module 12: “heat and mass exchange networks optimization”

Program for North American Mobility in Higher Education

Introducing Process Integration for Environmental Control in Engineering Curricula

MODULE 12: “Heat and Mass Exchange Networks Optimization”

1

PURPOSE OF MODULE 12

What is the purpose of this module?

This module is intended to convey and illustrate the basic principles

and methodology of heat and mass networks optimization. It is

applied to chemical engineering, especially touching the petroleum

and paper industry. At the end of the module, the student should

be able to understand the main concepts of the heat and mass

exchange network and apply it to real world context.

2

STRUCTURE OF MODULE 12

What is the structure of this module?

Module 12 is divided in 3 “tiers”, each with a specific goal: Tier 1: Basic concepts Tier 2: Application examples Tier 3: Open-ended problems in a real world context

These tiers are intended to be completed in order. Students are

quizzed at various points, to measure their degree of

understanding, before proceeding.

Each tier contains a statement of intent at the beginning, and a quiz

at the end.

3

BASIC CONCEPTS

Tier I

4

TIER 1 - STATEMENT OF INTENT

The goal of Tier 1 is to provide the basic

principles and solution methods for heat and

mass exchange networks optimization with

emphasis on retrofit, heat transfer and

mass transfer analogy and optimization

techniques.

5

TIER 1 - CONTENTS

Tier 1 is broken down into three sections:

1.1 Optimization of heat exchanger networks (HEN) by Pinch Analysis

1.2 Optimization of mass exchange networks

1.3 Application of optimization techniques to heat and mass exchange networks analysis

At the end of this tier there is a short multiple

answer Quiz.

6

1.1 OPTIMIZATION OF HEAT EXCHANGER NETWORKS (HEN) BY PINCH ANALYSIS

7

1.1 OPTIMIZATION OF HEAT EXCHANGER NETWORKS (HEN) BY PINCH ANALYSIS

Principles of Pinch Analysis Methodology Special problems in heat exchangers

network design Pinch analysis and energy integration Special case of heat exchange Retrofit design Pinch software

8

INTRODUCTION

One important goal in our industry today:

Minimize the utilities consumption (fuel, steam and cooling water)

Methods based on thermodynamic analysis,

that have the objective of minimizing the

utilities consumption, are based on fundamental

concepts that help to understand the problem of

heat exchange.

9

WHAT IS PINCH TECHNOLOGY?

Pinch Technology provides a systematic

methodology for energy saving in processes

and total sites. The methodology is based on

thermodynamic principles

10

WHAT IS THE ROLE OF PINCH TECHNOLOGY IN THE OVERALL PROCESS DESIGN?

The Onion Diagram The design of the process starts with the reactors (the core)

Once feeds, products, recycle concentrations and flowrates are known, the separators (the second layer) can be designed

The basic process heat and material balance is now in place and the heat exchanger network (the third layer) can be designed

The remaining heating and cooling duties are handled by the utility systems (the fourth layer)

Pinch Analysis starts with the heat

and material balance for the process at

this boundary

Reactor

Separator

Utilities

Heat Exchanger Network

Site-wide Utilities

11

THE PHASES OF PINCH ANALYSIS

PROCESS

SIMULATION

DATA EXTRACTION

TARGETING

DESIGN OPTIMIZATION

DATA EXTRACTION OF HOT AND COLD STREAMS FROM

PROCESS FLOWSHEET

DETERMINATION OF ENERGY TARGETS

(NEEDS FOR HEATING AND COOLING)

UTILIZATION OF HEURISTICS TO

CONCEIVE A HEAT EXCHANGER NETWORK

TO REACH ENERGY TARGETS AT A MINIMUM

COST

12

DATA EXTRACTION

Extraction of information required for Pinch

Analysis from a given process flowsheet ant the relevant heat and material balance

Data extraction is THE KEY link between process and pinch analysis

The quality of data extraction has a direct influence on the quality of the final result of the analysis

13

WHAT ARE WE SEARCHING FOR?

Thermal data must be extracted from the process

This involves the identification of process heating and cooling duties

14

DEFINITIONS (1-2)

Hot streams are those that must be cooled or available to be cooled. e.g. product cooling before storage (heat sources)

Cold streams are those that must be heated. e.g. feed preheat before a reactor (heat sinks)

Utility streams are used to heat or cool process streams when heat exchange between process streams is not practical or economic (e.g cooling water, air, refrigerant)

15

DEFINITIONS (2-2)

For each hot and cold stream identified,

the following thermal data is extracted: TS : supply temperature, the temperature at

which the stream is available (oC) TT : target temperature, the temperature the

stream must be taken to (oC) ΔH : enthalpy change of streams (kW) CP: heat capacity flow rate

CP = Cp * M (kW/oC = kJ/oC kg * kg/s)16

TYPICAL STREAM DATA

STREAMNUMBER

STREAM NAMETS

(oC)TT

(oC)CP

(kW/oC)H

(kW)1 FEED 60 205 20 29002 REACTOR OUT 270 160 18 19803 PRODUCT 220 70 35 52504 RECYCLE 160 210 50 2500

17

NOTION OF ΔTmin (1-2)

ΔTmin is the minimum temperature difference, imposed in the system; under this value, heat exchange between two streams is not possible

Thus, the temperature of the hot and cold streams at any point in exchangers must always have at least a minimum temperature difference (ΔTmin)

The selection of ΔTmin value has implications for both capital and energy costs

18

NOTION OF ΔTmin (2-2)

In each temperature interval, each cold and hot stream has to be separated at least by ΔTmin. The principle of modified temperatures has to be introduced:

for a cold stream : Tmodified = T + (ΔTmin/2)

for a hot stream : Tmodified = T - (ΔTmin/2)

19

COMPOSITE CURVES

Composite curves consist of temperature-enthalpy profiles of heat availability in the process (the hot composite curve) and head demands in the process (the cold composite curve)

Composite curves allow to determine and visualize the pinch point and the energy targets (heating and cooling demands)

20

HOW TO DO IT?

- A stream with a constant CP

value is represented by a

straight line running from TS

to TT

- When there are a number of

hot and cold streams, the

construction of hot and cold

composites curves involves

the addition of the enthalpy

changes of the streams in the

respective temperature

intervals See Fig. (a), (b)

21

RESULT

Internal recuperation of heat

Cooling required

QCmin

T (oC)

H (kW)

Pinch point

Cold composite curve

Hot composite curve

TPINCH

Heating required

QHmin

22

PINCH GOLDEN RULES

Do not transfer heat across pinch

Do not use cold utilities above the pinch

Do no use hot utilities below the pinch

23

SUMMARY

The composite curves provide overall energy targets

BUT... They do not clearly indicate how much

energy is supplied by different utility levels

SOLUTION... The utility mix is determined by the Grand

Composite Curve (GCC)

24

GRAND COMPOSITE CURVE

It shows the utility requirements in both enthalpy and temperature terms

It is used to optimize the utilities network when the utilities are available at different quality levels

It is useful for integrating special equipments: cogeneration, heat pump, etc.

25

GRAND COMPOSITE CURVE

Pockets of heat recovery

ΔH

T

Heat sink

Heat source

QHmin

QCmin

Pinch point

26

DESIGN A HEAT EXCHANGER NETWORK (HEN)

Application of heuristics to design a heat exchanger network with the objectives of:

Reaching energy targets

Respecting pinch rules

27

DEVELOP A HEN FOR A MAXIMUM ENERGY RECOVERY (MER) (1-2)

Divide the problem at the pinch: above the pinch and below the pinch

Design hot-end, starting at the pinch: Pair up exchangers according to CP and

number of streams “N” constraints Immediately above the pinch, pair up streams

such that CPHOT CPCOLD , NHOT NCOLD

Add heating utilities as needed (QHmin)

28

DEVELOP A HEN FOR A MAXIMUM ENERGY RECOVERY (MER) (1-2)

Design cold-end, starting at the pinch: Pair up exchangers according to CP and

number of streams “N” constraints Immediately above the pinch, pair up streams

such that CPHOT CPCOLD , NHOT NCOLD

Add heating utilities as needed (QCmin)

29

MINIMUM NUMBER OF HEAT EXCHANGERS (Umin)The minimum number of heat exchangers in a

network is given by

Umin = Nstream + Nutilities - 1

where Nstream is the total number of streams and Nutilities the total

number of utilities in the heat exchanger network

30

SPECIAL PROBLEMS IN HEN DESIGN Introduction on a same stream of:

Splitting Mixing

Elimination of loops

More opportunities

More complexFrequently the only way of getting Umin

31

NOTION OF OPTIMAL ΔTmin

At the beginning, an arbitrary Tmin is fixed The goal is to find an optimal Tmin for a

minimum cost

The total cost is function of the utility cost and the heat exchanger cost

Utility cost = f(Qc, Qh) it is an energetic cost Heat exchanger cost = f(exchange area)

it is a capital cost

32

ESTIMATION OF THE ENERGY COST

Energy cost = (Costcold utility X Qc) + (Costhot utility X Qh)

where the cost unit is $/kW and Qc unit is kW

33

ESTIMATION OF HEN CAPITAL COST (1-3)

