 1...-____ : __ + : : : :
PA PB P(MW) PA PB P(MW) PA PB P(MW) Option 1 Ootion 2 Option 3
Figure 5-15: Candidate gas turbines for the case of two scenarios
5.5.3 Superset of Boilers
The BHM is used to describe the performance of each fired boiler and waste heat boiler.
It is reminded that the BHM relies on the size of the boiler Mmax• The design model is
given by:
Qfuel = (C p!1Tsa, + q)«1 + b)M + aM max) (5-16)
The above expression relates the fuel flowrate with the steam load and the boiler size.
As both the steam load and the size of the boiler need to be optimised, the model results
in an MILP formulation by converting the bilinear model to a linear model.
78
Chapter 5 Layout Screening and Optimisation
Waste heat
Fuel . . .
VHP
Figure 5-16: Superset of boilers
The superset of the boilers is shown in Figure 5-16. The waste heat is the waste heat
from gas turbine cycles. The number, sizes and fuel requirements of the boilers are
detennined by the optimisation.
5.5.4 Superset of VHP Condensing Steam Turbines
The power output of the VHP condensing turbine for each scenario is determined with
the use of the TEes. In terms of efficiency, the optimum turbine size is the one that
exactly matches the power demand for a single scenario. For the mUltiple operation
scenarios, the maximum efficient sizes may not be the optimal sizes if the capital cost is
considered. The number and sizes of candidate condensing turbines of the superset for
multiple operation scenarios are determined by the discretisation scheme followed for
the gas turbines. The discretisation method is proposed for multiple operation scenarios
so that condensing turbines are sized to match the power demand of every scenario as
well as all their possible combinations.
The case of two scenarios is illustrated in Figure 5-17. There are three combinations and
three component condensing turbines. The first option features the lowest capital cost,
but lower part load efficiency for scenario A. The second option achieves the highest
overall efficiency but requires the highest capital cost. In option 3, The efficiency for
scenario B is smaller than the first two options, but achieves the highest efficiency for
scenario A and requires lower capital cost than the second option.
79
Chapter 5 Layout Screening and Optimisation
VHP
VAH
Superset of VHP condensing turbines
n
.. ··m~;,uu.T~ "~C~T ! uT'1····~CT~········ i·A····C···T·j·· : : CT: : : i : : 1; : : : · . . . . . · . . . . . · . . . . .
'------'----'--+
PA PB P(M'N) PA PB P(MW) PA PB P(M'N) Option 1 Option 2 Option 3
Figure 5-17: Candidate VHP condensing turbines for the case of two scenarios
5.5.5 Superset of Surplus Steam Condensing Turbines
The surplus heat of the processes for each level is obtained by total site analysis. The
optimum turbine size for each scenario exactly matches the surplus heat load. The
number and sizes of candidate surplus steam condensing turbines of the superset for
multiple operation scenarios are determined by the discretisation scheme followed for
the back pressure steam turbines. The discretisation method is proposed for mUltiple
operation scenarios so that condensing turbines are sized to match the surplus heat loads
of every scenario as well as all their possible combinations. The case of two scenarios
with the surplus heat loads is illustrated in Figure 5-18. There are three combinations
and three component surplus condensing turbines are identified.
80
Chapter 5
O~rp 0aurp P(MW)
Option 1
Layout Screening and Optimisation
IP
VAH
Superset of VHP condensing turbines
O~urp O~urp P[MW)
Option 2
O~urp 0Burp P(MW)
Option 3
Figure 5-18: Candidate surplus steam condensing turbines for the case of two scenarios
5.5.6 Reheat Cycles
In a reheat cycle, steam is first expanded to some intermediate pressure and then
reheated in the boiler. It next expands in the turbine to the exhaust pressure. Following
Chou and Shih (1987), the reheat cycle can improve the overall thermal efficiency only
if the thermal efficiency contributed by the reheat part is greater than that of the
remaining parts. The required large heat-exchange area and the increased complexity in
system design detract from the gain in efficiency due to reheating. The reheat cycle,
therefore, will be of interest to site utility system design only when a lot of heat is
exhausted to cooling water.
5.6 Optimisation Model
In thi s section , a mUlti -period MILP model is presented for the minimisation of capital
investment and operating cost. The model incorporates the BHM, THM, CTHM and the
GTHM models. The optimisation is a screening tool for the selected alternative design
81
Chapter 5 Layout Screening and Optimisation
options by using the thermodynamic analysis, rather than for the exhaustive structures.
The binary variables account for the selection of units and their operation status at each
scenario. The continuous variables relate to the stream flowrates (steam, fuel), the
power outputs and the operating and capital costs.
The optimisation problem involves the following definitions for sets, parameters and
variables:
Sets
IB = { ib I candidate boilers }
IT = { it I candidate BP steam turbines }
IC = { ic I candidate condensing turbines }
VC = { vc I candidate VHP condensing turbines }
p = { pi I power generation units }
I = { i I selected units}
IG = { ig I candidate gas turbines }
K = { k I operation scenarios}
Z = { z I expansion zones}
Parameters
a, b : regression parameters of BHM for boilers
Aic, Bic : regression parameters of CTHM for condensing turbines
Ag, Bg : regression parameters of GTHM for gas turbines
Az, Bz : regression parameters of THM for BP steam turbines of expansion zone z
Cp : specific heat of saturation water between Tin and Tout sat
cpg : specific heat of flue gas
Cpa : specific heat of air
ci : specific heat of fuel
EISic : isentropic enthalpy change of condensing turbine ic
EISz : isentropic enthalpy change of BP steam turbines of expansion zone z
F/,max : maximum fuel load of gas turbines Ig
H : operating hours per year
82
Chapter 5 Layout Screening and Optimisation
M-/i : specific enthalpy of gas turbine fuel reaction
LB : lower bound of boiler capacities
M i!'max : maximum steam load of boiler ib
M :.Tt·max : maximum steam load of BP steam turbine it of expansion zone z
M i?"'max : maximum steam load of condensing turbine ic
M ~.k : total steam load across each expansion zone z under scenario k
q : specific heat load of steam
r : temperature of inlet air of gas turbines
P : temperature of gas turbine fuel
AT:at : temperature difference between Tin and Tout sat
T/ : time fraction of scenario k
cf1 : upper bound of boiler capacities
U { : unit cost of fuel for boilers under scenario k
UfT,i : unit cost of fuel for gas turbines under scenario k
w/em : power demand of site processes under scenario k
Binary variables
Yi!·e : integers to denote the selection of boilers
y B•o : integers to denote the operation of boilers ib.k
yBT.e : integers to denote the selection of BP steam turbines Z.II
yBT.o : integers to denote the operation of BP steam turbines z.lI.k
Yi?,·e : integers to denote the selection of condensing turbines
/7.0 : integers to denote the operation of condensing turbines ic.k
ygT.e : integers to denote the selection of gas turbines
yGT.o : integers to denote the operation of gas turbines ig.k
83
Chapter 5 Layout Screening and Optimisation
Continuous variables
eE! : annual fuel cost of boilers
(fiT! : annual fuel cost of gas turbines
C·tot : total capital cost of selected units
C{ : capital cost for each unit
(;'01 : total annual cost
M i~.k : steam load of boiler ib under scenario k
M BT : steam load of BP steam turbine it under scenario k z.it.k
M i~ : steam load of condensing turbine ic under scenario k
M;:k : steam load of VHP condensing turbine vc under scenario k
M ;,k : amount of steam throttled through the let down valve of expansion zone z
under scenario k
Q B,J : fired fuel load of boiler ib under scenario k ih.k
QB.w : waste heat load from gas turbines to boiler ib in scenario k ih.k
QGT.w : waste heat load of gas turbine ig under scenario k ig,k
Fi{k : fuel load of gas turbine ig under scenario k
W BT : power output of BP steam turbine it of zone z under scenario k z.it,k
W/U)' : power import under scenario k
Wi;]' : power output of condensing turbine ic under scenario k
wi~I : power output of gas turbine ig under scenario k
5.6.1 Model Formulation
Given the parameters, sets and variables above, the design model includes consideration
for the following models:
84
Chapter 5 Layout Screening and Optimisation
(a) VHP boilers
The BHM yields:
The above bilinear model is replaced by the following mixed integer linear model:
(5-18)
Constraints include:
The above logical constraint denotes X i:.k equals M i:·rnax while the boiler is operating.
LB Y B.o < X B < U B B.o ib.k - ib.k - Y ib.k ' ib E IB, k E K (5-20)
The above logical constraint denotes X i:.k =0 while the boiler is not in operating status.
M~'rnax _y~.eUB <0 ibE IB ,b ,b -, (5-21)
(5-22)
The above logical constraints denote the boiler capacity should be zero if it is not
selected and the boiler capacity should be larger that its lower bound and smaller than
its upper bound.
(5-23)
The above logical constraint denotes the load of the boiler should be zero if it is off.
85
Chapter 5 Layout Screening and Optimisation
(5-24)
The above constraint denotes the load of the boiler shouldn't be larger than its capacity.
(5-25)
The above logical constraint denotes the boiler can't operate if it is not selected.
(b) Back-pressure steam turbines
The THM applied for the power output of a back-pressure steam turbine in zone z under
scenario k yields:
Z E Z, it E IT, k E K
(5-26)
If the turbine is not selected, it can't operate:
BT,o _ BT,e < 0 Z' IT k K Yz,it,k Yz,it - , ZE ,ltE ,E (5-27)
The load of the steam turbine shouldn't be larger than its capacity:
M HT _ Hr,oM HT,max < 0 Z' IT k K z.it.k Y z.it.k z,it -, Z E ,It E ,E (5-28)
( c) Condensing steam turbines
The CTHM applied for the power output of a condensing turbine under scenario k
yields:
86
Chapter 5 Layout Screening and Optimisation
W CT 6 1 (ElS Aic )(MCT 1 MCTmax era) ic k = -- if - CT ,'c t - - ic' Yit t' , , 5 B M. ,max '6 '
Ie Ie
iCE [C,kE K (5-29)
If the condensing turbine is not selected, it can't operate:
cr,o _ cr,e < 0 . IC k K Yic,k Yic -, ICE ,E (5-30)
The load of the condensing turbine shouldn't be larger than its capacity:
MCT - CT,oM CT•max < 0 . IC k K ic.k Yic,k ic -, IC E ,E (5-31)
(d) Gas turbines
The GTHM applied for the power output of a gas turbine under scenario k yields:
ig E IG,k E K (5-32)
Where the maximum fuel flowrate F;{maX can be calculated by Equation (3-30).
If the gas turbine is not selected, it can't operate:
GT.o _ yf?T,e < 0 ig E [G k E K Y,g,k 19 -, , (5-33)
The load of the gas turbine shouldn't be larger than its capacity:
Ff _yGT,OFf,max <0 igE [G kE K ,g.k 'g.k 'g -, , (5-34)
The waste heat from the gas turbine is given by:
87
Chapter 5 Layout Screening and Optimisation
GT,w _ [1 a a f f 1 1 ( A g ] f Qi k - -CpT +Cp T +Ml f -( +n)- Ml f - f ) Figk , igEIG,keK g, f Bg F ,max , Ig
(5-35)
(e) Steam mass balances
The mass balance across each expansion zone z for scenario k involves the steam
through the turbines and the steam throttled through the let down valves (in case the
installation of a turbine is not cost effective). The mass balances give:
L M :'Tr,k + M ~,k = M ~,k Z E Z, k e K (5-36) iteff
The VHP steam requirement is equal to the sum of the amount of steam across the first
expansion zone plus the amount of the steam through the VHP condensing turbines,
LMi!,k =Mtk + LM;:k' kE K ibelB vceVC
(j) Power balance
The electricity balance under scenario k is expressed as:
~w. +W buy =W dem kE K £.J pl,k k k' piEP
(g) Costs
The annual fuel cost of boilers is:
CB,f = LU! Qi!:{T/ H keK ibelB
88
(5-37)
(5-38)
(5-39)
Chapter 5 Layout Screening and Optimisation
The annual fuel cost of gas turbines is:
(5-40)
The capital cost incurred for the installation of the equipment is:
cc,tot = L CjC
jei (5-41)
The capital costs of the units are calculated using the functions presented by Bruno et
al. (1998). They are given in Table 5-2 along with linearized expressions for the boiler
cost. It is important to note that the discretisation methods (Section 5.5.2) treat the
capacities of the steam turbines, the gas turbines and the electric generators as
parameters in the optimisation model. Therefore, the nonlinear capital cost functions for
these units are applied.
Unit Type of Cost Function Investment Cost ($/year)
Large package boiler Nonlinear 4954p'·77fp2
F: steam flowrate (t/h) fp2=1.3794-0.5438P+0.1879p2
P: Pressure (MPa) Linear (9Mpa) 495384+13861F
Heat Recovery Boiler Nonlinear 941Ffgu.7)
Ffg: flue gas flowrate (t/h) Linear 6996+211.5Ffg
Steam turbine Nonlinear 2237WstU.41
W st: power (kW)
Gas turbine Nonlinear 952WgtU./b
Wgt: power (kW)
Electric generator Nonlinear 176Wegu.49
Weg: power (kW)
Deaerator Nonlinear 904FBu.Cll
FB: BFW Flowrate t/h
Table 5-2: Capital cost data (Bruno et al. t 1998)
89
Chapter 5 Layout Screening and Optimisation
(h) Objective function
The objective function minimises the total annual cost:
(5-42)
The total annual cost consists of the capital cost and the fuel cost.