The capital cost of a HEN depends on 3 factors: the number of exchangers the overall network area the distribution of area between the exchangers

Capital cost = + .A

where A is the exchange area and , , are

economical and technical factors

34

ESTIMATION OF HEN CAPITAL COST (2-3)Using a temperature-enthalpy diagram and the

composite curves, the estimation of the exchange

area can be obtained by:

Amin = (1/ TLM * qj/hj)

COMPLETER.....mettre le i!

where i: enthalpy interval

j: jth stream

TLM: log mean temperature difference or LTMD

qj: enthalpy change of the jth stream in the interval i

hj: transfert coefficient of jth stream

35

ESTIMATION OF HEN CAPITAL COST (3-3)Estimation of exchange area

T (oC)

H (kW)

A1

A2

A3

A4

A5

Enthalpy intervals in the

composite curves

HEN AREAmin = A1 + A2 + A3 +...+ Ai

36

OPTIMAL ΔTmin

To arrive to an optimum Tmin, the total annual cost (the sum of total annual energy and capital cost) is plotted at varying values (see next page). Three key observations can be made:

an increase in Tmin values result in higher energy costs and lower capital costs

a decrease in Tmin values result in a lower energy costs and higher capital costs

an optimum Tmin exists where the total annual cost of energy and capital costs is minimized

37

ENERGY-CAPITAL COST TRADE OFF (OPTIMAL ΔTmin)

Tmin

An

nu

ali

zed

co

st

Optimum Tmin

Total cost

Energy cost

Capital cost

38

RETROFIT DESIGN

For a new process: the application of pinch concepts is relatively easy:

low uncertainty for data extraction low constraints in the process

For an existing process: the application of pinch concepts is more complicated:

technical, geographical and economical constraints

39

DATA EXTRACTION FOR A RETROFIT DESIGN

Data is extracted from the existing process and indeed from a simulation that has to be validated on-site

Validate a simulation is difficult: it can take up to one year! The cost is too high!

Data are less reliable and the quality of the pinch analysis decreases

40

HEN IN RETROFIT DESIGN

There is already in the process violation of the golden rules

Some exchangers are already installed, used or not, have to be taken into account

important for the investment/capital cost

The geographical constraints are important for fitting of equipment in a limited space

41

OPTIMAL ΔTmin IN RETROFIT DESIGN New factors have an influence on the

determination of the optimum ΔTmin: Geographical constraints that have an impact

on the capital cost Investments already realized for the actual

network Preservation of the efficiency of the actual

network

In some cases, we can use Δtmin in the actual HEN or use a ΔTmin from similar processes

42

OPTIMAL ΔTmin IN RETROFIT DESIGN

Industrial sector Experience Tmin valuesOil refining 20 – 40 oC

Petrochemical 10 – 20 oCChemical 10 – 20 oC

Low temperatureprocesses

3 – 5 oC

43

PINCH SOFTWARES

Super Target (Linhoff March) Pinch Express (Linhoff March) Aspen Pinch (Aspentech) Hint (Angel Martin, freeware)

available on www.heatintegration.com

These softwares include the basic concepts of pinch analysis and optimization tools can be integrated

44

1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS

45

1.2 OPTIMIZATION OF MASS EXCHANGE NETWORKS

Heat transfer and mass transfer analogy Equipment configurations The three types of mass exchange

networks analysis

46

HEAT TRANSFER AND MASS TRANSFER ANALOGY

There is an analogy between the exchange potentials (temperature differences and concentration differences) and the quantities that are exchanged (enthalpy and mass)

Parameters such flux, transfer coefficient, exchange rate and other nondimensional numbers appear in the two fields, have similar roles, but the way they are expressed are sometimes really different

47

HEAT TRANSFER AND MASS TRANSFER ANALOGY

Source: Manousiouthakis, 1999

48

MASS EXCHANGE NETWORK

Mass exchange operations are important to limit or eliminate sources of industrial pollution

In process integration, mass exchange operations are used to transfer selectively some undesirable species starting from process streams (called rich streams) to mass separating agents (MSA) that act as receiving streams (called lean streams)

49

MASS EXCHANGER

Definition: a mass transfert unit by direct or indirect contact that use a MSA (lean phase) to remove selectively some compounds (for example pollutants) from a rich phase (for example a waste stream)

Mass exchangers are present in processes of absorption, adsorption, liquid-liquid extraction, desorption, etc.

50

TYPES OF EXCHANGE EQUIPMENTS (1-2)

Rich stream

Lean stream

1. Exchange by direct contact

2. Exchange by mixing of miscible phases non-redistributed

Main stream of the process

Dilution water

51

TYPES OF EXCHANGE EQUIPMENTS (2-2)

3. Exchange by direct contact of non-miscible phases

Washing water

Used water

Treated stream

Contaminated stream

52

TYPES OF MASS EXCHANGE NETWORK

Mass pinch

Water pinch

53

MASS PINCH

Optimization of the mass exchanger network by a method similar to the thermal pinch

Entity exchanged: chemical specie or group of species (e.g. contaminant or undesirable product in the stream of the main process)

The donor streams (analogues to hot streams) are the rich streams

The receiving streams (analogues to cold streams) are the lean streams

54

HOW TO DO IT?

Mass to exchange

Co

nc

en

tra

tio

n

Co

nc

en

tra

tio

n

Mass to exchange

Co

nc

en

tra

tio

n

Mass to exchange

Mass to exchange

Co

nc

en

tra

tio

n

55

RESULT

Internal exchange of materialNeed of MSA

Co

nc

en

tra

tio

n

Mass to exchange

Pinch point

Lean composite curve

Rich composite curve

Pinch

concentration

Need of MSA

56

WATER PINCH

Water pinch can be used to guide water and effluent management decisions while at the same time improving the efficiency of the processes

It is a tool for the rational analysis of the water networks to identify bottlenecks and where recycle/reuse loops should be located

57

WHAT IS THE RESULT?

The procedure enables the minimum amount of water to be determined by considering the introduction of recycle loops and reuse cascades

It highlights the operations that should be investigated for the improvement of their internal efficiencies of water management

58

LIMITING WATER PROFILE

Wastewater minimization application

Graphic of concentration (C) versus mass load (m)

59

DOMAINS OF APPLICATION (1-4)

The mass-exchange operations are necessary for pollution prevention

The realm of mass exchange includes the following applications:

Absorption : a liquid solvent is used to remove selected compounds from a gas using their preferential solubility (e.g. desulfurization of flue gases by alkaline solutions or ethanolamines, recovery of volatile-organic compounds using light oils, removal of ammonia from air using water)

see next page...

60


Adsorption : the ability of a solid adsorbent to adsorb specific component from a gaseous or a liquid solution onto its surface (e.g. activated carbon used to remove a mixture of benzene-toluene-xylene from the underground water, separation of ketones from aqueous wastes of an oil refinery, recovery of organic solvent from the exhaust gases of polymer manufacturing facilities)

Extraction : a liquid solvent is used to remove selected compounds from another liquid using their preferential solubility of the solutes in the MSA (e.g. wash oils used to remove phenol and PCBs from the aqueous wastes of synthetic-fuel plants and chlorinated hydrocarbons from organic wastewater)

61


Ion exchange : cation and/or anion resins are used to replace undesirable anionic species in liquid solutions with nonhazardous ions (e.g. cation-exchange resins contain nonhazardous, mobile, positive ions (sodium, hydrogen) which are attached to immobile acid groups (sulfonic, carboxylic); these resins are used to eliminate various species (dissolved metal, sulfides, cyanides, amines, phenols, and halides) from wastewater)

Leaching : a selective solution of specific constituents of a solid mixture is brought in contact with a liquid solvent (e.g. separating metals from solid matrices and sludge)

62


Stripping : desorption of volatile compounds from liquid or solid streams using a gaseous MSA (e.g. recovery of volatile organic compounds from aqueous wastes using air, removal of ammonia from the wastewater of fertilizer plants using steam, regeneration of activated carbon using steam or nitrogen

63

MULTI-COMPONENT EXCHANGE

Multi-component mass integration Tool to find the minimum utility cost for mass exchanger

networks with multicomponent targets The unit operations are mass-exchangers

Framework: 1st and 2nd laws of thermodynamics Infinite DimEnsional State Space (IDEAS) Conservation of mass Mass cascades from high to low chemical potential for

each component

Concepts: composition interval diagrams, mass exchange

diagrams for each component

64

1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS

65

1.3 APPLICATION OF OPTIMIZATION TECHNIQUES TO EXCHANGE NETWORKS ANALYSIS

Introduction Review of optimization techniques Mathematical programming Combinatory optimization algorithms

66

INTRODUCTION

Many problems in plant operation, design, location and scheduling involve variables that are not continuous but instead have integer values. For example, decision variables such as:

To install or not a new piece of equipment What is the optimum number of stages in a distillation

column? Should we use reactor 1 or reactor 2?

OPTIMIZATION IS NECESSARY!

67

3 DIFFERENT APPROACHES

Heuristics approach (intuition, engineering experience)

Thermodynamic approach (physical insight)

Mathematical programming approach

68

REVIEW OF OPTIMIZATION TECHNIQUES

3 groups Mathematical programming

Linear programming (LP) Non-linear programming (NLP) Mixed-integer linear programming (MILP) Mixed-integer non-linear programming (MINLP)

Combinatory optimization algorithms Branch and bound Simulated annealing Genetic algorithms

Fuzzy logic and heuristics

69

WHAT IS A MATHEMATICAL PROGRAM?A mathematical program is an optimization

problem of the form:

Maximize f(x): x in X, g(x) 0, h(x) = 0,

where X is a subset of Rn and is in the domain of the real-valued functions, f, g and h.

The relations, g(x) 0 and h(x) = 0 are called constraints, and f is called the objective function.

70

WHAT IS MATHEMATICAL PROGRAMMING ? (1-2)

Mathematical programming is the study or use of the

mathematical program. It includes any or all of the

following: Theorems about the form of a solution, including

whether one exists; Algorithms to seek a solution or ascertain that none

exists; Formulation of problems into mathematical

programs, including understanding the quality of one formulation in comparison with another;

Analysis of results, including debugging situations, such as infeasible or anomalous values;

71

WHAT IS MATHEMATICAL PROGRAMMING ? (2-2)

It includes any or all of the following:

Theorems about the model structure, including properties pertaining to feasibility, redundancy and/or implied relations (such theorems could be to support analysis of results or design of algorithms);

Theorems about approximation arising from imperfections of model forms, levels of aggregation, computational error, and other deviations;

Developments in connection with other disciplines, such as a computing environment.

72

MATHEMATICAL PROGRAMMING

LP: optimization technique where constraints and objective function are expressed by linear functions in relation to continuous variables

MILP: optimization where constraints and objective function are linear in relation to mixed variables: discrete and

continuous

NLP: optimization technique where constraints and objective function are expressed by non-linear functions

MINLP: optimization technique where constraints and objective function are non-linear in relation to mixed variable:

discrete and continuous

73

APPLICATION FIELDS FOR OPTIMIZATION TECHNIQUES

Heuristics

Exhaustive research

Fuzzy logic

NLP

MINLP

Simulated annealing

Genetic algorithms

Number of discrete parameters to optimize

Nu

mb

er

of

co

nti

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ou

s p

ara

me

ters

to

op

tim

ize

74

COMBINATORY OPTIMIZATION ALGORITHMS

Branch and bound Simulated annealing Genetic algorithms

75

BRANCH AND BOUND

Approach developed for solving discrete and combinatorial optimization problems. Discrete optimization problems are problems in which

the decision variables assume discrete values from a specified set; when this set is a set of integers, we have an integer programming problem.

Combinatorial optimization problems, on the other hand, are problems of choosing the best combination out of all possible combinations. Most combinatorial problems can be formulated as integer programs.

76

BRANCH AND BOUND

Example: minimize a function f(x), where x is restricted to some feasible region (defined, e.g., by explicit mathematical constraints).

To apply branch and bound, one must have a means of computing a lower bound on an instance of the

optimization problem a means of dividing the feasible region of a problem to create

smaller subproblems. there must also be a way to compute an upper bound (feasible

solution) for at least some instances; for practical purposes, it should be possible to compute upper bounds for some set of nontrivial feasible regions.

77

BRANCH AND BOUND

Consider the original problem with the complete feasible region, which is called the root problem. The lower-bounding and upper-bounding procedures are applied to the

root problem. If the bounds match, then an optimal solution has been found and the

procedure terminates. Otherwise, the feasible region is divided into two or more regions, each

strict subregion of the original, which together cover the whole feasible region; ideally, these subproblems partition the feasible region.

These subproblems become children of the root search node. The algorithm is applied recursively to the subproblems, generating a tree of subproblems.

78

BRANCH AND BOUND

If an optimal solution is found to a subproblem, it is a feasible solution to the full problem, but not necessarily globally optimal. Since it is feasible, it can be used to prune the rest of the tree: if the lower bound for a node exceeds the best known feasible solution, no global optimal solution can exist in the subspace of the feasible region represented by the node. Therefore, the node can be removed from consideration. The search proceeds until all nodes have been solved or pruned, or until some specified threshold is meet between the best solution found and the lower bounds on all unsolved subproblems.

79

SIMULATED ANNEALING

Definition 1: A technique which can be applied to any minimization or learning

process based on successive update steps (either random or deterministic) where

the update step length is proportional to an arbitrary set parameter which can play

the role of a temperature. Then, in analogy with the annealing of metals, the

temperature is made high in the early stages of the process for faster minimisation

or learning, then is reduced for greater stability.

Definition 2 : An algorithm for solving hard problems, notably combinatorial

optimization, based on the metaphor of how annealing works: reach a minimum

energy state upon cooling a substance, but not too quickly in order to avoid reaching

an undesirable final state. As a heuristic search, it allows a non-improving move to a

neighbor with a probability that decreases over time. The rate of this decrease is

determined by the cooling schedule, often just a parameter used in an exponential

decay (in keeping with the thermodynamic metaphor). With some assumptions

about the cooling schedule, this will converge in probability to a global optimum.

80

GENETIC ALGORITHMS (GA)

A class of algorithms inspired by the mechanisms of genetics, which has been applied to global optimization (especially combinatorial optimization problems). It requires the specification of three operations (each is typically probabilistic) on objects, called "strings" (these could be real-valued vectors): reproduction, mutation and crossover

81

THREE OPERATIONS OF GA Reproduction - combining strings in the population to create a new string

(offspring);

Example: Taking 1st character from 1st parent + rest of string from 2nd parent:

[001001] + [111111] ===> [011111]

Mutation - spontaneous alteration of characters in a string;

Example: Just the left-most string:

[001001] ===> [101001]

Crossover - combining strings to exchange values, creating new strings in their place.

Example: With crossover location at 2:

[001001] & [111111] ===> [001111], [111001]

These can combine to form hybrid operators, and the reproduction and crossover

operations can include competition within populations.

82

GENERIC GA STRATEGY

0. Initialize population.

1. Select parents for reproduction and GA operators (reproduction, mutation and crossover).

2. Perform operations to generate intermediate population and evaluate their fitness values.

3. Select members of population to remain with new generation.

Repeat 1-3 until some stopping rule is reached.

83

FUZZY LOGIC

Problem-solving control system methodology that lends itself to implementation in systems ranging from simple, small, embedded micro-controllers to large, networked, multi-channel PC or workstation-based data acquisition and control systems.

It can be implemented in hardware, software, or a combination of both.

FL provides a simple way to arrive at a definite conclusion based upon vague, ambiguous, imprecise, noisy, or missing input information. FL's approach to control problems mimics how a person would make decisions, only much faster.

84

HEURISTICS

The central idea of this approach is the application of empirical rules based on the experience and the “know-how” of the engineer.

The advantage of this method is the exploitation of the knowledge to simplify a problem and identify rapidly some solutions, usually good quality solutions.

The inconvenience of this method is that some heuristics rules for a given problem can enter in contradiction when used in applied problems

85

END OF TIER 1

At the end of Tier 1, you have now a global view

of the basic concepts of heat and mass exchange

networks optimization.

The next steps are the integration of all these notions in

order to solve Case Studies (Tier 2) and finally proceed to

solve real world “open Ended Problems” (Tier 3).

A short quiz and a list of bibliographic references are

completing Tier 1

86

QUIZ

Question 1

What is the objective of Pinch Analysis?

The prime objective of Pinch Analysis is to achieve financial savings in the process industries by optimizing the ways in which process utilities (particularly energy and water), are applied for a wide variety of purposes.

With the application of Pinch Analysis, savings can be achieved in both capital investment and operating cost. Emissions can be

minimized and throughput maximized.

87

QUIZ

Question 2

What is the significance of the pinch point?

The pinch point is defined as the enthalpy at which the

hot and cold composite curves are separated by the

minimum temperature difference, which corresponds with

the enthalpy of the energy cascade at which the heat flux

is zero.

88

QUIZ

Question 3

What analogy can be made between HEN and MEN?

The analogy can be made

between the exchange potentials

(temperature differences and

concentration differences) and

the quantities that are exchanged

(enthalpy and mass)

89

QUIZ

Question 4

When is it necessary to apply mass-exchange operations?

Mass-exchange operations are mainly used for pollution prevention

It is used to remove selectively some compounds (for example pollutants) from a rich phase (for example a waste stream)

Mass exchangers are present in processes of absorption, adsorption, extraction liquid-liquid, desorption, etc.

90

QUIZ

Question 5

Why do we need to optimize chemical processes?

In many plants, we are confronted to make decisions regarding the choice of operating conditions, the use of an equipment, the choice between two pieces of equipment or the determination of an optimal number of operations. Optimization is then necessary to make these decisions

91

QUIZ

Question 6

What optimization technique should you use if you have a

high number of continuous parameters and low number of

discrete parameters to optimize? Describe the chosen

technique.