5.6.2 Remarks and Discussion
The optimisation model consists of linear constraints and integer variables, and
comprises a multi-period MILP model. The structure and the operation strategy are
optimised to minimise the total cost consisting of capital cost and operating cost. The
development of the MILP model requires the following information:
(a) steam level specifications
(b) data on total site profiles for each scenario
(c) power demand for each scenario
(d) cost correlations for the utilities
(e) capital cost correlations for the units
It should be noted that the original problem is a Mixed Integer Non-Linear
Programming (MINLP) formulation with a very large number of variables. The use of
total site analysis and thermodynamic analysis has reduced the problem into a
reasonably sized.
5.7 Synthesis of Complex Steam Turbines
The outcome of the optimisation stage is a set of simple steam turbines and condensing
turbines. The simple turbines can be used to synthesise practical complex or multi-stage
90
Chapter 5 Layout Screening and Optimisation
turbines. The synthesis of the complex turbines relies on the operation schedule of the
simple turbines as provided by the optimisation stage. For two cylinders to merge into a
complex unit, they both have to be loaded during the same scenario. Depending on
whether the steam flow through the upper cylinders of a complex turbine is larger or
smaller than that in the lower sections, the turbines can be of an extraction or induced
type.
5.8 Case Studies
Two case studies are selected to illustrate the capabilities of the methodology. The
operating conditions of the four steam levels, the vacuum header and the de aerator are
shown in Table 5-3. The steam used for heating can be returned as condensate. The
difference between the two case studies relates to the utility demands. The cost data of
the utilities used are given in Table 5-4. The capital costs are given in Table 5-2.
Unit Operating Conditions
VHPHeader Saturation Temperature: 303°C
HPHeader Saturation Temperature: 275°C
MP Header Saturation Temperature: 210°C
LPHeader Saturation Temperature: 140°C
Vacuum Header Temperature: 60°C, Pressure: 0.02MPa
Deaerator Vent Ratio: 0.0015
Table 5·3: Summary of operating conditions
Demineralized Water Fuel (Natural Gas) Electricity
Temperature: 27°C LHV: 13856kWhffon
Cost: 0.24${fon Cost: 223${fon Cost: O.I$/kWh
Table 5·4: Utility data
91
Chapter 5 LAyout Screening and Optimisation
5.8.1 Case Study 1
The Site Utility Grand Composite Curves (SUGCC) of Figure 5-19 reflect the steam
demand/generation of the site under three operation scenarios. The power demands for
the scenarios are given in Table 5-5. On the basis of the SUGCC, the aim is to find the
optimal configuration of the site utility system that satisfies the utility demands and
minimises the annual total cost.
Scenario B ScenarlOC ScenorloA 260
180 VHP VHP HP
HP
VHPI==="""""-~~-..., HP
MP MP 130
30 50
LP LP
MPI-----=-=30=-=-0-------1
lP 60
VAC VAC VAC
HUh} H !h} H !h}
Figure 5·19: The SUGCC of a site
Scenario A Scenario B Scenario C
Power demand (MW) 22 35 42
Table 5·5: Power demands of Case 1
5.S. 1. 1 Total Site Analysis
The SUGCC are given in Figure 5-19. The steam across each expansion zone is
obtained in Table 5-6. LP steam is in surplus and used by the condensing turbines.
Back-pressure turbines are installed in the steam expansion zones VHP-HP and HP-MP.
The power outputs for the possible SCT and BBPT cycles are calculated and shown in
Table 5-7.
92
Chapter 5 Layout Screening and Optimisation
Scenario A Scenario B Scenario C
VHP-HP 180 220 260
HP-MP 130 260 300
MP-LP
LP-Vacuum header 30 50 60
Table 5-6: Steam amount across each expansion zone of Case 1 (tIh)
Scenario A Scenario B Scenario C
SCT(MW) 2.5 4.1 5
BBPT(MW) 13 22.9 26.7
Table 5-7: Power outputs of possible SCT and BBPT cycles of Case 1
5.8.1.2 Thermodynamic Analysis
The characteristic values of power to heat ratio of the site for the three scenarios are
presented in Table 5-8. The PIH values are lower than the characteristic value of the
simple gas turbine cycle. A simple gas turbine cycle is then employed instead of a
regenerative gas turbine cycle. By calculating the efficiency and the maximum power
output for every potential cycle, the TEC is constructed starting with the most efficient
option with the corresponding power capacity limit. The TECs for the three operation
scenarios are shown in Figure 5-20. On the basis of the TECs and the utility demands,
the promising candidate utility structures include the Boiler and Back-Pressure steam
Turbine (BBPT) cycles, the Surplus Condensing steam Turbine (SCT) cycles and the
Gas Turbine and Waste heat Boiler (GTWB) cycles. All the other design options are
screened out because of their lower efficiencies. By using the TECs, the power outputs
of the GTWB cycles are obtained for all scenarios as shown in Table 5-9.
93
Chapter 5
seT
2.5
,....
'JMW
lAyout Screening and Optimisation
Scenario A Scenario B Scenario C
PIH ratio 0.22 0.285 0.29
Table 5-8: PIH characteristics of Case 1
Sconarto A
, I , , I
~ ~ I=q ~ 6.5MN I
seT I--~l-. l
Scenario 8
GTWB
GTWIICT
IICT
~ I.~ ····_··········1 22.9MIN "l ....................... ~ ..... .
PIIAW)
ScenaloC
B8PT GT'M!
I GlWIICT
IICT
_G' .. 26,1WNI f---- --·-1 1 OJMW ~.
Figure 5-20: TECs for Case 1
Scenario A Scenario B Scenario C
Power output (MW) 6.51 7.98 10.32
Table 5-9: Power outputs of the GTWB cycles of Case 1
5.8.1.3 Generation of the Superstructure
On the basis of the steam amount across each expansion zone for each scenario,
candidate sizes of the BP steam turbines expressed as maximum steam capacities can be
obtained for each zone. The sizes are given in Table 5-10.
94
Chapter 5 Layout Screening and Optimisation
BTl BT2 BT3 BT4 BTs
VHP-HP 180 220 260 40 80
HP-MP 130 260 300 30 170
Table 5·10: Candidate sizes ofBP turbines of Case 1 (tIh)
Similarly, for every scenario the surplus heat provided by the processes determines the
candidate sizes of the condensing turbines. These are given in Table 5-11. The simple
gas turbines are used. Expressed in terms of power capacities, the candidate sizes of the
gas turbines are given in Table 5-12.
CTl CT2 CT3 CT4 CTs
Size (tJh) 30 50 60 10 20
Table 5·11: Candidate sizes of condensing turbines of Case 1 (tIh)
OTl OT2 OT3 OT4 OTs OT6
Capacity (MW) 6.51 7.98 10.32 1.47 3.81 2.34
Table 5·12: Candidate sizes of gas turbines of Case 1 (MW)
VHP boilers are fired by fuel and heated by the waste heat from the gas turbine cycles.
An HP waste heat boiler and an MP waste heat boiler recover surplus heat from the
processes. Without heat exhausted to cooling water, the reheat cycle is excluded as an
option. The superstructure of the site utility system is shown in Figure 5-21.
95
Chapter 5 Layout Screening and Optimisation
VHP
HP • __ -r ---.-.-.-----.-.. - ....
MP
LP
~~~-I Deaerator L-___ .
'-------"
--,......:I-__ ... __ ....z... CONDo
Figure 5·21: Superstructure of Case 1
5.8.1.4 Optimisation
The superstructure is formulated as an MILP model. The optimisation minimises the
total annual cost. The model is developed using GAMS and the optimisation is
conducted by employing the OSL solver. The model involves 195 continuous variables,
92 binary variables and 242 constraints.
The optimum configuration is given in Figure 5-22. The selected units include three BP
steam turbines, one condensing turbine, one gas turbine, a VHP boiler, an HP waste
heat boiler, an MP waste heat boiler and the de aerator. The HP and MP waste heat
boilers are selected to produce HP and MP steam respectively. One of the back-pressure
turbines operates between the VHP and HP levels. The other two back-pressure turbines
96
Chapter 5 Layout Screening and Optimisation
operate between the HP and MP levels. They supply power by exploiting the
cogeneration potential. The condensing turbine is employed to generate power by using
surplus heat from the site processes. The back-pressure turbines and the condensing
turbine do not meet the power demands. The gas turbine is installed to supply the
remaining power. The total annual cost is 33.341 MM$. The annual fuel cost is 27.718
MM$ and the annual capital cost is 5.623 MM$. The capacities of the selected units are
given in Figure 5-22.
Max360tfrl
I
I UDeoeratO'
Max lO.32MN
VHP
Max6.91MW
HP
Max 19.78MN
LP
Max4.99MW
.&...,... _________ VAC.
.....,...lIr..-_ ...... r..-__ .z.. COND.
Figure 5-22: Optimal structure of Case 1
The optimal loads of the units are obtained under each scenario. These are given in
Table 5-13. The back-pressure turbine BTl (HP-MP) operates during A, but not during
Band C. Turbine BT3 (HP-MP) operates during Band C, but not during A. During A
turbine BTl (HP-MP) is more efficient than turbine BT3 (HP-MP) and during Band C
97
Chapter 5 Layout Screening and Optimisation
turbine BT3 (HP-MP) is more efficient than turbine BTl (HP-MP). The HP waste heat
boiler shuts down during B and C because there is no waste heat during these periods.
All other units operate for all three scenarios.
Unit Scenario A Scenario B Scenario C
BT3 (VHP-HP) 180tlh 220tlh 260tlh
(steam load! power output) 4.36MW 5.64MW 6.91MW
BTl (HP-MP) 130tlh Otlh Otlh
(steam load! power output) 8.38MW OMW OMW
BT3 (HP-MP) Otlh 260tlh 300tlh
(steam load! power output) OMW 16.61MW 19.78MW
CT3 30tlh 50tlh 60tlh
(steam load! power output) 2.0MW 4.0MW 5.0MW
GT 3 (power output) 7.26MW 8.76MW 1O.32MW
VHP BI (steam load) 180tlh 220tlh 260tlh
HP WB (steam load) 50tlh Otlh Otlh
LP WB (steam load) 30tlh 50tlh 60tlh
Deaerator (water load) 21O.3t1h 31O.5t1h 360.5t1h
Table 5-13: Optimal loads of the units of Case 1
5.S.1.5 Synthesis of Complex Turbines
As shown in Table 5-14, no steam turbines have the same operation schedule.
Therefore, no complex turbines can be synthesised.
98
Chapter 5 Layout Screening and Optimisation
S.8.2 Case Study 2
The SUGCC account for the steam demand/generation of the site under the three
operation scenarios of Case 1. These are shown in Figure 5-19. The power demands for
this case are given in Table 5-14.
Scenario A Scenario B Scenario C
Power demand (MW) 12 25 30
Table 5-14: Power demands of Case 2
Based on the TECs of Figure 5-20 and the power demands, the candidate utility
structures include the Boiler and Back-Pressure steam Turbine (BBPT) cycles and the
Surplus Condensing steam Turbine (SCT) cycles. The other power units are not
economic and are excluded. The superstructure is shown in Figure 5-23 and is smaller
than the one studied in Case 1. The candidate sizes of the turbines are apparently the
same.
L---
I
~.~
;Deoeralor
VHP
HP
MP
LP
...:...._ ... .-.lI ..... __ .....&_ ..... _ VAC .
....,.-.lI ..... _--l'--__ .L CONDo
Figure 5-23: Superstructure of Case 2
99
Chapter 5 Layout Screening and Optimisation
The MILP model is optimised against the total annual cost. The model involves 97
continuous variables, 60 binary variables and 157 constraints.
The optimum configuration is shown in Figure 5-24. It includes two BP steam turbines,
one condensing turbine, one VHP boiler, one HP waste heat boiler, one MP waste heat
boiler and the deaerator. One back-pressure turbine operates between the VHP and the
HP steam levels. Another one operates between the HP and the MP steam levels. The
condensing turbine generates power using surplus heat from the site processes. There is
no need for a gas turbine. The total annual cost is 30.751 M$. It is lower than Case 1
because of the lower power demand. The annual fuel cost is 26.325 M$ and the annual
capital cost is 4.426 M$. The capacities of the units are given in Figure 5-24. The
optimal loads for each scenario are given in Table 5-15.
VHP t-::--, Max 5.78MN ~
HP
Max19.78MN
MP
LP
Max5.0MN
..z...,... ____ ..... ____ VAC.
--,......lI ____ .... __ ..&.. COND.
Figure 5-24: Optimal structure of Case 2
The back-pressure turbine BT2 (VHP-HP) and the turbine BT3 (HP-MP) maintain
identical operation schedules as shown in Table 5-15. Therefore, the two turbines can be
synthesised as a single complex turbine.
100
Chapter 5 Layout Screening and Optimisation
Unit Scenario A Scenario B Scenario C
BT 2 (VHP-HP) 180tlh 220tlh 220tlh
(steam load! power output) 4.52MW 5.78MW 5.78MW
BT3(HP-MP) 119t1h 243t1h 300tlh
(steam load! power output) 5.49MW 15.23MW 19.78MW
CT3 30tlh 50tlh 60tlh
(steam load! power output) 2.0MW 4.0MW 5.0MW
VHP B, (steam load) 180tlh 220tlh 260tlh
HP WB (steam load) 50tlh Otlh Otlh
LP WB (steam load) 30tlh 50tlh 60tlh
Deaerator (water load) 21O.3t1h 31O.5t1h 360.5t1h
Table 5·15: Optimal loads of the units of Case 2
5.8.3 Discussion
Although the SUGCC of the two studied cases are the same, the optimal configurations
of the site utility systems are different because of the different power demands. It
implies that different PIH ratios assume different optimal structures. By using the
proposed thermodynamic analysis, the reduced superstructure is obtained.