NLP: optimization technique where constraints and objective function are expressed by non-linear functions

92

REFERENCES

Here is a list of the main references used to elaborate

Tier 1 Books

Douglas, J.M, Conceptual Design of Chemical Processes, McGraw-Hill, Singapore, 1988.

Edgar, T.F., Himmelblau, D.M., Optimization of Chemical Processes, McGraw-Hill, 1988.

El-Halwagi, M.M, Pollution Prevention through Process Integration: Systematic Design Tools, Academic Press, San Diego, 1997.

Smith, R., Chemical Process Design, McGraww-Hill, New-York, 1995.

93

REFERENCES

Papers Linnhoff, M., Introduction to Pinch Technology, 1998.

(available at www.linnhoffmarch.com) Maia, L.O.A. et al, Synthesis of Utility Systems by

Simulated Annealing, Computers Chem. Eng., Vol. 19, No. 4, 1995, pp. 481-488.

Maréchal, F., Advanced energy: process integration and exergy analysis. 4. Heat exchangers network synthesis, Ecole Polytechnique Fédérale de Lausanne, 2002.

Courses notes, GCH6211 - Process Integration Course, Ecole Polytechnique de Montréal, 2002.

94

REFERENCES

Websites Pinch Analysis

www.cheresources.com/pinchtech4.shtml Mass Exchange Network

http://www.eng.auburn.edu/users/edenmar/6460/6460_Chapter_3.pdf

http://www.epa.gov/ORD/NRMRL/std/mtb/Manousiouthakis2.ppt

Optimization techniques Glossary of mathematical programming:

http://carbon.cudenver.edu/~hgreenbe/glossary/index.php?page=nature.html

95




96

APPLICATION

EXAMPLES

Tier 2

97


The goal of Tier 2 is to demonstrate the application

of heat and mass networks optimization

techniques for a few case study examples

including thermal Pinch Analysis, mass exchange

networks analysis and optimization techniques

98

TIER 2 - CONTENTS

The tier 2 consists into three sections:

2.1 Application examples for Thermal Pinch Analysis

2.2 Application examples for Mass Exchange Network Analysis

2.3 Application examples for Optimization techniques

For each section we present example problem statements and then

the solution.

99

2.1 APPLICATION EXAMPLES FOR THERMAL PINCH ANALYSIS

100

EXAMPLE 1 - Data extraction

The Figure 1 below shows the flowsheet of an existing

process

20oC

20oC 120oC

120oC T=120oC

140oC

160oC

180oC

90oC

150oC

RECYCLE A (PURE A)FLOWRATE= 50 kg/hr

RECYCLE B (PURE B)FLOWRATE= 10 kg/hr

REACTOROUTLET

ISOTHERMIC

REACTORCOLUMN 1

COLUMN 2

TO STORAGE AT AMBIENT TEMPERATURE

68.2 MJ/h

51.9 MJ/h73.1 MJ/h

46.3 MJ/h

Fig. 1

FEED A

FEED B

101


Additional data:

Flowrate = 100 kg/hrTBoiling Point = 90 oCHvap = 184.2 kJ/kg

Cpliq = 2.47 kJ/kgoC

Feed A

Cpvap = 1.07 kJ/kgoCFlowrate = 50 kg/hrTBoiling Point = 180 oCHvap = 317.1 kJ/kg

Cpliq = 4.72 kJ/kgoC

Feed B

Cpvap = 2.36 kJ/kgoCTBoiling Point = 160 oCCpliq = 764.4 kJ/oC

Reactor Outlet

Cpvap = 451.6 kJ/oCCpliq = 468.3 kJ/oCProductCpvap = 279.5 kJ/oC

102


Extract the stream data needed to perform a pinch

analysis from the flowsheet given in Figure 1

103

EXAMPLE 1 - Solution

20oC

20oC 120oC

120oC T=120oC

140oC

160oC

180oC

90oC

150oC


RECYCLE B (PURE A)FLOWRATE= 10 kg/hr

REACTOROUTLET

ISOTHERMIC

REACTORCOLUMN 1

COLUMN 2


68.2 MJ/h

51.9 MJ/h73.1 MJ/h

46.3 MJ/hTEMPERATURE VARIATION

Identification of all the streams where there is a change in the temperatureand or enthalpy

Feed A

Feed B

104


20oC

20oC 120oC

120oC T=120oC

140oC

160oC

180oC

90oC

150oC


RECYCLE B (PURE A)FLOWRATE= 10 kg/hr

REACTOROUTLET

ISOTHERMIC

REACTORCOLUMN 1

COLUMN 2


68.2 MJ/h

51.9 MJ/h73.1 MJ/h

46.3 MJ/h

Cpvap = 1.07Cpliq = 2.47

Cpliq = 4.72

CPliq = 764.4

STREAM 1COLD

STREAM 2COLD

STREAM 3COLD

STREAM 7HOT

CPliq = 468.3

STREAM 4COLD

STREAM 5HOT

STREAM 6HOT

Feed A

Feed B

105


The stream data for the process are given in the following table

(streams 1 to 3).

Stream Tin

(0C)

Tout (0C) CP

1. COLD

20

90

91

90

91

120

2.47 kJ/kgoC

Hvap = 184.2 kJ/kg

1.07 kJ/kgoC

2. COLD 20 120 4.72 KJ/Kg0C

3. COLD 120 160 764.4 Kj/0C

106


The stream data for a process are given in the following table

(streams 4 to 7).

Stream Tin ( 0C) Tout ( 0C) Information needed for Pinch Analysis

4. Cold 179 180 Vap. Heat

68.2 MJ / h

5. Hot 140 139 Cond. Heat

73.1 MJ / h

6. Hot 90 89 Cond. Heat

46.3 MJ / h

7. Cold 149 150 Vap. Heat

51.9 MJ / h

107

The stream data for a process are given in the table

below

Stream Tin ( 0K) Tout ( 0K) CP (kW/ 0K)

1. Cold 311 478 1139

2. Cold 339 455 1292

3. Cold 366 478 1303

4. Hot 522 394 1662

5. Hot 578 339 1330

EXAMPLE 2 - Composite curves and HEN design

108


The hot utility is steam at 509 K and the cold utility is

water at 311 K Plot the composite curves for the above system

and determine QH,min, QC,min and the pinch temperature for Tmin = 24 K

Design a network that features the minimum number of units for maximum energy recovery

109

Step 1 - Define temperature intervals Hot stream :

interval temp. = actual temp. – 1/2 Tmin

Cold stream :

interval temp. = actual temp. + 1/2 Tmin

Stream Actual temperature TS / TT ( 0K)

Interval temperature TS / TT ( 0K)

1. Cold 311 / 478 323 / 490

2. Cold 339 / 455 351 / 467

3. Cold 366 / 478 478 / 490

4. Hot 522 / 394 510 / 382

5. Hot 578 / 339 566 / 327


110


Step 2 - Interval thermal balance

Interval temp Flux IntervalTi (oC)

Cpcold-Cphot(kW/ oC)

Hi (kW) Surplus/deficit

566 ---510 56 -13.3 -744.8 surplus490 20 -29.92 -598.4 surplus467 23 -5.5 -126.5 surplus382 85 7.42 630.7 deficit378 4 24.04 96.16 deficit351 27 11.01 297.27 deficit327 24 -1.91 -45.84 surplus323 4 11.39 45.56 deficit

5

4

1

2

3

111


Step 3 - Heat energy cascades

Heating utility = 0 kW

Pinch point at 566 K (where the energy flux between 2 intervals is 0 kW)

Cooling utility = 446 kW

HOT UTILITY 0 kW HOT UTILITY 0 kW566 K

-744.8 744.8 -744.8 744.8

510 K

-598.4 1343.2 -598.4 1343.2

490 K

-126.5 1469.7 -126.5 1469.7

467 K

630.7 839 630.7 839

382 K

96.16 742.84 96.16 742.84

378 K

297.27 445.57 297.27 445.57

351 K

-45.84 491.41 -45.84 491.41

327 K

45.56 445.85 45.56 445.85

323 K

COLDUTILITY

COLDUTILITY

112


Step 4 - Composite curves

113


Step 5 - Network design

EXHAUST ALL HOT STREAMS WITH COLD STREAMS

EXHAUST ALL COLD STREAMS WITH HOT STREAMS

RESPECTING THE FOLLOWING

RULES:

- CPHOT CPCOLD

- ΔTmin respected between streams

114


578554

1

2

3

4

5

CP / H

11.39 / 1902.13

12.92 / 1498.72

13.03 / 1459.36

16.62 / 2127.36

13.30 / 3178.7

311

339

366

478

455

478

522

578339

394

E1

E3

E4

E2

E5

1902.13

1285.57

411

380

182.79

511

1498.72

421

446.28

578554COLD UTILITY

Step 5 - Network design - below the pinch point

115



Above the pinch point, 0 heat exchanger are necessary

Below the pinch point, 5 heat exchangers are necessary

In total, 5 heat exchangers are necessary for this network

Min Number of HX for MER = Umin MER = Umin above + Umin below

Umin above = 0 Umin below = N – 1 = 6 – 1 = 5 where N is the total number of

streams including utilities

116


The stream data for a process are given in the table below

Stream TS

( 0C)

TT

( 0C)

CP

(KW/ 0C)

1. Hot 170 88 2.3

2. Hot 278 90 0.2

3. Hot 354 100 0.5

4. Cold 30 135 0.9

5. Cold 130 205 2.0

6. Cold 200 298 1.8

117

EXAMPLE 3 - Composite curves and HEN designThe hot utility is to be supplied by a hot oil circuit at 380oC

and the cold utility by a cooling media at 20oC. For a Tmin

of 10oC: Plot the composite curves and determine QH,min,

QC,min and the pinch temperature Design a network that features the minimum

number of units for maximum energy recovery, Umin MER.

118


Step 1 - Define temperature intervals

Stream Actual temp.

TS / TT (0C)

Interval temp.

TS / TT (0C)

1. Hot 170 / 88 165 / 83

2. Hot 278 / 90 273 / 85

3. Hot 354 / 100 349 / 95

4. Cold 30 / 135 35 / 140

5. Cold 130 / 205 135 / 210

6. Cold 200 / 298 205 / 303

119


Step 2 - Interval thermal balance

Interval temp Flux IntervalTi (oC)

Cpcold-Cphot(kW/ oC)

Hi (kW) Surplus/deficit

349 ---303 46 -0.5 -23 surplus273 30 1.3 39 deficit210 63 1.1 69.3 deficit205 5 3.1 15.5 deficit165 40 1.3 52 deficit140 25 -1 -25 surplus135 5 -0.1 -0.5 surplus95 40 -2.1 -84 surplus85 10 -1.6 -16 surplus

83 2 -1.4 -2.8 surplus35 48 0.9 43.2 deficit

1

2

3

5

4

6

120


Step 3 - Heat energy cascades

Heating utility = 153 kW

Cooling utility = 85 kW

Pinch point at 165oC (where the energy flux between 2 intervals is 0 kW)

HOT UTILITY 0 kW HOT UTILITY 152.8 kW349oC

-23 23 -23 175.8

303 oC

39 -16 39 136.8

273 oC

69.3 -85.3 69.3 67.5

210 oC

15.5 -100.8 15.5 52

205 oC

52 -152.8 52 0

165 oC

-25 -127.8 -25 25

140 oC

-0.5 -127.3 -0.5 25.5

135 oC

-84 -43.3 -84 109.5

95 oC

-16 -27.3 -16 125.5

85 oC

-2.8 -24.5 -2.8 128.3

83 oC

43.2 -67.7 43.2 85.10

35 oC

COLDUTILITY

COLDUTILITY

121


Step 4 - Composite curvesT (oC)

H (kW)

Tmin

Hpinch

122


Step 5 - Network designH (kW) m.cp (kW/oC)




RULES:

- CPHOT CPCOLD


123


Step 5 - Network design - above the pinch point

Heating utility calculated with energy cascade = 153 kW

Cooling utility calculated with energy cascade = 85 kW

2

3

5

6

170278

354 170

160

200

205

298

CP/H

0.2/21.6

0.5/92

2/90

1.8/176.4

E1

90

E2 E3E4

152.8

HOT UTILITY

2

21.6

174

212213

124



1170 88

90

CP/H

2.3/188.6

0.2/162 170

100 0.5/353 170

130 2.0/605160

30 0.9/94.54135

E5

60

E6

94.5

E7

E8

E9

34.1

16

35

COLD UTILITY

COLD UTILITY

COLD UTILITY

144 103

125



Above the pinch point, 4 heat exchangers are necessary




Umin above = N – 1 = 5 – 1 = 4 Umin below = N – 1 = 6 – 1 = 5 where N is the total number of

streams including utilities

126

EXAMPLE 4 - GCC

Using the given energy

cascade, draw the

grand composite

curve associated

GCC?

From Int. Energy Agency

127


From Int. Energy Agency

128

EXAMPLE 5 - A complete problem

The stream data for a process are given in the table below

Stream TS (0C) TT (0C) CP (MW/0C)

1. Hot 327 40 3.0

2. Hot 220 160 4.8

3. Hot 220 60 1.8

4. Hot 160 45 12.0

5. Cold 100 300 3.0

6. Cold 35 164 2.1

7. Cold 85 138 10.5

8. Cold 60 170 1.8

9. Cold 140 300 6.0

129

EXAMPLE 5 - A complete problem

At the correct setting of the capital-energy trade-off,

Tmin = 26oC Plot the composite curves for the above system

and determine QH,min, QC,min and the pinch temperature

Plot the grand composite curve of the process Design a network to achieve the target without

violating Tmin = 26oC

130


Step 1 - Define temperature intervals

Stream Actual temp.

TS / TT (0C)

Interval temp.

TS / TT (0C)

1. Hot 327 / 40 314 / 27

2. Hot 220 / 160 207 / 147

3. Hot 220 / 60 207 / 47

4. Hot 160 / 45 147 / 32

5. Cold 100 / 300 113 / 313

6. Cold 35 / 164 48 / 177

7. Cold 85 / 138 98 / 151

8. Cold 60 / 170 73 / 183

9. Cold 140 / 300 153 / 313

131


Step 2 - Interval thermal balanceInterval temp Flux Interval

Ti (oC)

Cpcold-Cphot

(MW/ oC)

Hi(kW)

Surplus/deficit

314 ---313 1 -3 -3000 surplus207 106 6 636 000 deficit183 24 -0.6 -14 400 surplus177 6 1.2 7200 deficit153 24 3.3 79 200 deficit151 2 -2.7 -5400 surplus147 4 7.8 31 200 deficit113 34 0.6 20 400 deficit98 15 -2.4 -36 000 surplus

73 25 -12.5 -322 500 surplus48 25 -14.7 -367 500 surplus47 1 -16.8 -16 800 surplus32 15 -15 -225 000 surplus27 5 -3 -15 000 surplus

2

1

3

4

5

6

7

8

9

132


Step 3 - Heat energy cascades (1 of 2)

Heating utility = 751 200 kWHOT UTILITY 0 kW HOT UTILITY 751 200 kW314 oC

-3000 3000 -3000 742 200

313 oC

636 000 -633 000 636 000 118 200

207 oC

-14 400 -618 600 -14 400 132 600

183 oC

7200 -625 800 7200 125 400

177 oC

79 200 -705 000 79 200 46 200

153 oC

-5400 -699 600 -5400 51 400

151 oC

31 200 -730 800 31 200 20 400

147 oC

20 400 -751 200 20 400 0

133


Step 3 - Heat energy cascades (2 of 2)

Cooling utility = 982 800 kW

Pinch point at 113oC (where the energy flux between 2 intervals is 0 kW)

147 oC

20 400 -751 200 20 400 0

113 oC

-36 000 -715 200 -36 000 36 000

98 oC

-322 500 -392 700 -322 500 358 500

73 oC

-367 500 -25 200 -367 500 726 000

48 oC

-16 800 -8400 -16 800 742 800

47 oC

-225 000 216 600 -225 000 967 800

32 oC

-15 000 231 600 -15 000 982 800

27 oC

COLDUTILITY

COLDUTILITY

134


Step 4 - Composite curves

ΔΤmin

135


Step 5 - Grand composite curve

136



H (kW) m.cp (kW/oC)




RULES:

- CPHOT CPCOLD


137

EXAMPLE 5 - SolutionStep 6 - Network design - above the pinch point

1126327

CP/H

3000 / 603 000

2160220

4800 / 288 000

3126220

1800 / 169 200

4126160

12 000 / 408 000

5100300

3000 / 600 000

6100

2100 / 134 400

7100

10 500 / 399 000

8100

1800 / 126 000

9140

6000 / 960 000

164

138

170

300

E3

288000

E6

E2

603000 204000

274.5

127.4

168

102000

111000

134224.4

E4

H1

H2

H3

226800

134400

153000

174

E1

E5

102000169200

H4

H5

126000

138



140126

360126

445126

635

785

860

CP/H

3000 / 258 000

1800 / 118 800

12 000 / 972 000

2100 / 136 500

10 500 / 157 500

1800 / 72 000

100

100

100

102

72 000

E2

157 500E1

E3

C1

C2

C3

COLD UTILITY

COLD UTILITY

COLD UTILITY

186 000

118 000

136 500

294 000

113 101.5

139



Above the pinch point, 11 heat exchangers are necessary




Umin above = N – 1 = 12 – 1 = 11 Umin below = N – 1 = 7 – 1 = 6

where N is the total number of streams including utilities

140

2.2 APPLICATION EXAMPLE FOR MASS EXCHANGE NETWORK ANALYSIS

141

EXAMPLE 1

Recovery of benzene from gaseous emission of

a polymer production facility (Source: Pollution

prevention through process integration, El

Halwagi, M.M)

A simplified flowsheet of the copolymerization

process can be found next

142

EXAMPLE 1

Monomers Mixing Tank

Recycled Solvent

Second Stage Reactor

Additive Mixing Column

SeparationFirst Stage Reactor

Unreacted Monomers

Catalytic Solution

(S2)

Monomers

Solvent Makeup

Inhibitors + Special Additives

Extending Agent

Copolymer (to

Coagulation and

Finishing)

S1Gaseous

Waste (R1)

COPOLYMERIZATION PROCESS WITH A BENZENE RECOVERY MEN

143

EXAMPLE 1

Data of rich stream for the benzene removal example

Candidate MSA’s :

Two process MSA’s and one external MSA Process MSA’s :

Additives (S1) : The additives mixing column can be used as a absorption column by bubbling the gaseous waste into the additives

Liquid catalytic solution (S2) : The equilibrium data for benzene in the two process MSA’s are given by:

y1 = 0.25x1

y1 = 0.50x2

For control purpose, the minimum allowable composition difference for S1 and S2 should not be less than 0.001.