For Case 2, the MILP model is also optimised by integrating the gas turbine cycles into
the superstructure. The same optimal solution is obtained. However, the model involves
195 continuous variables, 92 binary variables and 242 constraints, which is much bigger
than the proposed method. If other possible design options are integrated with the
superstructure, the size of the optimisation problem should be even much bigger.
101
Chapter 5 Layout Screening and Optimisation
5.9 Conclusions
A systematic methodology is presented for the optimal design of site utility systems
under operational variations. The methodology combines the benefits of total site
analysis, thermodynamic analysis and optimisation techniques. The approach accounts
for the interactions between the site utility systems and the site processes. The design
task is addressed in view of the anticipated variations in the process demands and the
effect of the unit capacities and varying loads on the efficiencies of the selected units.
These aspects normally give rise to highly complex and large problems. The proposed
methodology utilises total site analysis and thermodynamic analysis to reduce the size
and complexity of the design problem. The total site analysis is employed to screen and
identify all possible design options. A thermodynamic curve is proposed in this
approach. It is a useful tool to identify the promising candidate design options to be
included in the superstructure by screening among all alternative design options. The
size of the optimisation problem can be reduced by screening out the uneconomic
design options.
By using the engineering knowledge and analytical insight, a discrete scheme is
proposed to identify the sizes of the candidate steam turbines, condensing turbines and
gas turbines. The optimisation problem is formulated as a mUlti-period MILP model that
relies on the THM, CTHM, GTHM and the BHM to describe the performance of the BP
steam turbines, condensing turbines, gas turbines and boilers. The models account for
the efficiency variations with operating conditions and capacity. It should be
emphasised that, had conventional models for the units been applied, the use of an
MINLP formulation would be inevitable.
102
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Chapter 6
Debottlenecking and Planning Optimisation of an Existing Site
6.1 Introduction
Industrial plants are in need for debottlenecking technology and planning techniques to
accommodate with the best investment scheme and their process operations (Hirsheld
1987). There are additional incentives and challenges for site utility systems. First, one
has to assess the potential for the purchase of new equipment. The challenge has to
consider a dynamic environment with changes in utility demands and prices, changes in
technology and changes in markets and regulations. The site utility system addresses a
particularly dynamic market. Changes consider the operation of the chemical processes,
changes in the feed/product specifications and the modifications in the schedule of
production.
The purpose of this chapter is to present a systematic debottlenecking and planning
methodology for site utility systems. The objective is to determine the best investment
scheme for an existing site and the optimal operational strategies to adopt. Options
consider the minimisation of the total cost so that utility demands are met by the
utilities.
The problem assumes a given utility system. Also given are forecasts for the prices and
demands of utilities, the ambient conditions and the regulations over a finite number of
time periods. The problem identifies a number of time periods of different duration. The
heat requirements are satisfied in preference to the power requirements. A
superstructure is developed that considers existing processes and potential new
equipment. The candidates for debottlenecking are generated with the use of total site
103
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
analysis and thermodynamics. The superstructure is formulated as an optimisation
problem that minimises the total cost over the given time horizon and determines:
• the new equipment to purchase: equipment include boilers, steam turbines,
condensing turbines, gas turbines, waste heat boilers and auxiliary units.
• optimal operational strategies over the considered period. The units are possible to
tum on and off and the approach considers different operating levels in the plant.
• the amount of fuel, the appropriate type of fuel, the amount of water and assesses
available options to import power.
Non-linear and bilinear models are converted to MILP models by using piecewise
linearisation and integer programming techniques. Non-linear cost models are used for
the steam and gas turbines.
Potential steam boilers include:
1. Heat recovery system generators (HRSG) for recovering heat contained in gas
turbine or furnace gases and for generating super heated very high-pressure (VHP)
steam. Supplementary firing is allowed in these units.
2. Fuel fired units for generating VHP steam.
3. Waste heat units for recovering heat from process flue gases or from process units
such as chemical reactors.
The approach makes use of the BHM, so that capacities of the boilers can be
determined, and the boiler efficiency appears to be a variable of capacity, heat load and
operating conditions.
Gas and steam turbines are considered as potential electricity generators. Options for
steam turbines include:
1. Back-pressure steam turbines exhausting to lower pressure levels.
2. Extraction back-pressure steam turbines exhausting to medium and low pressure.
3. Condensing steam turbines.
4. Multi-stage simple turbines.
104
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Complex turbines are decomposed into simple turbines and the use of the THM and
CTHM enables the turbine efficiency to vary with the turbine capacity, its load, the
operating conditions and the type of exhaust.
Options for gas turbines include:
(1) Simple gas turbines.
(2) Regenerative gas turbines.
By using the GTHM, the gas turbine efficiency remains variable and depends on the
turbine size, its load and the operating conditions. The exhaust flue gas is possible to
use by a HRSG to generate steam.
6.2 Optimisation Strategy
Efficient methodologies are required to address debottlenecking and planning
challenges for total site utility systems under operational variations. In this chapter, a
systematic strategy is proposed whose outline is schematically shown in Figure 6-1.
Optimisation of existing system
cr;;i site ana~)-----I •• Possible debottlenecking options
~odynamiC~ Promising debottlenecking OPtions
Superstructure generation (Existing system + promising debottlenecking options)
Synthesis of complex turbines
Figure 6-1: Outline of debottlenecking and planning strategy
105
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
The strategy comprises the following stages:
1. Optimise the existing system.
2. The total site analysis identifies the debottlenecking options that meet the variable
utility demands for the different periods.
3. The thermodynamic analysis screens out uneconomic options. A superstructure is
postulated out of the remaining candidates and includes the existing and new units.
4. The superstructure is formulated as an MILP model. The model minimises the total
cost and identifies the structure and the operational strategies to adopt. The
component back-pressure and condensing turbines are synthesised into practical and
complex turbines.
6.3 Stage I: Optimisation of the Existing System
The existing system is optimised for the maximum power output of the system over the
considered periods.
6.4 Stage II: Total Site Analysis
The Site Composite Curves account for integration between the site processes and the
site utility systems. Figure 6-2 shows the representation of a total site utility system that
uses the SCC. The shaded units are the candidates need to be installed; the others are
existing units. The capacities and the placement of the debettlenecking units are
possible to identify using the Sec.
In order to target the capacities of the potential steam turbines, one has to identify the
capacities of the existing complex turbines for each expansion zone. It is accomplished
by decomposing the complex turbines into sets of simple turbines with specific
capacities. A decompose strategy is presented following Chou and Shih (1987). Figure
6-3 illustrates a decomposition problem. The decomposition produces individual simple
turbines aJ, a2 and a3 which are of the same capacity. Similarly, simple turbines bi and
106
Chapter 6 Debottlenecking alld Planning Optimisation of an Existillg Site
b2 are of identical capacities. The decomposition strategy reduces the analysis at a level
where si mple turbines are only used.
VHP
cw
Figure 6-2: Identification of debottlenecking turbines of a site by using the S
Figure 6-3: Decomposing a complex turbine into different sizes of cylinders in eac h expansion
zone
107
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
6.5 Stage III: Thermodynamic Analysis
The debottlenecking includes options for boiler and back-pressure steam turbine
(BBPf) cycles, gas turbine and waste heat boiler (GTWB) cycles, boiler and
condensing turbine (BCT) cycles, gas turbine, waste heat boiler and condensing turbine
(GTWBCT) cycles, diesel drivers and option to import power (IP) from a utility grid.
The thermodynamic analysis screens out the inefficient options and identifies sensible
scenarios to include in a superstructure representation. After the thermodynamic
analysis the size of the problem is reduced dramatically.
6.5.1 The Thermodynamic Efficiency Curve for Debottlenecking
The basic idea is to employ the TEC first on the existing utility system and next with the
consideration of additional options.
BBPT Exis1ing System
GlWBCT
IP
PelOsi II~f1 PG1W8 1+1 PGTWBCT I-~I- --CD PA
PB Pc PD PE Power (MW)
Figure 6-4: Typical TEe for debottlenecking
The construction of the TEC is based on the assumption the heat requirements from the
chemical processes are satisfied before the power demands are considered. Efficient
debottlenecking options are identified by comparing the thermodynamic efficiencies.
Given is the steam demand at each steam level. Then, the thermodynamic efficiency and
the maximum power output are calculated for the existing system. The maximum power
108
Chapter 6 DebottLenecking and PLanning Optimisation of an Existing Site
output of the exi ting system IS calculated by optimising the existing system.
Calculations of efficiencies for the debottlenecking options follow the propositions of
Section 5.4.1. The de elopment of the TEC is shown in Figure 6-4. The first part (i.e.
"existing system") excludes new equipment. Subsequent parts account for new units.
6.5.2 Identification of the Promising Debottlenecking Options
The superstructure is de eloped on the basis of the options suggested by the TEe. In
reference to Figure 6-4 for example, a power demand to P A would imply the existing
system is sufficient to satisfy it. Figure 6-5 explains scenarios with power requirements
above P A and up to PB , it is necessary to invest on a new BBPT cycle. The additional
power can be targeted wi th the hardware capacity. The capacity equals the difference
between power requirement and P A. It is inefficient to explore other debottlenecking
options.
Til BBPT E»sIlng~ GlWB
p. P,
cw
Figure 6-5: The boiler and back-pressure turbine cycle for debottlenecking
Fi gure 6-6 exp lain cases of power requirements above PB and up to Pc. The gas turbine
and waste boiler c c le i required to consider as an additional option . The capacity of
the gas turbine hould be consi dered from the difference between the power requirement
and PB.
109
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
'l' bistro~S!em
P-
P,
66PT GTWB
GTWBCT
IP
P- P~~ ~ P, Po p. Ft>wer (MW)
F'
+ ~ ........ .
~",,"",,!;;=9 VHp:
HP
. .
........................................... . ........... •••• 1
Figure 6-6: The gas turbine and waste heat boiler cycle for debottlenecking
WB
Between Pc and Po as shown in Figure 6-7, the additional power should be available
from a GTWBCT cycle. The power capacity of the cycle should equal the difference
between the power requirement and Pc.
n.
WB
GT
BBPT ......................................................... GTWBCT
Fuel
BCT
VHP I:::::::::::.
-'~ I HP
~ ...................... .. .... ... ... ..................... 0.:
+
VAC
Figure 6-7: The gas turbine and waste heat boiler and condensing turbine cyc le for
debottlenecking
110
Chapter 6 Deboulellecking and Planning Optimisation of an Existillg Site
Similarly Figure 6-8 explains the picture between PD and PE. A BeT cycle should
produce the additional power. The power capacity equals the difference between the
power requirement and PD. Beyond PE, power should be imported from the utility grid.
BCT
r .......... ·~~~; .... · .. · ...... · .... · ...... · .. · .. · .. · ·~ WB
~ Fuel VHP!.
F"";;;;;;;!;=i +
GTWBCT VHP
HP
Iff Power (MW)
: C : ... ....................................... ................ : VAC
Figure 6-8: The boiler and condensing turbine cycle for debottlenecking
Figure 6-9 shows that if the chemical processes generate surplus steam, the surplus
condensing turbines can be integrated to generate additional power using surplus steam
for diffe rent levels.
VHP
I SSPT 11 E.omg $vslem
SCT
IP
~-[~} P, P, Power IMW)
VAC
Figure 6-9: Surplus condensing turbines for debottlenecking
III
Chapter 6 Debottlellecking and Planning Optimisation of all Existing Site
So far, the TEC is discussed to identify the most efficient debottlenecking options for a
single period operation . The discrete scheme presented in Section 5 .5 is applied to
generate the debottlenecking superstructure.
6.5.3 The Debottlenecking Superstructure
The superstructure consists of existing units and new units. The superstructure
development is schematically shown in Figure 6-10. The capacities of the
debettlenecking options are identified with the use of the TEC for each single operation
period and the discretisation schemes. The superstructure is modelled over all operation
periods.
+
Figure 6-10: Debottlenecking superstructure
112
Period n •.
Period 2
Pe riod 1
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
6.6 Stage IV: Optimisation
The postulated superstructure is formulated as an optimisation problem. It yields a
multi-period Mll..P model that is optimised for the minimum capital investment and
operating cost. The model incorporates the BHM, THM, CTHM and the GTHM
models. The MILP model is a screening tool with binary variables to represent the
selection of the new units and the operation mode of the units. The continuous variables
relate to the stream flowrates (steam, fuel), the power outputs and the operating and
capital costs.