Stream Description FlowrateGi, kg mol/s

Supply composition(mole fraction) ys

i

Target composition(mole fraction) yt

i

R1 Off-gas fromproduct separation

0.2 0.0020 0.0001

144

EXAMPLE 1

Data of process lean streams for the benzene removal example

The external MSA, S3, is an organic oil which can be regenerated using flash separation. The operating cost of the oil (including pumping, makeup and regeneration) is $0.05/kgmole of recirculating oil

The equilibrium relation for transferring benzene from the gaseous waste to the oil is given by:

y1 = 0.10x3

Data for the external MSA for the benzene removal example

Stream Description Upper bound onflowrate Lc

j

kg mol/s

Supply compositionof benzene (mole

fraction) xsj

Target compositionof benzene (mole

fraction) xtj

S1 Additives 0.08 0.003 0.006S2 Catalytic solution 0.05 0.002 0.004

Stream Description Upper bound onflowrate Lc

j

kg mol/s

Supply compositionof benzene (mole

fraction) xsj

Target compositionof benzene (mole

fraction) xtj

S3 Organic oil infinite 0.0008 0.0100

145

EXAMPLE 1 SIMPLIFIED FLOWSHEET OF THE COPOLYMERIZATION PROCESS

Monomers Mixing Tank

Recycled Solvent

Second Stage Reactor

SeparationFirst Stage Reactor

Unreacted Monomers

Catalytic Solution S2

Monomers

Solvent Makeup

Copolymer (to

Coagulation and

Finishing)

Gaseous Waste R1Benzene Recovery MEN

Re

ge

ne

ratio

n

To atmosphere

Benzene

Oil Makeup

OilS3

Additive (Extending Agent, Inhibitors and Special Additives S1

146

EXAMPLE 1

Construct the pinch diagram of this process Find where the pinch point is located and

what is the excess capacity of the process MSA’s

Find the outlet composition of the additives-mixing column (S1)

147

EXAMPLE 1 - SOLUTION

1. Construct the pinch diagram (1 of 4)

148


Representation of the two process MSA’s


149



150



151


2. Interpret de results of the pinch diagram

(1 of 3)

Pinch is located at the corresponding mole fractions (y, x1, x2) = (0.0010, 0.0030, 0.0010)

The excess capacity of the process MSA’s is 1.4X10-4 kgmole benzene/s

152


2. Interpret de results of the pinch diagram

(2 of 3) There are infinite combination of L1 and x1

out that can be used to remove the excess capacity of S1 according to the following mass balance:

Benzene load above the pinch to be remove by S1=L1(x1

out - x1S) i.e 2.4X10-4 = L1(x1

out - 0.003)

Since the additives-mixing column will be used for absorption, the whole flowrate S1 (0.08 kgmole/s) should be fed to the column. The outlet composition of S1 is 0.0055.

153


2. Interpret de results of the pinch diagram (3 of 3)

Graphical identification of x1

out

154

2.3 APPLICATION EXAMPLES FOR OPTIMIZATION TECHNIQUES

155

A process consists of the following set of hot and coldprocess streams:

Stream Tin( 0C) Tout( 0C) F Cp (kW 0C-1)

H1 95 75 5

H2 80 75 50

C1 30 90 10

C2 60 70 12.5

Example taken from Floudas and Ciric (1989)

This example features constant flow rate heat capacities, one hot and one cold utility being steam and cooling water, respectively.

EXAMPLE 1 - Linear programming (LP)

156

Assumption: the costs of hot utility i (Ci) and cold utility j (Cj) are equal to 1, for the minimum utility consumption.

Formulate the linear programming (LP) transshipment model, and solve it to determine the minimum utility cost.

EXAMPLE 1 - Linear programming (LP)

157

The temperature interval partitioning along with the transshipment representation is shown in Figure 1.

Figure 1.

(120) (90)

(95) (65)

TI - 1

TI - 2

(90) (60)

TI - 3

(80) (50)

(60) (30)

TI - 4

QS

R1

R2

R3

QW

H2

H1

C2

C1

25

50

25

250

250

50

100200

62.5

62.5


158

Then, the LP transshipment model for minimum utility consumption takes the form:

min QS + QW

s.t. R1 – QS = -312.5

R2 – R1 = -87.5

R3 – R2 = -50

QW – R3 = 75

QS, QW, R1, R2, R3 ≥ 0


159

This model features four equalities, five variables and has linear objective function constraints. Its solution obtained via GAMS/MINOS (General Algebraic Modeling System / Modular Incore Nonlinear Optimization System) is:

QS = 450

QW = 75

R1 = 137.5

R2 = 50

R3 = 0


160

Since R3 =0, there is a pinch point between TI – 3 and TI - 4. hence, the problem can be decomposed into two independent subnetworks, one above the pinch and one below the pinch point.

Remind that when we have one hot and one cold utility, it is possible to solve the LP transshipment model by hand. This can be done by solving the energy balances of TI – 1 for R1, TI – 2 for R2, TI – 3 for R3, and TI – 4 for QW which become


161

Since R1, R2, R3, R4 ≥ 0 we have

QS ≥ 312.5

QS ≥ 400

QS ≥ 450

QS ≥ 375


R1 = QS – 312.5

R2 = R1 – 87.5 = QS – 400

R3 = R2 – 50 = QS – 450

QW = R3 + 75 = QS – 375

162

The objective function to be minimized becomes

QS + QW = 2*QS – 375

Then, we seek the minimum QS that satisfies all the above four inequalities. This is

QS = 450


163

Etching of copper is achieved through ammoniacal solution and etching efficiency is higher for copper concentrations in the ammoniacal solution between 10 - 13 w/w%. To maintain the desired copper concentration in the solution, copper must be continuously removed. Copper must also be removed from the rinse water, with which the etched printed circuits are washed out, for environmental and economic reasons.

EXAMPLE 2

164

Thus, two rich streams in copper must be purified up to concentrations dictated by environmental regulations and process economics. Mass flow rate data and concentration specifications are given in table I.

Stream No.

Description Mass flow rateGi (Kg/s)

Initial concentration

Yis

Targetconcentration

yit

R1 Ammoniacal solution 0.25 0.13 0.10

R2 Rinse water 0.10 0.06 0.02Table I. Rich streams of copper recovery problem

EXAMPLE 2

165

A simplified representation of the etching process is illustrated in Fig 1.

Etching Line

Rinse Bath

MassExchangeNetwork

To solventRegeneration

S1

S2

R2

R1

R2

EtchantEtchantMakeup

Printed CircuitBoards

Spent Echant

RinseWater

Makeup

Rinse Water

Etched Boards

Treated Rinse Water

Regenerated Etchant

Fig. 1. Recovery of streams of copper in an etching plant.

EXAMPLE 2

166

Two extractants are proposed for copper recovery, LIX63 (an aliphatic α- hydroxyoxime, S1) and P1 (an aromatic β-hydroxyoxime, S2). The initial concentrations in copper of the available lean streams, an upper bound on their final concentration and their costs are given in table II.

Stream Description Initial concentration

xjs

Maximum outlet concentration

xjT, up

Cost (US$/Kg)

Ann. Cost (US$/Kg)

S1 L1X63 0.030 0.07 0.010 88,020

S2 P1 0.001 0.02 0.120 1,056,240

Table II. Lean streams of copper recovery problem

EXAMPLE 2

167

Within the ranges of copper concentrations of interest, the copper transfer between the given rich and lean streams is governed by the following linear equilibrium relations (Henry equation):

R1 - S1 : y1* = 0.734 x1

* + 0.001

R2 - S1 : y2* = 0.734 x1

* + 0.001

R1 - S2 : y1* = 0.111 x2

* + 0.008

R2 - S2 : y2* = 0.148 x2

* + 0.013


168

Two types of contactors are considered:

• a perforated plate column for S1 (LIX63)

• a packed tower for S2 (P1)

Where y1*, y2* and x1*, x2* are the copper concentrations of R1, R2 and S1, S2, respectively, at equilibrium.