The optimisation problem involves the definitions for sets, parameters and variables:
Sets
EB = { eb I existing boilers }
IB = { ib I candidate new boilers }
IT = { it I all BP steam turbines }
NT = { nt I candidate new BP steam turbines }
IC = { ic I all condensing turbines}
NC = { nc I candidate new condensing turbines }
VC = { vc I all VHP condensing turbines }
p = { pi I power generation units}
I = { i I selected new units }
IG = { ig I all gas turbines}
NG = { ng I candidate new gas turbines }
K = { k I operation periods }
Z = { z I expansion zones}
Parameters
a, b : regression parameters of BHM for boilers
A ic, Bic : regression parameters of CTHM for condensing turbines
Ag, Bg : regression parameters of GTHM for gas turbines
Az, Bz : regression parameters of THM for BP steam turbines of expansion zone z
113
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Cp : specific heat of saturation water between Tin and T outsat
Cp : specific heat of flue gas
Cpa : specific heat of air
Cp : specific heat of fuel
ElSie : isentropic enthalpy change of condensing turbine ic
ElSz : isentropic enthalpy changes of BP steam turbines in expansion zone z
F/'max : maximum fuel loads of gas turbines Ig
H : operating hours per year
Mlf : specific enthalpy of gas turbine fuel reaction
LB : lower bound of boiler capacities
M !.max : maximum steam load of boiler eb
M BT,'max : maximum steam load of BP steam turbine it in expansion zone z Z.I
M i;r·max : maximum steam load of condensing turbine ic
M ;,k : total steam load across each expansion zone z in period k
q : specific heat load of steam
r : temperature of inlet air of gas turbines
P : temperature of gas turbine fuel
!:IT:al : temperature difference between Tin and Tout sat
T/ : time fraction of period k
if : upper bound of boiler capacities
U f : unit cost of fuel for boilers in period k
U~T,J : unit cost of fuel for gas turbines in period k
w/em : power demand of site processes in scenario k
Binary variables
y!',~ : integers to denote the operation of boiler eb
yj~'O : integers to denote the operation of boiler ib
yB.e : integers to denote the selection of boiler ib ib.k
114
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Y BT.e : integers to denote the selection of BP steam turbine nt z.nI
y:::;:~ : integers to denote the operation of BP steam turbine it
y;;.e : integers to denote the selection of condensing turbine nc
yCl'.o : integers to denote the operation of condensing turbine ic ie.k
y~T.e : integers to denote the selection of gas turbine ng
yGT.o : integers to denote the operation of gas turbine ig ig.k
Continuousva~ks
cH! : annual fuel cost of boilers
cGT! : annual fuel cost of gas turbines
C·lot : total capital cost of the selected units
C{ : capital cost for each unit
Cot : total annual cost
M i!.k : steam load of new boiler ib in period k
M i!'rnax : maximum steam load of new boiler ib
M !.k : steam load of existing boiler eb in period k
M BT : steam load of BP steam turbine it in period k z.it.k
M i~ : steam load of condensing turbine ic in period k
M ;;:k : steam load of VHP condensing turbine vc in period k
M ~.k :amount of steam throttled through the let down valve of expansion zone z in
period k
QB,J : fired fuel load of new boiler ib in period k ib.k
Q B,J : fired fuel load of existing boiler eb in period k eb.k
QB.w : waste heat load from gas turbines to new boiler ib in period k ib.k
QB.w : waste heat load from gas turbines to existing boiler eb in period k eb.k
QGT.w : waste heat load of gas turbine ig in period k ig.k
115
Chapter 6 Debottlenecking and PLanning Optimisation of an Existing Site
Fi:,k : fuel load of gas turbine ig in period k
W BT : power output of BT steam turbine it in period k Z,il,k
W/UY : power import in period k
Wi;:I : power output of condensing turbine ct in period k
Wi~r : power output of gas turbine ig in period k
Wp~ : power output of power generation unit pi in period k
6.6.1 Mathematical Formulation
Given the parameters, the sets and the variables above, the model includes consideration
for the following models:
(a) VHP boilers (existing boilers and debottlenecking boilers)
Using the BHM, the fuel requirement of an existing boiler in period k is given:
The BHM is applied for the fuel requirement of a new boiler. As the boiler is optimised
both load and size, straightforward modelling with the BRM would result in the bilinear
tenn:
The above bilinear tenn is modelled instead as a mixed integer linear tenn:
116
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Logical constraints include:
M i!'max - U B (1- Y!::) :S X !,k 5 M !,max - LB (1- Yi!::)' ib E IB, k E K (6-5)
The above constraint denotes X :,k equals M ;!,max while the boiler is operating,
L B B ,0 < X B < U B B ,0 Y ib ,k - ib ,k - Y ib ,k ' ib E IB, k E K (6-6)
The above constraint denotes X :,k =0 while the boiler is not in operating status,
(6-7)
The above constraint denotes the boiler capacity should be zero if it is not selected.
(6-8)
The above constraint denotes the load of the boiler should be zero if it is off.
(6-9)
The above constraint denotes the load of the boiler shouldn't be larger than its capacity.
(6-10)
The above constraint denotes the boiler can't operate if it is not selected.
117
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
(b) Back-pressure steam turbines (existing and debottlenecking turbines)
Using the THM, the power output of a back-pressure steam turbine in zone z in period k
yields:
BT 6 1 W.I'I. =--(EIS. ... ~ 5 B
z -
A: )(M BT _'!"M BT•max BT.O) M BT.max :.it.k 6 :.il Y:.it.k'
Z,ll
Z E Z, it E IT, k E K
(6-11)
The logical constraints that relate the above model are:
Y:::: _y::e SO, zE Z,itE NT,ntE NT,kE K (6-12)
M BT BT.oM BT.max < 0 Z't IT k K :.i1.1: - Y:.il.k ;;.il -, Z E ,I E ,E (6-13)
(c) Condensing steam turbines (existing and debottlenecking turbines)
The power output of a condensing turbine in period k is given by the CTHM:
CT 6 1 S Aic )(M CT 1 M CT.max CT,o) Wid = ST(EI ic - M CT.max ic,k - 6 ic Yic.k'
Ie IC
iCE IC,kE K (6-14)
The logical constraints that relate the above model are:
YLT.·o - y;:.e ~O, iCE NC,nCE NC,kE K IC.~
(6-15)
M cr _ M cr.max cr ,0 < 0 . E IC k E K ie,/( ic Yie,k - ,IC , (6-16)
(d) Gas turbines (existing and debottlenecking turbines)
The power output of gas turbine ig in period k is given by the GTHM:
118
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
GT 1 W· k =-(Mlf Ig, Bg
The logical constraints relating to this model are:
GT.o GT,e <0 NG' NG k K Yig.k -Yng - ,nge ,lge ,e (6-18)
F' - F"max GT.o <0 . 1G k K ig.1: ig Yig.k - , 19 e I' , E (6-19)
The waste heat from the gas turbine can be obtained by:
(6-20)
(e) Steam mass balances
The mass balance across each expansion zone z in period k involves the steam through
the turbines and the steam throttled through the let down valves (in case the installation
of a turbine is not cost effective). The mass balances yield:
"LM:';;.k +M~,k =M~,k zE Z,ke K (6-21) ilErr
The VHP steam requirement is the sum of the amount of stream across the first
expansion zone plus the amount of steam through the VHP condensing turbines:
"LMi!.k + "LM!,k = Mtk + "LM;:k' kE K (6-22) ibEIB ebEEB vceVC
119
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
(f) Power balance:
The electricity balance in period k is expressed as:
~w W buy Wdi!m ~ pi.k + k = k ' kE K (6-23) pieP
(g) Costs:
The costs include the fuel cost of the utility system and the capital cost incurred for the
installation of the new equipment.
The annual fuel cost of boilers is:
CBJ = ~UIQ.BJr,sH+ ~UfQBJT,sH ~ k ib.k k ~ k eb.k k (6-24)
keK keK ibelB ebeEB
The annual fuel cost of gas turbines is:
CGT.! = ~ U GT.! pi r,s H ~ k Ig.k k (6-25)
keK igelG
The total capital cost of all new units is:
Cc,tot = Lct (6-26) iel
The capital costs of the units are calculated using the functions presented by Bruno et
al. (1998). They are given in the Table 5-2.
(h) Objective junction:
The objective function minimises the total annualised cost:
120
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
min C IOI = C B./ + CGT./ + ec,lol (6-27)
The total annual cost consists of the capital cost and fuel cost.
6.6.2 Solution Methods
The proposed model is an MILP problem and can be solved using a full space LP based
Branch and Bound method. A large number of the time periods however automatically
increases the size of the MILP model. The alternative approach followed in this work
solves the large MILP model using a decomposition algorithm such as the one proposed
by Iyer and Grossmann (1998). The algorithm is schematically shown in Figure 6-11.
The multi-period MILP is decomposed into a debottlenecking problem (Master
problem) and an operation-planning problem (Operation problem). Both problems are
formulated as MILPs. The master problem is a relaxed version of the original problem
in that it contains only a subset of its constraints and debottlenecking options. Its
solution provides a lower bound on the objective. The solution of the master problem is
used to set up the operation problem. The operation problem involves the
debottlenecking design options as they are fixed from the master problem. Its solution
provides an upper bound on the objective. Successive solution of these problems is
repeated until convergence criteria are met.
Original MILP model
1 .1 Master problem 1
~~"I (MILP) II---.-~
Structure cuts Tnal new structure
Operation problem (MILP)
Figure 6-11: Decomposition strategy
121
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
6.7 Cllse Studies
The methodology is illustrated with two examples. The first example considers a
debottlenecking and operation-planning problem. The second example considers an
industrial application.
6.7.1 Case Study 1
Figure 6-12 shows the configuration of an existing system. The current system consists
of a main boiler (Bl), two complex steam turbines (Tl and T2) and the de aerator. The
capacities of the units are shown in Figure 6-12. There are four steam levels (VHP, HP,
MP and LP). The operating conditions of the levels and the de aerator are shown in
Table 6-1. The steam is used for heating and can be returned as condensate. The utility
system should satisfy the heat requirements in preference to the power requirements.
Letdown steam from higher levels is available. There is no option to sell power. Ten
operating periods are considered, each one occupying 0.1 year. The utility demands are
shown in Table 6-2. The cost data are given in Table 6-3. The objective is to find the
optimal debottlenecking options and the operational planning for the site utility system.
VHP
HP
MP
LP
+ ,~Io-----
L-___ -..J
....,....&. __ :..-_--1. CONDo
i OeaeralOl , ,
Figure 6-12: The existing utility system of Case 1
122
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Unit Operating Conditions
VHPHeader Saturation Temperature: 303 °C,
Specific heat load: 0.557MWhlt
HPHeader Saturation Temperature: 270°C,
Specific heat load: 0.557MWhlt
MPHeader Saturation Temperature: 210°C,
Specific heat load: 0.557MWhlt
LP Header Saturation Temperature: 110°C,
Specific heat load: 0.557MWhlt
Deaerator Vent Ratio: 0.0015
Table 6-1: Summary of Operating Conditions of Case 1
Period 1 2 3 4 5 6 7 8 9 10
Power(MW) 25 35 50 55 45 60 55 60 63 56
VHP (tIh) 0 0 0 0 0 0 0 0 0 0
HP (tIh) 100 100 130 130 190 130 180 130 130 80
MP (tIh) 100 130 160 210 110 180 170 170 180 220
LP (tIh) 100 120 150 150 190 230 190 190 230 190
Table 6·2: Utility demands of Case 1
Fuel (Natural Gas) Electricity
LHV: 13856kWhlTon
Cost: 223$ffon Cost: O.1$IkWh
Table 6-3: Utility data of Case 1
123
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
6.7.1.1 Optimisation of the Existing System
The existing system is optimised for maximum power over the operation periods. The
results are given in Table 6-4.
Period 1 2 3 4 5 6 7 8 9 10
Power 28.2 35.5 46.4 46.4 45.4 46.4 46.4 46.4 46.4 46.4
Table 6-4: Maximum power generation of the existing system of Case 1 (MW)
6.7.1.2 Total Site Analysis
The amount of steam for each expansion zone is calculated from the steam demand data
of Table 6-2. The amount of steam across each expansion zone is given in Table 6-5.
Period 1 2 3 4 5 6 7 8 9 10
VHP-HP 300 350 440 440 490 540 540 490 540 490
HP-MP 200 250 310 360 300 410 360 360 410 410
MP-LP 100 120 150 150 190 230 190 190 230 190
Table 6-5: Steam amount across each expansion of Case l(tlh)
There is no surplus of steam at the available levels. Therefore, surplus condensing
turbines (SeT) are not considered for debottlenecking. The capacities of the
debottlenecking back-pressure turbines require the capacities of the existing turbines.
Turbine TJ is decomposed into Til and T)2. Turbine T2 is decomposed into T2J. T22 and
T 23. The capacities of the simple turbines are given in Table 6-6.
124
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Expansion zone Tll Tl2 T2l T22 T23
VHP-HP 80 90 50 70 150
HP-MP 90 70 150
MP-LP 150
Table 6-6: Capacities of simple turbines in every expansion zone of Case l(tlh)
The sizes of the potential steam turbines are determined by comparing the maximum
steam loads of the existing turbines and the total amount of steam across each expansion
zone. The capacities are given in Table 6-7.
Period 1 2 3 4 5 6 7 8 9 10
VHP-HP 0 0 0 0 50 100 100 50 100 50
HP-MP 0 0 0 50 0 100 50 50 100 100
MP-LP 0 0 0 0 40 80 40 40 80 40
Table 6-7: Capacities of potential steam turbines of Case l(tlh)
6.7.1.3 Thermodynamic analysis
Once the capacities are determined, efficiencies are calculated for the existing system
and the system with new units. The TECs are constructed for all periods. These are
given in Figure 6-13. On the basis of the TECs and the power demands, the options
should consider boiler and back-pressure turbine (BBPT) cycles and gas turbine and
waste heat boiler (GTWB) cycles. The capacities of the back-pressure turbines are given
in Table 6-7. The capacities of the GTWB cycles are given in Table 6-8.
125
Chapter 6
Period 1 '1. ExJsIing....-
-j 2S.2MW -, ' (MW]
Period 2
'1. Exlltrog .... _
--j ~~.~ f--_2
' (MW]
Period 3
'1. EJdIIIrQ .........
G1W1I
, G1W8CT H I I acT ~ : ,
'P
46.4MW 3.6MW
_3 P(MW]
Period 4
'1. EJdIIIrQ .........
4b.4MW
P(MW]
PeriodS
--j 46._ f- _._, _5 P(MW]
Debottlenecking and Planning Optimisation of an Existing Site
1].
1].
'1.
1].
Exlltrog .... _
'6._
ExIo1IrQ .... _
.•. -ExIatIrQ .... '.."
-- ~ '6._
ExIltIrQ .... _
46.4MW
Period 6 B6P!
, , , , , ,
b -.'(MW]
Period 7 asP!
, , , , , , , I 19.7MW I
!-TO-I _ 7 P(MW)
Period 8
, ,
i ~o_, d ~T ' , , , 7.'l'lMW H 'P , ,
~ ""TO ' 6 .61MW
, , , , , ,
_8
Period 9
asP!
Period 10
asP!
P(MW]
.---4"'6--:._=----,.10 ,,~ ~========~~~--~ _ '0 P(MW]
Figure 6-13: TECs for different operation periods for Case 1
126
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Period 1 2 3 4 5 6 7 8 9 10
Capacity 0 0 3.58 5.81 0 0 0 5.61 0 0
Table 6-8: The capacities of potential GTWB cycles (MW) of Case 1
6.7.1.4 Superstructure Development and Optimisation
The discretisation procedure (Section 5.5.1) is applied to determine the capacities and
number of the back-pressure turbines for debottlenecking. The capacities are given in
Table 6-9.
Zone BTl BT2
VHP-HP 50 100
HP-MP 50 100
MP-LP 40 80
Table 6-9: Capacities of candidate steam turbines of Case l(tIh)
From Table 6-8, the capacities of the gas turbines in periods 4 and 8 are close.
Therefore, the size 5.61 is dropped from the superset. The discretisation procedure
(Section 5.5.2) is used to determine capacities of the potential gas turbine and waste
heat boiler cycles. These capacities are given in Table 6-10. Hence, resulting
superstructure is generated and shown in Figure 6-14.
GTWB GT I GT2 GT3
Capacity 3.58 5.81 2.23
Table 6-10: Capacities of candidate GTWB cycles of Case l(MW)
The MILP model minimises the total annual cost. The model is developed using GAMS
(Brooke et al .• 1992) and the optimisation has been conducted by using the full space
search (Branch and Bound) as well as the proposed decomposition method (Section
6.6.2). The optimisation yields identical solutions. However the full space search
127
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
appears less efficient. Table 6-11 summaries the size of the original problem and the
decomposition result with respect to the subproblems discussed earlier.
Max2.23MW
VHP
HP
MP
LP
~I""""I-__ ..L.. __ -I.. CONDo
Figure 6-14: Debottlenecking superstructure of Case 1
Original problem Debottlenecking Operational planning
problem problem
0-1 variables 170 70 160
Cont. variables 379 370 379
Constraints 479 419 479
Table 6- 11: Summary of the problem size
128
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
The optimal structure is shown in Figure 6-15. It consists of three new back-pressure
steam turbines, one new gas turbine and a new waste heat boiler. The back-pressure
turbines exploit the cogeneration potential and since they are unable to generate enough
power the gas turbine and waste heat boiler are employed to address the remaining
power demands. The total annual cost is 59.77 M$. The annual fuel cost is 56.95 M$
and the annual capital investment cost is 2.82 M$. The resulting optimal capacities are
given in Table 6-12.
VHP
HP
Max90t/h Max 70tJh MP
Max l5Ot1h LP
COND.
Figure 6·15: Optimal structure of Case 1
129
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Unit Capacity
VHP-HPBT2 2.88MW
HP-MPBT\ 2.77MW
MP-LPBT2 8.20MW
Gas turbine GT2 5.81 MW
Boiler B2 100t/h
Table 6-12: Optimal capacities of the new units of Case 1
The optimal loads of all units are given in Table 6-13. Boilers Bl and B2 are operating
to raise steam in all periods because of the high steam demand from the site processes.
The steam turbines are employed to fully use the potential for cogeneration and generate
power to meet the demand of the site processes. The gas turbine is shut down unless the
power outputs of the steam turbines are unable to meet the demand for power.
Period 1 2 3 4 5 6 7 8 9 10
Til (t/h) 0 80 0 0 0 80 80 80 80 80
TI2 (t/h) 90 90 90 90 90 90 90 90 90 90
T2\ (t/h) 0 0 0 30 0 50 50 0 50 0
Tn (t/h) 0 0 70 70 70 70 70 70 70 70
T23 (t/h) 87 120 150 150 140 150 150 150 150 150
BT 2 (VHP-HP) (t/h) 100 60 100 100 100 100 100 100 100 100
BT I (HP-MP) (t/h) 23 40 0 50 0 50 50 50 50 50
BT 2 (MP-LP) (t/h) 13 0 0 0 50 80 40 40 80 40
BJ (t/h) 200 250 340 340 390 440 440 390 440 390
B2 (t/h) 100 100 100 100 100 100 100 100 100 100
GT2 (MW) 0 0 4.13 5.73 0 0 0 5.81 1.73 1.87
Table 6·13: Optimal operation of all units of Case I
130
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
6.7.2 An Industrial Case Study
The methodology is illustrated as it has been applied to an industrial complex. The
configuration of the site utility system is shown in Figure 6-16. The current system
consists of three main boilers (BI, B2, B3), two local boilers (PI and P2), six steam
turbines (Tl to T6, where TI, T5 and T6 are allocated turbines which are allocated to
some specific units of processes), one BFW pump and the deaerator. The capacities of
the units are given in Figure 6-16. There are five steam levels (VHP, HP, MP, LP and
VLP) and one vacuum level. Steam can be generated at two levels: very high pressure
(Bl, B2, B3 and P2) and high-pressure (PI). The operating conditions of the steam
levels and the de aerator are shown in Table 6-14. The steam used for heating is returned
as condensate. Letdown steam from higher levels is also available.
¢Jc;D . I .
I Condenser I
Figure 6-16: The existing utility system of the industrial case
131
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
The site utility system is connected with several chemical processes. There is no option
to sell power. The chemical processes are expanded in three periods and the utility
demands for each period are given in Table 6-15. The three periods span over 0.4, 0.3
and 0.3 year respectively. The power demands of the allocated turbines for each period
are given in Table 6-16. The cost data of the utilities are given in Table 6-17. The load
on the local boilers PI and P2 are 50tlh and 59.6 tIh respectively for all periods.
The current utility system can't satisfy the increasing heat and power demands of the
chemical processes. The optimum investment scheme for new units to be added into the
current system and the operational strategies are optimised so that the utility demands
are met at a minimum cost.
Unit Operating parameters
VHPheader Pressure: 12.1 Mpa, Temperature: 550°C
lIP header Pressure: 3.1 Mpa, Temperature: 236°C
MP header Pressure: 1.4 Mpa, Temperature: 195°C
LP header Pressure: 0.4 Mpa, Temperature: 144°C
VLPheader Pressure: 0.11 Mpa, Temperature: 110°C
Condenser level Pressure: 0.01 Mpa, Temperature: 50°C
Deaerator Pressure: 0.14 Mpa, Vent rate: 0.15
Table 6-14: Summary of operating conditions of the industrial case
Period Period 1 Period 2 Period 3
Electricity (MW) 168.6 239.1 338
VHP steam (tIh) 0 0 0
lIP steam (tIh) 171 181 220
MP steam (tIh) 133 183 267
LP steam (tIh) 108 159 170
VLP steam (t/h) 54 94 120
Table 6-15: Utility demands of the industrial case
132
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Period Period 1 Period 2 Period 3
Power demand of T 1 (MW) 1.6 5.4 0.0
Power demand of T5 (MW) 9.0 0.0 9.0
Power demand of T6 (MW) 30.8 35.5 43.0
Table 6-16: Power demands of the allocated turbines of the industrial case
Period Period 1 Period 2 Period 3
Demineralized water 0.47 $/ton 0.47 $/ton 0.47 $/ton
Electricity O.I$/kWh O.I$/kWh O.I$/kWh
Fuel cost of boiler 1 11.05 $/mmkcal 11.05 $/mmkcal 11.05 $/mmkcal
Fuel cost of boiler 2 11.22 $/mmkcal 11.22 $/mmkcal 11.22 $/mmkcal
Fuel cost of boiler 3 14.56 $/mmkcal 14.56 $/mmkcal 14.56 $/mmkcal
Fuel cost of gas turbine 245 $/ton 245 $/ton 245 $/ton
Fuel cost of new boiler 16.1 $lMWh . 16.1 $IMWh 16.1 $IMWh
Table 6-17: Utility cost data in different periods for the industrial case
Once the existing utility system is optimised, maximum power outputs and total steam
flowrates across expansion zones are determined for all operating periods. The results
are given in Table 6-18 and Table 6-19.
Period Period 1 Period 2 Period 3
Power output 172 172 172
Table 6-18: Maximum power generation of the existing system of the industrial case (MW)
133
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Steam zone Period 1 Period 2 Period 3
Zone 1 1204 1509 1852
Zone 2 991 1262 1538
Zone 3 748 939 1098
Zone 4 551 669 791
ZoneS 356 396 450
Table 6-19: Total steam flowrates across expansion zones for the industrial case (t/h)
For our case there is no surplus steam for the available levels. Therefore no condensing
turbines are considered for debottlenecking. To determine the capacities of the potential
back-pressure turbines, the capacities of the existing turbines are required. The
suggested capacities of the existing turbines in each steam zone are given in Table 6-20.
Tl T2 T3 T4 T5 T6
Zone 1 0 215 420 568 0 0
Zone 2 0 215 400 214 48 0
Zone 3 0 112 270 214 48 0
Zone 4 0 0 8 214 48 400
Zone 5 80 0 8 0 48 400
Table 6-20: Capacities of existing turbines in every expansion zone for the industrial case (t/h)
The maximum steam loads across the existing turbines and the total steam across the
expansion zones determine the capacities of the potential steam turbines. The capacities
are given in Table 6-21.
134
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Period 1 Period 2 Period 3
Zone 1 0 306 649
Zone 2 162 433 709
Zone 3 104 295 455
Zone 4 0 0 121
Zone 5 0 0 0
Table 6-21: Capacities of potential steam turbines for each period for the industrial case (tlh)
The discretization procedure of Section 5.5.1 suggests 3 candidate steam turbines in
zone 1 with capacities 306, 649 and 343 tlh. A total of 5 steam turbines are suggested
for zone 2 with capacities 162, 433, 709, 296 and 547 tlh. In zone 3 five turbines are
suggested with capacities 104, 295, 455, 351, 160 tlh. Zone 4 features a single capacity
of 121 tIh .
The development ofTECs is shown in Figure 6-17. The debottlenecking options include
the boiler and back-pressure turbine (BBPT) cycles and the gas turbine and waste heat
boiler (GTWB) cycles.
Perbd 1 Perbd 2 Period 3
'1. 1'1, ExIling.,.".", BBPI 1'1, ExlSr.g .,."""" 88P!
ExlSr.g .,."""" • GlWB ,
r I I I I I
H G1W8CT
I ~ ~T I I I I
:-, IP I I
InWi 1--1159 .4_ I'~ 7.7Wi --I 172 MIl In""" H
168.6_ P IMNj 239.1_ PI""")
Figure 6-17: Thermodynamic Efficiency Curves for the industrial case
The capacities of the GTWB cycles are presented In Table 6-22. The discretized
capacities include units of 6.6,62.1 and 55.5 MW.
135
PIWi)
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
Period 1 Period 2 Period 3
GTWB capacity (MW) 0 6.6 62.1
Table 6-22: Capacities of GTWB cycles for different periods for the industrial case
The synthesis superstructure is shown in Figure 6-18. The shaded units represent the
new units.
Figure 6-18: DebottIenecking superstructure of the industrial case
The MILP model minimises the total annual cost. The model consists of 166 binary
variables, 351 continuous variables and 462 constraints.
136
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
The optimal structure is shown in Figure 6-19. The solution includes seven new bac k
pressure steam turbines (NTI to NT7), two new gas turbines (OT1 and OT2) and one new
waste heat boiler (NB). The capacities of the units are given in Figure 6-19. As shown
in the Figure, two small gas turbines are selected instead of a bigger gas turbine. The
result contradicts conventional wisdom that would advocate a bigger turbine. For the
low power demands , the smaller gas turbine has higher efficiency than a big partly
loaded gas turbine. Simjlarly, in expansion zones VHP-HP, HP-MP and MP-LP two
small steam turbines are preferred instead of a bigger turbine. In periods 1 and 2 there is
not steam between the LP level and the VLP level and a single turbine is se lected to
exploit the cogeneration potential in period 3.
Max S7.SMW
Max20.3MW I
r.T • •
Max 6.1MW
[::j I
I Make-up wale, I
Figure 6·19: Optimal structure of the industrial case
137
Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site
The optimal loads are given in Table 6-23, Table 6-24 and Table 6-25. In period 1, the
existing system satisfies all power demand. The new steam turbines and the gas turbines
are all shut down. In period 2, some of the new steam turbines and the smaller gas
turbine are active. In period 3, the power demand reaches its maximum value. All
turbines are in use generating power to satisfy the additional power demand.