169

LmG

LmG

bmxybxmy

LmG

Ninout

inin

St

ln

1ln

The annualized investment cost of a plate-column is based on the number of plates NSt which is determined through Kremser equation.

x )( * RRTotal

yOR NHH

yyK

GH


The cost of packed tower is based on the overall height of the column:

170

The annualized investment costs are given in table III

Cost of plate column 4 552 NSt $ / Yr

Cost of packed column 4 245 H $ / Yr

Table III. Capital cost data for copper recovery problem

(Papalexandri et al., 1994)


171

The obtained mass exchange network for copper recovery is illustrated in Fig 2. the model was solved in 3GBD (Generalized benders decomposition) iterations.

1

1 1R2

R1

S1 S2

N2 = 4 N3 = 1

N1 = 1

xs = 0.0300.278 kg/s

xs = 0.0010.019 kg/s

ys = 0.0600.100 kg/s

ys = 0.1300.250 kg/s

xT = 0.070

xT = 0.020

yT = 0.100

yT = 0.020

Fig 2.


172

It features 3 mass exchangers in series and a total annualized cost of $15,933/yr, with $52,591/yr corresponding to operating cost.

A flexibility analysis (Grossmann and Floudas, 1987) of the proposed MEN reveals that it is flexible to operate in the whole uncertainty range of GR.


173

System closure in pulp and paper mills

One can formulate the problem as having two types of white water streams:

•Sources: white water streams that are produced in different operations and are available to be used in other operations. They are characterized by fiber, fine and contaminant concentrations and by flow rate.

•Demands: white water streams that are required by operations, and on which limiting concentrations in fibers, fines and, contaminants are imposed.

EXAMPLE 3 Problem statement & solution structure

174

The objective is to establish a white water network configuration such that all demands are satisfied and yet optimization goals such as minimized fresh water consumption, fiber loss degree of contamination are met. The method consists of encoding structure elements in the general framework of a genetic algorithm problem and relating network characteristics to linear programming problem. A superstructure is formed by respecting the following rules:


175

•Each source stream and fresh water enters a splitter in which it can be divided into several streams that are directed to various demands while the excess is sent to the waste water effluent.

•Before each demand there is a mixer, which gathers all the streams coming from the different sources; wastewater effluents are also collected into a single stream.


176

This form of superstructure is encoded as follows. Each individual configuration of the superstructure is characterized by chromosome in which each gene represents a potential connection between a splitter and a mixer. The value of a gene is one or zero indicating the existence or absence of connection. All possible configurations for a given set of sources and demands can thus be represented by a set of chromosomes in a unique one-to-one correspondence. Figure 1 shows an example of a structure and corresponding code.


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S1

D2

D1

D3

Waste Fresh Water

S4

S3

S2

Splitters Mixers

1 0 01 1 1 11 1 0 01 0 1 00

Figure 1: example of coding for a system of 4 sources and 3 demands


178

Knowing the number of sources and demands the number of genes and hence, the length of chromosomes is determined. For example if there are m sources and n demands, the number of genes will be (m+1)(n+1). This includes the genes needed to take into account fresh water as a source stream and the effluent stream as a demand.

Overall and component material balances are written for each splitter and mixer for any structure considered.


179

The balance equations constitute constraints of the optimization problem with specified objective function. A linear or non-linear programming problem is thus formed and is solved to give the value of the objective function for the given structure. The optimization of the network is treated a two levels; at the master problem level a set of feasible structures is proposed by GA and at slave problem level the proposed structures are optimized by mathematical programming methods to obtain the optimal value of the objective function.


180

This value in turn is passed to the master problem by means of an adaptation index to be used in the generation of new structures. At the end of the iterative procedure a set of structures is available that have near optimal objective function values.


181

Genetic algorithm procedure (GA)

The GA implemented follows the classical iterative procedure introduced by Goldberg (1989):

Generation of the initial population

Evaluation of the fitness of the initial population

Iteration of the following sequence until total number of generations is reached


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Generation of the offspring population

Selection of surviving individuals

Synthesis of offspring obtained by cross-over

Mutation of individuals

End of search

The initial population consists of 20 structures that have been created randomly by assigning to the genes.


183

For each generation subsequently generated, a fixed fraction is conserved in the offspring generation and the rest of the population is created by crossover of randomly selected pairs of individuals (Figure 2). In crossover the chromosomes are cut and recombined at a randomly selected crossover point (CP)


184

The individuals interchange chromosome sections and two new individuals are thus created. In mutation one gene is selected randomly and its value is changed.

1 01 11 0

1 01 1 1 1

Crossover

P1

E2E1

P2

CPCP

Mutation

Before mutation

After mutation

Muted Gene

Figure 2. Crossover and mutation operations


185

Each interesting solution given by the program in the final population is compared with the base case of the mill by PS. The necessary changes to be made are extracted from the solution and a scenario is formulated. This scenario is executed in the mill simulation and the changes in concentration of the different species in important points of the process are determined. Figure 3 shows the flow of information at different stages of the overall procedure.


186

Figure 3.General structure of procedure

Superstructure Mass

Balance

ProcessSimulation

Demand Constraints

ObjectiveFunction

Master problemGenetic Algorithm

Superstructure

Retained Solutions

AdaptationIndex

Feasibility Engineering

OPTIMIZATION

IMPLEMENTATION

PROBLEM DEFINITION


187

In this process four sources of water and three demands are identified. The specification of the sources and demands are given on table I

Sources Available flowrate (L/min)

Fines concentration (%)

Contaminant concentration (ppm)

S 1 500 0.3 100

S 2 2000 0.1 110

S 3 400 0.5 110

S 4 300 0.5 60

Demands Required flowrate (L/min)

Limiting fines concentration (%)

Limiting contaminant concentration (ppm)

D 1 1200 0.5 120

D 2 800 0.4 105

D 3 500 0.1 80Table I


188

The initial configuration of the process is given on figure I, the demands D2 and D3 are satisfied by fresh water and all the sources are sewered except a fraction of source 2, used to satisfy demand 1. The goal is to find the optimal configuration of the water network, minimizing the fresh water consumption.


189

D1

S1S2

D2

S3

D3

S4

Pulp Pulp

Fresh Water Fresh Water800 5001200

waste waste waste500 400 300

waste800

Flow sheet general diagram


190

800

1200

2000

500

500

2000

400

300

1300

S1

D2

D1

D3

SewerFreshWater

S4

S3

S2

Splitters Mixers

Superstructure

EXAMPLE 3 - Solution (GA)

191

The initial solution of the process is given on table II. The fresh water consumption is 122 L/min, it is 90% reduced from the initial data (1300 L/min)

D1 D2 D3 Waste

S1 500

S2 540 290 348 822

S3 390 10

S4 270 30

Fresh water

122

800

1200

822

500

500

2000

400

300

122

S1

D2

D1

D3

WasteFreshWater

S4

S3

S2

Splitters Mixers

First solution

Table II

EXAMPLE 3 – Solution (GA)

192

The second solution of the process is given on table III. The fresh water consumption is 172 L/min.

D1 D2 D3 Waste

S1 500

S2 764 364 872

S3 400

S4 300

Fresh water

36 136

800

1200

872

500

500

2000

400

300

172

S1

D2

D1

D3

WasteFreshWater

S4

S3

S2

Splitters Mixers

Second solution

Table III


193

On table IV are compared the first and second solutions of the process using a Genetic Algorithms

Water consumption

(L/min)

Fibers Waste

g/min

GA1 122 0.822

GA2 172 0.872

Table IV


194

•El-Halwagi, MM and Manousiouthakis, V., “Synthesis of Mass Exchange Networks”, AIChE Journal, 35,(8), 1233-1244, (1989)

•El-Halwagi, MM and Manousiouthakis, V., “Simultaneuos Synthesis of Mass Exchange and Regeneration Networks, AIChE Journal, 36,(8), 1209, (1990a)

•Floudas C. A. and Paules IV G. E. “A mixed-integer non linear programming formulation for the synthesis of heat-integrated distillation sequences”, Comp. Chem. Eng., 12, 259-372, (1998)

REFERENCES

195

•Garrard A., Fraga E. S., “Mass exchange network synthesis using genetic algorithms” Computers and Chemical Engineering, 22, (12), 1837-1850, (1998).

•Goldberg D.E., “Genetic Algorithms in Search, Optimization, and Machine Learning” Ed. Addison Wesley, (1997).

•Jacob, J., H. Kaipe, F. Couderc and J.Paris, “Water network analysis in pulp and paper processes by pinch and linear programming techniques”, Chem. Eng. Communication, 189, (2), 184-206 (2002b).

REFERENCES

196

•Shafiei S., Domenech S., Koteles R., Paris J., “System Closure in Pulp and Paper Mills: Network Analysis by Genetic Algorithm” Pulp and Paper Canada (soumis).

REFERENCES

197




198

OPEN-ENDED PROBLEMS IN A REAL WORLD CONTEXT

Tier 3

199


The goal of Tier 3 is to present an open-ended problem to

solve an industrial case study of actual heat or mass

exchange network optimization in which the student must

interpret results and evaluate a range of potential

solutions. The problem involves defining objective

functions, generating solutions, evaluating their technical

and economical feasibilities. Problem will be drawn from

actual cases in the petroleum and pulp and paper

industries.