Unit Tl T2 T3 T4 IT5 T6 NT! NTz NT3 NT4 NT'! NT6 NT, Period 1 1.6 29.0 67.S 71.9 9.0 30.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0
Period 2 5.4 0.0 67.S 63.2 0.0 35.5 0.0 57.0 0.0 20.1 0.0 IS.1 6.1
Period 3 0.0 0.0 67.S 67.0 9.0 43.0 26.6 57.0 7.S 20.3 5.2 IS.1 6.1
Table 6-23: Optimal operation of all turbines of the industrial case (MW)
Unit PI P2 Bl B2 B3 NB
Period 1 50 60 170 425 550 0
Period 2 50 60 170 425 588 266
Period 3 50 60 170 425 588 610
Table 6-24: Optimal operation of all boilers of the industrial case (t/h)
Unit GT! GT2
Period 1 0.0 0.0
Period 2 6.6 0.0
Period 3 6.6 55.5
Table 6-25: Optimal operation of all gas turbines of the industrial case (MW)
138
Cluzpter6 Debottlenecking and Planning Optimisation of an Existing Site
6.B Conclusions
The chapter presents a systematic optimisation methodology for the optimal
debottlenecking and planning of site utility systems. Given forecasts for the demands
and prices of utilities, the approach determines investment schemes and schedules the
operation for maximum efficiencies.
A straightforward modelling effort results in a highly complex and large problem. A
new strategy is employed that combines advantages of total site analysis,
thermodynamics and mathematical optimisation. The total site analysis screens and
targets possible debottlenecking options. The thermodynamics excludes inefficient
options and the mathematical optimisation finalises the best structure and operation
options. The proposed methodology has been successfully used to solve an industrial
application.
139
Chapter 7 Total Site Maintenance Scheduling
Chapter 7
Total Site Maintenance Scheduling
7.1 Introduction
Maintenance assumes an important part in the operation of a total site system. It reduces
the risk of capacity outrage and improves the availability of units. The maintenance
scheduling problem minimises the overall operating cost over the given operating
period subject to maintenance and system hardware and reliability constraints.
Scheduling methods have been proposed by Chattopadhyay et al. (1995) and Dapazo et
al. (1975), but they only considered power systems and assumed identical maintenance
needs for the system units. A typical chemical plant usually consists of several chemical
production processes that consume heat and power in order to make products. The
central utility systems supplies the heat and power of the processes that in tum have to
shutdown and start-up allowing, sometimes significant changes in the demands. By
product fuels of site process units can also be used to generate heat and power enabling
strong interactions between the site utility system and the processes. The optimal
maintenance schedule of the site utility system and the process units consequently
allows for a simultaneous consideration of the options, as it is schematically shown in
Figure 7-1.
This approach assumes given shutdown, start-up and maintenance periods for each unit
and applies a multi-period MILP model to develop the optimal maintenance schedule.
The optimisation further determines optimal switches for the fuel and economic
schemes for power import/export. The maintenance periods are allowed to be different,
the optimisation considers the maintenance of the chemical processes and the site utility
system, and the decisions are made to minimise the total operating cost.
140
Chapter 7
Time
TotaL Site Maintenance Scheduling
Site uti lity system
Figure 7-1: Total site optimisation
7.2 Mathematical Model
Sets, parameters and variables are defined as fo llows:
Sets
EB = { eb I set of boilers}
I = { u, p I set of all units }
Ie = { ic I set of condensing turbines }
IG = { ig I set of gas turbines}
IT = { it I set of BP steam turbines}
K = { k I set of operation periods}
L = { I I set of steam levels }
p = { p I set of process units}
U = { u I set of utility units}
UF = { uf I set of units consuming fuel}
141
Chapter 7 Total Site Maintenance Scheduling
Parameters
a, b : regression parameters of BHM for boilers
: regression parameters of CTHM for condensing turbines
CEPk
CESk
CFuk,k
Cp
Cp Cpa
ci CWk
DIp
D2p
D3p
EISit
: regression parameters of GTHM for gas turbines
: regression parameters of THM for BP steam turbines
: unit cost of purchased electricity in period k
: unit cost of sold electricity in period k
: unit cost of fuel for unit uk in period k
: specific heat of saturation water between Tin and T outsat
: specific heat of flue gas
: specific heat of air
: specific heat of fuel
: unit cost of water in period k
: shutdown duration of process unit p
: maintenance duration of process unit p
: start-up duration of process unit p
: maintenance duration of utility unit u
: isentropic enthalpy change of condensing turbine ic
: isentropic enthalpy change of BP steam turbine it
Fj{max : maximum fuel load of gas turbine ig
Mil : specific enthalpy of gas turbine fuel reaction
M !,max : maximum steam load of boiler eb
MBT,rnax : maximum steam load of BP steam turbine it II
Mj;r'max: maximum steam load of condensing turbine ic
MINu : earliest time unit u can be taken for maintenance
MAXu : latest time unit u can be taken for maintenance
MINp : earliest time process unit p can be shutdown for maintenance
MAXp : latest time process unit p can be shutdown for maintenance
qeb : specific heat load of steam
yo : temperature of inlet air of gas turbines
T : temperature of gas turbine fuel
142
Chapter 7 Total Site Maintenance Scheduling
T/ : time duration of period k
I1T sal : temperature difference between Tin and Tout sat
eb.1:
Binary variables
Xu = 1 denotes the unit i is in operation in period k, otherwise Xi.k = 0
Yu.k = 0 denotes the utility unit u is on maintenance in period k, otherwise Yu.k = 1
Y1p.k = 0 denotes the process unit p is shutting down in period k, otherwise Y1p,k =1
Y2p.k = 0 denotes the process unit p is starting up in period k, otherwise Y2p.k =1
Y!.k = 1 denotes the boiler eb is in operation in period k, otherwise Y:b.(~ =0
y/~.o = 1 denotes the BP steam turbine it is in operation in period k, otherwise
YBT.o=o II.k
YeT = 1 denotes the condensing turbine ic is in operation in period k, otherwise ic.k
YeTk=o IC.
Y GT = 1 denotes the gas turbine ig is in operation in period k, otherwise Yf~gT.k·() =0 ig.k
Zu.k = 0 denotes the utility unit u starts its maintenance in period k, otherwise 2u.k = 1
ZIp.k = 0 denotes the process unit p starts shutting down for maintenance in period k,
otherwise 21 pj = 1
Z2p•k = 0 denotes the process unit p starts starting up in period k, otherwise Z2p.k = 1
Continuous variables
EDp.k : power demand of process unit p in period k
F f : fuel load of gas turbine ig in period k ig.k
FWk : water requirement of the utility system in period k
M B : steam load of boiler eb in period k "h.k
M B : steam load of boiler eb to steam level I in period k eh.l.k
Mi:~ : steam load ofBP steam turbine it in period k
M BT.I : steam load of BP steam turbine it to steam level I in period k it.l.k
M BT.O : steam load from steam level I to BP steam turbine it in period k if .I.k
143
Chapter 7 Total Site Maintenance Scheduling
M ft : steam load of condensing turbine ic in period k
M :.k : amount of steam throttled through let down valves to steam level I in period k
QB.! : fired fuel load of boiler eb in period k eb.k
QB.w : waste heat load from gas turbines to boiler eb in period k eb.k
QGT,W : waste heat load of gas turbine ig in period k ig,k
Quf,k : fuel requirement of unit uf in period k
SDp,l,k : I level steam demand by process unit p in period k
Wil~ : power output of BT steam turbine it in period k
W/UY : power import in period k
wi;,1' : power output of condensing turbine ic in period k
Wi~r : power output of gas turbine ig in period k
Wkexp
: power export in period k
7.2.1 Objective Function
The objective function minimises the total operating cost. The cost includes the fuel
cost, the boiler feed water cost and the electricity cost / revenue. It is expressed by:
min COST = L[ L CFuf.kQu/,k + LCWkFWk + LCEPkW:UY - LCESkWkexP 1r/ (7-1)
keK u/eUF keK keK keK J j
7.2.2 Performance Models
These include:
144
Chapter 7 Total Site Maintenance Scheduling
7.2.2.1 Utility Units
The utility models consist of:
(a) Boilers
The fuel requirement of each boiler in period k is provided by the Boiler Hardware
Model (Section 3.2):
The logical constraints that relate the above model are:
M!.1c -M!,maxY!,k :::; 0, ebE EB,kE K (7-3)
(b) Back-pressure steam turbines
The power output of each back-pressure steam turbine in period k is provided by the
Turbine Hardware Model (Mavromatis and Kokossis, 1998a):
BT 6 1 W'le = --(EISil '. 5 B
/I
.4;, )(M BT _! M BT.max BT) • IT k K M BT,max i/.k 6 il YiI,k' It E , E .,
(7-4)
The logical constraints that relate the above model are:
M BT BTMBT,max < 0 . IT k K i/.1e - Y iI.k il -, It E , E (7-5)
(c) Condensing steam turbines
The power output of each condensing turbine in period k is given by the Condensing
Turbine Hardware Model (Section 3.3):
145
Chapter 7 Total Site Maintenance Scheduling
WCT - 6_1_(ElS C _ A;~ )(M CT _.!..MCT,max CT) , IC k K ie,k - 5 Be ie M CT,max ie,k 6 ic Yic,k' IC E ,E
IC IC
(7-6)
The logical constraints that relate the above model are:
M CT _MCT,max CT < 0 ' IC k K ic,k ic Yic,k - , ~CE ,E (7-7)
(d) Gas turbines
The power output of each gas turbine in period k is given by using the Gas Turbine
Hardware Model (Section 3.4):
W GT 1 (M! Ag
)«1 + )F! Ff,max GT) ig,k = B g ! - F1,max n ig,k - n ig Yig,k'
Ig
The logical constraints relating to this model are:
F ! F! ,max GT < 0 ' IG k K ig,k - ig Yig,k - ,lgE ,E
The waste heat from the gas turbine can be obtained by:
ig E IG,kE K (7-8)
(7-9)
QGT,,,,=[~caTa+C!Tf+M! -(I+n)_I_(Mf - Ag )]F.! igEIG,kEK Ig,t f P P ! B g ! FI,max Ig,k'
Ig
(7-10)
7.2.2.2 Process Units
The utility demands of the process units are formulated as general functions of the
operation conditions (i,e, start-up, shut down) as follows:
146
Chapter 7 Total Site Maintenance Scheduling
The steam demand function of process unit p in period k is:
(7-11)
The power demand function of process unit p in period k is:
EDp.k = !edp.k(Ylp.k,Y2p.k,Dlp,D2p,D3p), pe P,ke K (7-12)
The by-product fuel function of process unit p in period k is:
(7-13)
7.2.3 Steam Mass Balances
Steam inputs at each team level include steam raised by boilers, steam exhausted from
BP steam turbines and steam throttled through let down valves. Steam outputs at each
steam level include steam loads to BP steam turbines and condensing turbines, steam
throttled through let down valves and steam loads to site processes. The mass balances
of all steam levels give:
"LM/:J.: +M:.k + "L M!.I.k = LMi:;'~ +M:+l.k + "LSDp.l.k' Ie L,ke K(7-14) i/Err ebEEB i/Err peP
7.2.4 Power Balance
The power balance in period k is expressed as:
L W,:r + L Wc7.I + "L Wi~r + WkbUY = LED p.k + wtP , k E K (7-15)
IIErr eleCT ige/G peP
147
Chapter 7 Total Site Maintenance Scheduling
7.2.5 Maintenance Constraints
The maintenance constraints include:
1. Maintenance period constraints:
Within a given time period, each unit is scheduled for maintenance for a period of a pre
specified duration.
Within a given time period from M1Nu to MAXu, utility unit u needs to start its
maintenance:
MAXu
LZu,k =MAXu -MINu' UE U k=MIN.
(7-16)
Within a given time period from MINp to MAXp, process unit p needs to shut down for
maintenance:
MAXp
LZ1 p,k =MAXp -MINp' pE P k=MINp
(7-17)
After shutting down and maintenance, process unit p needs to start up for operation. The
start-up should start in a time period between MINp + Dlp+D2p and MAXp+ Dlp+D2p:
MAX p+D1p +D2p
LZ2p,k =MAXp -MINp' pE P (7-18) k=MIN p +D1p+D2p
Beyond the given time period from MINu to MAXu, utility unit u doesn't start its
maintenance:
Zu.k = 1, k < MINu or k > MAXu (7-19)
148
Chapter 7 Total Site Maintenance Scheduling
Beyond the given time period from MINp to MAXp, process unit p doesn't shut down for
maintenance:
Z1 p,t = 1, k < MIN p or k > MAX p (7-20)
Beyond the time period from MINp + DIp+D2p to MAXp+ Dlp+D2p, process unit p
doesn't need to start up for operation:
(7-21)
2. Maintenance completion constraints:
Additional constraints ensure maintenance times span over the pre-specified
maintenance slots without any interruption. Once the unit maintenance starts, it
automatically occupies the time required for its completion.
The constraints are formulated as follows:
k
Yu.* = 1- k + LZu,j, 1:5 k :5 Du ,u E U j=1
k
Yu,k = 1- Du + LZu,j' j=k+I-D.
N is the total number of time periods
3, Shut down/start up completion constraints:
(7-22)
The constraints ensure that start up and shut down times develop within the appropriate
time, This means once time is allocated for shut down or start-up operation, the
operation complete without interruption,
149
Chapter 7 Total Site Maintenance Scheduling
The shutdown completion constraints are formulated as follows:
I:
Yl p ,l: = l-k + LZlp,}, 1 ~ k ~ Dl p ,pe P j=1
I:
Yl p,l: = 1-Dl} + L Zl p,} ,
}=Ie+l-D1p
DI p ~ k ~ N, peP
The start-up completion constraints are formulated as follows:
k
Y2 p ,A: = l-k + LZ2 p ,j, 1 ~ k ~ D3 p ,pe P j=1
Ie
Y2 L = 1-D3 . + ~ Z2 ., P,A } £J P,} D3 p ~ k ~ N, peP j=le+l-D3p
4. Logical constraints:
Before they shut down, process units cannot start up. Therefore,
k-1
D1p(1-Z2p,k)~k-1- LY1 p ,j' pe P,ke K j=1
After the maintenance of process units is completed, the units start up immediately:
Units under maintenance cannot operate:
Xi,k ~ Yu,k' iE U,u E U,k E K
150
(7-23)
(7-24)
(7-25)
(7-27)
(7-28)
Chapter 7 Total Site Maintenance Scheduling
5. Co-ordination constraints:
There is a maximum number of units that can be maintained in each period. Therefore.
L (1 - Yu,k ) :5; UMAX, k e K (7-29) ueU
UMAX = Maximum umber of utility units can be put on maintenance in one period.
6. Resource constraints:
A separate set of constraints ensure the resources assigned for maintenance is not
exceeding available limits:
where:
L(1-Yu,k)Ru,m ~ RESm,k' ke K,m = 1,2, ... M ueU
Ru,m = amount of resource type m required by unit u
RESm.k = amount of mth resource available in period k
M = number of resources
7.3 Maintenance Case Study
(7-30)
The optimisation model that is used for maintenance scheduling is illustrated with a
case study. Figure 7-2 shows the configuration of a total site. The site consists of four
steam levels, four boilers, five steam turbines, the deaerator and one gas turbine. The
utility system serves four process units. The capacities of the utility units are given in
Figure 7-2. The operating conditions of steam levels are shown in Table 7-1. The steam
used for heating can be returned as condensate. The process units operate in normal
conditions and the utility demands from each unit are given in Table 7-2. The utility
151
Chapter 7 Total Site Maintenance Scheduling
plant is interconnected with the utility grid. Cost data for the utilities are given in Table
7-3.
~ . ~- ....... -- ... . -....••... --- .. .
~--
VHP
HP
MP
: ! I I I I I l I !
LP
---------------------------------r------ -- ----------r------- -- .---------r--- - -------------)
Export/,mpn,9ctricitY " .---.l.-.!..L.!.....L...,
COND.
Figure 7·2: The configuration of a total site
Steam levels Operating Conditions
VHP level Temperature: 550 °C, Pressure: 121Bar
HP level Temperature: 236°C, Pressure: 31Bar
MP level Temperature: 195 °C, Pressure: 14Bar
LP level Temperature: 144 °C, Pressure: 4Bar
Table 7·1: Summary of operating conditions of the utility system
Thirty-six operating periods are considered, each occupying 10 days . The total time
hori zon is one year. Process and utility units all undergo maintenance. Process P4 takes
longer times to start up and shut down and this all has been taken into account by the
model. It takes Process P4 10 days to start up and 10 days to shut down . Maintenance
times are given in Table 7-4. No more than 5 units can be maintained at a given period.
152
Chapter 7 Total Site Maintenance Scheduling
The optimisation simultaneously determines the optimal maintenance and the optimal
operating schedules for the utility system and the process plant.
Process unit PI P2 P3 P4
Power(MW) 20 65 35 100
VlIP steam (tJh) 40 240 0 300
lIP steam (tJh) 40 60 0 400
MP steam (tJh) 0 0 50 200
LP steam (tIh) 0 0 150 100
Table 7-2: Utility demands of process units in normal operating conditions
Fuel used by B 1 Fuel used by B2 Fuel Used by Purchased Sold
B3 andGT electricity Electricity
0.OO98$/KwH O.OI$IkWh 0.0 13$IkWh O.l$IkWh 0.085$/kWh
Table 7-3: Utility cost data
Unit BI B2 B3 TI T2 T3 T4 Ts GT PI P2 P3 P4
Duration 20 20 20 20 20 10 20 10 20 10 10 10 30
Table 7-4: Maintenance times of all units (days)
The scheduling MILP model involves 1200 integer variables, 1320 continuous variables
and 2453 constraints.
The optimisation results are given in Figures 7-3 to 7-8. The minimum operating cost is
78.3 M$. The optimal maintenance and operation schedule is shown in Figure 7-3,
where shaded M-bars account for maintenance, I-bars for idle, St-bars for start-up and
Sh-bars for shutdown times. Processes PI, P2 and P3 are shut down for maintenance in
periods 26, 29 and 27 respectively. Process P4 is shut down in period 25. It is
maintained during periods 26, 27 and 28 and starts up in period 29. Most utility units
are maintained during the time processes are maintained. For example, during periods
153
Chapter 7 Total Site Maintenance Scheduling
26, 27, 28 and 29, PI, P2. P3 and P4 are down for maintenance. The optimal profile of
steam consumed by processes is given in Figure 7-4. Figure 7-5 explains the optimal
power consumption of processes. Figure 7-6 shows the optimal boiler operation and
Figure 7-7 gives the optimal turbine operation. The optimal power export profile is
shown in Figure 7-8. The power export is quite stable except for the periods where the
process and utility units are shut down for maintenance. No electricity import is
required during maintenance.
7.4 Conclusions
A multi-period MILP model is presented for the total site. The model can obtain a
minimum cost maintenance and operation schedule. The optimisation method
simultaneously considers the maintenance and the operation of the site processes and
the site utility systems. It is shown that interconnection mode of the utility system and
the process plant can lead to substantial changes in utility demand decisions and the
overall operating costs are reduced significantly. As the site processes start up and shut
down gradually. the start-up and shutdown models of site processes are incorporated in
the optimisation model. The model is capable of accounting for different maintenance
duration of operating units instead of same maintenance duration of the units proposed
by conventional methods. The practical maintenance constraints of industrial plants
have also been modelled in the proposed optimisation model.
154
ChapTer 7 Total Site MainTenance Schedfllillg
Period I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18
PI
P2
P3
P4
BI 1-
B2
B3
Tl
T2
T3 I I f/d' I I T I J I 1 I I I I I I
T4
T5 I I I I I I [ r J J J r [ I I I I
GT
Periods 19 ::w 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 !-
36 .-
PI i-
P2
P3
P'+ Sh
Bl
B2
B3
TI
T2
T3 T I I I I I I 1 I I I [ J J I I I
T-+
TS T I I I [ I T I I I f J I I r T
GT
~ Idle Mai nlenance Shut down Slarl -up D Operation
Figure 7-3: Optimal maintenance and operation schedule of all units
155
Chapter 7 Total Site Maintenance Scheduling
_ 700
~ 600 ,..... -+-VHP st. "0 500
c: ___ HP st. co 400 E CI) 300
~ ;\0( MP st.
"0
E 200 a LP st. co 100 CI) -en 0 0 6 12 18 24 30 36
Time (10 days)
Figure 7-4: Optimal profile of steam consumed by processes
_ 300
~ 250 -"0 200 c: co 150 E CI)
100 "0 ...
/ \ 1 ~ ~ ~
CI) 50 ~ 0 a a..
o 6 12 18 24 30 36
Time (10 days)
Figure 7-5: Optimal power consumption profi Ie of processes
700 J? 600 I e. 500 ~.~ ..... ., '\0 I~
-+-B1 ell r. ...... ,.,~ ... io, ...... A .. ".:.~ ..... 1,J .. • ......... ,. ..... 1 ~ ___ B2 ~ 400 I i 0 -= 300 II" B3 ... .!! 200 HRSG '0 100 T In \ ~rv~ 0
0 6 12 18 24 30 36
Time (10 days)
Figure 7-6: Optimal boiler operation
156
Chapter 7
c 0 :;::
C'::S ... G) c G) C) ... G)
:: 0 Q.
Total Site Maintenance Schedulillg
120
100 O\)()()ooOOOOOOOOOOOv '.,. ~, )(tOE
I 80 r
60
I 40 ~ ...
20 I~ ~V /
0 ~~- . - ... .. .. - .. ....
0
120
~ 100 ~
~ 80
&. 60 >< 4) ... 40 ~ 20 o Il. 0
6 12 18 24 30 36
Time (10 days)
Figure 7-7: Optimal turbine operation
.... . ~ T\ J I \
t ~
o 6 12 18 24 30
Time (10 days)
Figure 7-8: Optimal power export profile
157
-+-T1
--T2
T3
T4
-.-T5
-+-GT
36
Chapter 8 Conclusions and Future Work
Chapter 8
Conclusions and Future Work
8. 1 Introduction
This chapter consists of two parts. The first part summarises the work presented in this
thesis. The second part gives some suggestions for future work.
8.2 Conclusions
An integrated approach has been proposed for the analysis and optimisation of total site
utility systems. The approach makes combined use of total site analysis, thermodynamic
analysis and mathematical optimisation techniques, in order to provide a comprehensive
solution to a multi-faced problem. A systematic methodology has been presented for the
design of total site utility systems, with particular emphasis on the anticipated
operational variations. In addition, the approach has proposed systematic optimisation
methods to address the debottlenecking and planning of site utility systems as well as
the maintenance scheduling of total sites.
8.2.1 Design of Total Site Utility Systems
A set of hardware models CTHM, BHM and GTHM are proposed. The use of the
models for the analysis and optimisation of site utility systems are explained in the
work. The models combine thermodynamic principles, engineering knowledge and
performance data for condensing turbines, boilers and gas turbines. They enable for an
158
Chapter 8 Conclusions and Future Work
accurate prediction of unit efficiencies and embody the efficiency trends of realistic
units in terms of their variation with capacity, load and operating conditions. These
effects are accounted for in a simple and linear fashion, the importance of which are
illustrated in the work.
The hardware models CTHM, BHM and GTHM provide results of good accuracy, by
considering the dependence of the efficiency on the capacity and operating conditions.
In view of operational variations, the effect of the part-load operation is well accounted
for all these models.
With respect to the analysis and optimisation problem, the CTHM, BHM and the
GTHM models provide the basis for modelling the condensing turbines, boilers and gas
turbines respectively in a manner that the efficiency trade-offs of the various design
alternatives can be considered. The linear relations of the power output to the steam
load of condensing turbines, the steam load to the fuel requirement of boilers and the
power output to the fuel requirement of gas turbines are essential for simple
formulations for the optimisation of site utility systems.
A powerful optimisation methodology is proposed to address the needs of the
preliminary steam level selection for the total site system under operational variations.
By exploiting engineering knowledge, the BHM and THM models are capable of
predicting the real efficiency trends of units, by considering the dependency of the
efficiency on load and operating conditions. The application of the two models are
particularly important in the case of multiple operation scenarios, where the steam loads
and the respective efficiencies may vary significantly. By exploiting total site analysis
techniques, a new transhipment network is developed to represent the total site system.
It can be used to describe the interaction between the placement of steam levels and
steam loads of site processes. Based on the transhipment representation and combined
with the BHM and THM models, a multi-period MILP model is applied to minimise the
total utility cost for the total site under multiple operation scenarios. Major decision
variables include the overall fuel requirement, the cogeneration potential and the
cooling utility demand. The MILP model is a general model which can not only be used
159
Chapter 8 Conclusions and Future Work
for the Minimum Utility Cost (MUC) case but also for the Minimum Fuel Requirement
(MFR) case.
As regards configuration design of site utility systems under operational variations, a
systematic methodology has been developed. The methodology combines the benefits
of total site analysis, thermodynamic analysis and optimisation techniques. The
approach accounts for the interactions between the site utility systems and the site
processes. The design task is addressed in view of the anticipated variations in the
process demands and the effect of the unit capacities and varying loads on the
efficiencies of the selected units. These aspects normally give rise to highly complex
and large problems. The proposed methodology utilises total site analysis and
thermodynamic analysis to reduce the size and complexity of the design problem. The
total site analysis is employed to screen and identify all possible design options. A
thermodynamic curve is proposed in this approach. It is a useful tool to identify the
promising candidate design options to be included in the superstructure by screening
among all alternative design options. The size of the optimisation problem can be
reduced by screening out the uneconomic design options.
By using the engineering knowledge and analytical insight, a discrete scheme is
proposed to identify the sizes of the candidate steam turbines, condensing turbines and
gas turbines. The optimisation problem is formulated as a multi-period MILP model that
relies on the THM, CTHM, GTHM and the BHM to describe the performance of the BP
steam turbines, condensing turbines, gas turbines and boilers. The models account for
the efficiency variations with operating conditions and capacity. It should be
emphasised that, had conventional models for the units been applied, the use of an
MINLP formulation would be inevitable.
8.2.2 Debottlenecking and Planning Optimisation of the Existing Site
A systematic optimisation methodology has been presented for the optimal
debottlenecking and planning of site utility systems. Given forecasts for the demands
160
Chapter 8 Conclusions and Future Work
and prices of utilities, the approach determines investment schemes and schedules the
operation for maximum efficiencies.
A straightforward modelling effort results in a highly complex and large problem. A
new strategy is employed that combines advantages of total site analysis,
thermodynamics and mathematical optimisation. The total site analysis screens and
targets possible debonlenecking options. The thermodynamics excludes inefficient
options and the mathematical optimisation finalises the best structure and operation
options. The proposed methodology has been successfully used to solve an industrial
application.
8.2.3 Total Site Maintenance Scheduling
A multi-period MILP model is presented for the total site. The model can obtain a
minimum cost maintenance and operation schedule. The optimisation method
simultaneously considers the maintenance and the operation of the site processes and
the site utility systems. It is shown that interconnection mode of the utility system and
the process plant can lead to substantial changes in utility demand decisions and the
overall operating costs are reduced significantly. As the site processes start up and shut
down gradually, the start-up and shutdown models of site processes are incorporated in
the optimisation model. The model is capable of accounting for different maintenance
duration of operating units instead of same maintenance duration of the units proposed
by conventional methods. The practical maintenance constraints of industrial plants
have also been modelled in the proposed optimisation model.
8.3 Future Work
The following recommendations for future work are made:
In the design problem of this thesis, it is assumed that the design conditions of site
processes are fixed. However, the design of site processes without simultaneously
161
Chapler8 Conclusions and Future Work
considering the design of site utility systems may not be the optimal design in total site
context. There is a need for a methodology making simultaneous design of site
processes, heat exchanger network and site utility system under operational variations.
The debottlenecking and planning methodology presented has concentrated on site
utility systems. Apparently, the modifications in the design of site processes result in
changes in the utility demands, the debottlenecking and planning method can be
extended to account for the modifications in the design of site processes.
The simple models of site processes are applied in the total site maintenance scheduling
approach. More rigorous models of site processes need to be developed.
Finally, due to growing environment concern on the fuel-related emissions, there is a
need to develop an efficient methodology for the design and operation of total site
utility systems under operational variations to reach emission limits at a minimum total
cost.
162
References
References
AI-Khamis, T.M., Vemuri, S., Lemonidis, L. and Yellen, 1., 1992, Unit maintenance
scheduling with fuel constraints. IEEE Transactions on Power System 7,933-939.
Brooke, A., Kendrick, D. and Meeraus, A., 1992, GAMS: A User Guide, Release 2.25,
The Scientific Press.
Bruno, J.c., Fernandez, F., Caste]]s F. and Grossmann I.E., 1998, A rigorous MINLP
model for the optimaJ synthesis and operation of utility plants. Chemical Engineering
Research & Design 76, 246-258.
Chattopadhyay D., Bhattacharya K. and Parikh J., 1995, A systems approach to least
cost maintenance scheduling for an interconnected power system. IEEE Transactions on
Power System 10,2002-2007.
Chen, L.N. and Toyoda, J., 1990, Maintenance scheduling based on two-level
hierarchical structure to equalize incremental risk. IEEE Transactions on Power System
5, 1510-1516.
Chou, c.c. and Shih Y. 1987, Thermodynamic approach to the design and synthesis of plant utility system. Ind. Engng. Chem. Res. 26, 1100-1108.
Church, E.F., 1950, Steam Turbines, McGraw-Hill Book Company.
Cohen H., Rogers G.F.C. and Saravanamuttoo H.I.H., 1987, Gas turbine theory,
Harlow: Longman Scientific & Technical.
163
References
Colmenares, T.R. and Seider, W.D., 1989, Synthesis of utility systems integrated with
chemical processes. Ind. Eng. Chern. Res. 28, 84-93.
Dhole, V.R. and Linnhoff, B., 1992, Total site targets for fuel, co-generation, emissions
and cooling. Comput. Chern. Engng 17, s101-s109.
Dopazo J. F., and Merrill H. M., 1975, Optimal generator maintenance scheduling using
integer programming. IEEE Transactions on Power Apparatus and System PAS·94,
1537-1545.
EI-Masri, M.A., Magnusson, I.H.I., 1984, Thermodynamics of an isothermal gas
turbine combined cycle. Eng. Gas Turbines Power 106, 743
Garginkel R.S. and Nemhauser G.L., 1972, Integer Programming. Wiley, New York.
Hirshfeld, 1987, Mathematical programming and planning, scheduling and control of
process operation. FOCAPO Coni, Parkcity.
Hui, C.W. and Natori, Y., 1996, An industrial application using mixed integer
programming technique: a multi-period utility system model. Computers Chern. Engng
20, sI577-s1582.
Huang, S.l., 1998, A generic-evolved fuzzy system for maintenance scheduling of
generating units. International Journal of Electrical Power & Energy Systems 20, 191-
195.
Ito K., Yokoyama R., Akagi S. and Matsumoto Y., 1990, Influence of fuel cost on the
operation of a gas turbine-waste heat boiler cogeneration plant. ASME Journal of Eng.
for gas turbines & power 112, 122-128.
Iyer, R.R. and Grossmann I.E., 1997, Optimal Multiperiod operational planning for
utility systems. Computers Chern. Engng 21, 787-800.
164
References
Iyer, RR and Grossmann, I.E., 1998, Synthesis and operational planning of utility
systems for multiperiod operation. Computers Chern. Engng 22, 979-993.
Linnhoff, B. and Turner, I.A., 1981, Heat recovery networks: New insights yield big
savings, Chemical Engineering 88, 56-70.
Maia, L.O.A. and Qassim, RY., 1997, Synthesis of utility systems with variable
demands using simulated annealing. Computers Chern. Engng 21, 947-950.
Makwana, Y., 1997, Energy retrofit and debottlenecking of total sites. Ph.D. thesis,
Dept. of Process Integration, UMIST, Manchester, UK.
Marechal, F. and Kalitventzeff, B., 1996, Targeting the minimum cost of energy
requirements: a new graphical technique for evaluating the integration of utility
systems. Computers Chern. Engng 20, s225-s230.
Marechal, F. and Kalitventzeff, B., 1998, Process integration: selection of the optimal
utility system. Computers Chern. Engng 22, sI49-s156.
Mavromatic, S.P. and Kokossis, A.C., 1998a, Conceptual optimisation of utility
networks for operational variations - 1: Targets and level optimisation. Chern. Eng. Sci.
53, 1585-1608.
Mavromatic, S.P. and Kokossis, A.c., 1998b, Conceptual optimisation of utility
networks for operational variations - 2: Network development and optimisation. Chern.
Eng. Sci. 53, 1609-1630
Moro, L.M. and Ramos, A., 1999, Goal programming approach to maintenance
scheduling of generating units in large scale power systems. IEEE Transactions on
Power System 14, 1021-1027.
165
References
Morton, RJ. and Linnhoff, B., 1984, Individual process Improvements in the context of
site-wide interactions. IChemE Annual Research Meeting, Bath, UK.
Nath, R. and Holliday, J., 1985, Optimizing a process plant utility system. Mechanical
Enginreering 44, 44-50.
Nishio, M., 1977, Computer aided synthesis of steam and power plants for chemical
complexes. Ph.D. thesis, The University of Western Ontario, London Canada.
Nishio, M, Itoh, J., Shiroko, K & Umeda, T., 1980, A thermodynamic approach to
steam and power system design. Ind. Engng Chern. Process Des. Dev. 19,306-312.
Olsbu, A., Loeken P. A. and Grossmann I. E., 1988, A Mixed-integer programming
model for the design and planning of power systems in oil production platforms.
Engineering Costs and Production Economics 14, 281-296
Papalexandri, KP. and Pistikopoulos, E.E., 1996, Operation of a steam production
network with variable demands modelling and optimization under uncertainty.
Computers Chem. Engng 20, s763-s768.
Papoulias S. A. and Grossmann I.E., 1983a, A structural optimization approach in
process synthesis - I: Utility systems, Computers chem. Engng 7,695-706.
Papoulias S. A. and Grossmann I.E., 1983b, A structural optimization approach in
process synthesis - II: Heat recovery networks, Computers chem. Engng 7, 707-722.
Papoulias S. A. and Grossmann I.E., 1983c, A structural optimization approach in
process synthesis - III: Total processing systems, Computers chem. Engng 7, 723-734
Pattison and Sharma, 1980, Selection of boiler plant and overall system efficiency.
Studies in Energy Efficiency in Buildings, British Gas.
166
References
Peterson, J.F. and Mann, W.L., 1985, Steam system design: how it evolves. Chemical
Engineering. October 14, 62-74.
Petroulas, T. and Reklaitis, G.V., 1984, Computer aided synthesis and design of plant
utility systems. A.I.Ch.E. J. 30 (1), 69-78.
Raissi. K .. 1994. Total site integration. Ph.D. thesis, Dept. of Process Integration.
UMIST, Manchester, UK.
Salisbury, 1.K., 1942, The steam turbine regenerative cycles - an analytical approach.
Tran. ASME 64,231-245.
Satoh, T. and Nara, K., 1990, Maintenance scheduling by using simulated annealing
method. IEEE PES Summer Meeting. Minneapolis, MN, USA.
Townsend, D.W. and Linnhoff, B., 1983, Heat and power networks in process design.
Part I: Criteria for placement of heat engines and heat pumps in process networks. Part
II: Design procedure for equipment selection and process matching. A. I. Ch.E. J. 29 (5),
742-771.
Wilkendorf, F., Espuna, A. and Puigjaner, L., 1998, Minimization of the annual cost for
complete utility systems. Chemical Engineering Research & Design 76, 239-245.
Yokoyama R., Ito K. and Matsumoto Y., 1994, Optimal sizing of a gas turbine
cogeneration plant in consideration of its operational strategy. ASME Journal of
Engineering for Gas Turbines and Power 116, 32-38
Yokoyama R. and Ito, K., 1996, Operational strategy of a cogeneration system under a
complex utility rate structure. ASME Journal of Engineering for Gas Turbines and
Power 118. 256-262.
167
Appendix A Correlations o/the THM
Appendix A
Correlations of the THM
A.I. Correlationfor Ml is
As suggested by Mavromatis and Kokossis (1998a), the isentropic enthalpy change,
Ml is of expansion can be correlated to the specific heat load, qin, entering the turbine
and the saturation temperature difference of expansion aT sa, as:
aT Sa/
Ml ------is - 1854-1931qill
(Ai)
where !l.T sa, is in °e, Mlis in MWhlt and qin in MWhlt.
A.2. Correlation for Ml is
Mavromatis and Kokossis (1998a) provided correlation equations for parameters A and
B. All these equations use the saturation temperature of steam at turbine inlet pressure
rat.
for wmax < 1.2MW
A = -0.0131 + 0.00117T sa' (A2)
B = 0.989 + 0.00152T sa' (A3)
168
Appendix A Correlations of the THM
for wmax > 1.2MW
A = -0.928 + O.00623T sat (A4)
B = 1.12 + O.OOO47T sa, (AS)
169
Appendix B Regression o/Condensing Turbine Efficiency Data
Appendix B
Regression of Condensing Turbine Efficiency Data
The regression parameters used in the condensing turbine hardware model are derived
from typical efficiency data as shown in Figure 3-6. By definition the maximum
efficiency is:
hence:
Emax
llis.max = b.H. M max ...
_ E max
MlisMmax =--
1]is.max
These curves are regressed by an expression of the form for each inlet pressure:
E max
Ml ;.,M max = --= AC + BC E
max
T/;s.max
(Bl)
(B2)
(B3)
Parameters A C and Be are extracted by regression for each inlet pressure. The plots of
parameters AC and BC against that saturation temperature corresponding to the inlet
pressure are given in Figure Bl and Figure B2 respectively. These parameters are in
tum approximated by the following expressions:
A C = -0.0896 + O.0013T sar (B4)
BC = 1.1752 + 0.OOO3T sQr (B5)
170
Appendix B Regression o/Condensing Turbine Efficiency Data
where the inlet saturation temperature is in DC. However, the above expressions don't
give accurate estimates of the maximum efficiency when the power output is below
1.5MW. More accurate estimates for the efficiency are obtained by conducting
regression below 1.5MW and above 1.5MW. The two segments' regression gives
efficiency estimates within 3% error. The corresponding expressions for the regression
parameters are:
for Emax < I.5MW
A C = -0.0981 +O.OOlT sat (B6)
BC = 1.2059 + 0.OOO6T sat (B7)
for Emax > 1.5MW
AC = -0.0376 +0.OOI4T sat (B8)
(B9)
0.35 0.3
0.25
AC 0.2 0.15 • 0.1 0.05
0 150 200 250 300 350
Figure 81: Regression parameter N as a function of inlet saturation temperature
171
Appendix B Regression a/Condensing Turbine Efficiency Data
1.35 -r-------------------,
1.3
1.25
1.2 +------r-------,----...,..-----I 150 200 300 350
Figure B2: Regression parameter Be as a function of inlet saturation temperature
172
Appendix C Regression olGas Turbine Efficiency Data
Appendix C
Regression of Gas Turbine Efficiency Data
The regression parameters used in the gas turbine hardware model are derived from
typical electrical efficiency data, such as the plot in Figure 3-8. The curve fitting of the
plot in Figure 3-8 yields the following expression:
wmax --=Ag + BgW max (Cl) lle,max
The parameters Ag and Bg are obtained by conducting regression for the curve in Figure
3-8. The resulting values of Ag and Bg are 6.7571 and 2.4381 respectively. But the
above expressions do not give accurate estimates of the maximum efficiency when the
power output is below 6.9MW by using the parameters. More accurate estimates for the
efficiency are obtained by conducting regression below 6.9MW and above 6.9MW. The
two segments' regression gives efficiency estimates within 2% error. The corresponding
regression parameters are:
for Wmax < 6.9MW
A g = 2.0836 (C2)
Bg = 3.1724 (C3)
for Wmax > 6.9MW
A''1 = 8.817 (C4)
B g = 2.3905 (C5)
173