200

TIER 3 - CONTENTS

The tier 3 is broken down into two sections:

3.1 Design of a heat and mass exchange network for the efficient management of energy, water and hydrogen in a selected oil refinery process.

3.2 Design of a whitewater network in an integrated thermomecanical pulp and newsprint mill for minimum fresh water consumption and minimum fiber loss

201

3.1 PETROLEUM OPEN-ENDED PROBLEM

202

PROBLEM DEFINITION

A mill is designed to eliminate the sulfuric compounds

present in a feed stream of diesel and light oil.

The mill is divided in 7 sections: Reaction and load section Gaz separation Hydrogen purification Diesel stabilization Product cooling Treatment with DEA Compression of recirculated hydrogen

PROBLEM DEFINITION

A mill is designed to eliminate the sulfuric compounds

present in a feed stream of diesel and light oil.

The mill is divided in 7 sections: Reaction and load section Gaz separation Hydrogen purification Diesel stabilization Product cooling Treatment with DEA Compression of recirculated hydrogen

203

REACTION AND LOADSECTION The objective of this section is to eliminate the

sulfur components and nitrogen, throught the hydrogenation reaction in a fixed bed catalytic reactor.

First, a stream of diesel and a stream of oil are mixted together (MX-801***). The resultant mix is then heated and transported to the decantation tank (FA-801) where the aqueous phase is remove.

The water-free mix is then heated in the three heat exchangers (EA-802, EA-803, EA-804)

The mix is then sent to a heater to reach the temperature of 346oC.

204

REACTION AND LOADSECTION The vapor mix or charge is then transported to the

reactor (DC-801) where the reactions of hydrogenation and the transformation of the nitrogen and oxygen compounds are done.

The reactor effluent is then passed another time in the three heat exchangers (EA-802, EA-803, EA-804)

*** The identification equipment numbers can be founded on the process diagram following the present description of the process

205

GAS SEPARATION SECTION

The vapor and liquid mix is separated in a liquid phase and a gaseous in the FA-802 tank.

The gaseous phase is cooled and a water stream is then injected to eliminate the last impurities.

The resultant mix is then cooled in the aerocooler EC-801

The aqueous phase is separated from the gaseous phase rich in sulfur compounds in the separator FC-803.

The aqueous phase is sent to the stabilization section

The gaseous phase is sent to the DEA treatment section

206

HYDROGEN PURIFICATION SECTION The hydrogen from the reformation plant is sent to a

separator (FA-805) to remove heavy compounds. The hydrogen pass through three steps of compression

(GB-802, GB-803, GB-804) Between each compression, the hydrogen is cooled (EC-

803, EC-804) and is entering a separator (FA-806, FA-807) to remove the heavy compounds from the hydrogen stream.

After the third compression, the hydrogen is at the conditions of pressure and temperature necessary to be utilized in the process.

207

DIESEL STABILIZATION SECTION The liquid phase resulting from the separation in FA-

802 is sent to heat exchanger EA-806. The preheated phase is then sent to the stabilization tower DA-801

The liquid phase resulting from the separation in FA-803 is also sent to the stabilization tower DA-801

The stabilization tower is used to separate the lightweight hydrocarbures from the heavyweight ones.

At the top of the tower, vapor containing sulfur compounds exit and are condensated in EC-805. The separation is done in FA-808.

208

DIESEL STABILIZATION SECTION At the bottom of the tower, the stream containing

mainly heavyweight hydrocarbures is divided in two streams. The first stream is sent to the heater BA-802 where it acquire the heat necessary to be injected in the stabilization tower another time. The second stream is sent to the heat exchanger EA-806. The hydrodesulfurized and stabilized diesel is sent to the vapor generator EA-807, and then the diesel at a temperature of 215oC is transported to the preheater EA-801.

209

PRODUCT COOLING SECTION

The diesel from the heatexchanger EA-801 is sent to the heat exchanger EA-808 where it is cooled until 153oC.

The cooled stream enters the aerocooler EC-802 and the watercooler EA-809.

After these two steps, the diesel is at the conditions necessary to be stock.

210

TREATMENT WITH DEA SECTION The gaseous phase rich in sulfur compounds from

the separator FA-803 is feeded the last tray of the absorption column DA-802. A stream of DEA (dietanolamine) in aqueous phase is sent to the first tray to absorb the sulphuridric acid contained in the feed stream.

The gas obtained at the top of the column is transported to the recirculated gas compression section.

The amine obtained at the bottom of the column, rich in H2S, is sent to the amine recuperation plant.

211

RECIRCULATED HYDROGENCOMPRESSION SECTION The gas free of H2S and rich in hydrogen is feeded

to the separator FA-804 where traces of amine can be totally eliminated.

The gaseous phase is sent to the hydrogen compressor GB-801 to increase its pressure

The compressed gas obtained is either mixted with the hydrogen coming from the gas purification section, or directly sent to the hydrodesulfurized reactor DC-801.

212

PROCESS FLOWSHEET AND DATA The process flowsheet can be found at the

following link: ProcessFlowsheet _PetroleumProb.pdf

The process data can be found at the following link:

ProcessData_PetroleumProb.xls

213

WHAT YOU HAVE TO DO?

Perform a complete pinch analysis using the following

steps

a) Extract the hot and cold streams from the process

flowsheet and extract all the data necessary from the

data flowsheet (flowrate, temperature, enthalpy or Cp)

b) Determine QH,min, QC,min , the minimum consumption of

external utilities (energy targets)

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c) Propose a ΔTmin using Introduction to Pinch

Technology, 1998.of Linnhoff, M., (disponible atwww.linnhoffmarch.com) or using the experience ΔTmin

presented in the first tier - basic concepts.

d) Propose a heat exchanger network for the chosen

ΔTmin and respecting the energy targets.

e) Design a network that features the minimum number

of units for maximum energy recovery

215

3.2 PULP & PAPER OPEN-ENDED PROBLEM

216

PROBLEM DEFINITION

An integrated newsprint mill is located in Canada. The nominal production of the mill is 1230 odt/d (oven dried tons per day) of paper with a feedstock of 1060 odt/d of thermomechanical pulp (TMP) and 170 odt/d of deinked pulp (DIP) also produced on site.

A simplified process flow diagram focusing on steam and fresh water requirements is given in Fig.1.

217

PROBLEM DEFINITION

Fig. 1. Simplified reference process flow diagram. Abbreviations: CPH: chips pre-heather, HRU: heat recovery unit, OM: old magazines, ONP: old newsprint, PM: paper machine.

218

PROBLEM DEFINITION

High pressure steam (16.5 bar, 540 K) is produced by boilers burning biomass( wood residues) and natural gas (NG). It is in part directly used to meet some mill needs and in part depressurised through turbines and headers to three lower pressure levels: MP (4.5 bar, 421 K), LP (3.4 bar, 415 K) and VLP (1.7 bar, 408K).

As indicated on Fig. 2, steam is then directed to the TMP, DIP, paper making plants and other miscellaneous operations. Steam is also exported to an adjoining saw mill. The turbines produce 2 MWe of electricity, while the mill purchases 125 MWe.

219

PROBLEM DEFINITION

Fig. 2. Reference steam distribution system. Abbreviations, NG: natural gas, WM: water make-up.

220

PROBLEM DEFINITION

The two most important operations from the energy standpoint are wood chips refining and paper drying.

Refining consists in disintegrating wood into individual fibres by forcing the chips between two grooved disks rotating at very high speed. In the mill analysed, the refiners consume 83.7 MWe or 6820 kJ/odt. The mechanical energy supplied to the refiners is largely dissipated into heat, which evaporates whitewater injected with the chips.

221

PROBLEM DEFINITION

The heat content of this medium steam is recovered through heat exchanges with fresh water in the heat recovery unit (Fig.1) since it contains wood contaminants and cannot be reused directly. The steam from the primary refiners is released at medium pressure (MP) but is subsequently depressurised to low pressure (LP). The steam from the secondary refiners (1 bar, 273 and 1.4 bar, 282 K) is not recovered currently.

Paper is dried in the end section of the paper machine by passing the sheet of paper over a series of steam-heated steel rolls.

222

PROBLEM DEFINITION

High-pressure steam is used at the beginning and MP in the intermediate zone.

In the follwowing sections are refer types of operation in the paper mill and the thermodynamic requirements.

Preheating by steam injection

The chip washing operation and the three main whitewater chests are heated by direct contact with steam (Fig. 1). This steam must be treated as loss by the utility network since it is not returned to the boilers as condensate.

223

PROBLEM DEFINITION

The thermodynamic requirement is defined by two cold streams in order to separate mass exchange from heat exchange. The first represents the heat required to raise the temperature of the process stream to tank mixing conditions. The second cold stream represents the heat required to raise the liquid water makeup that completes the mass balance from ambient (i.e. the water inlet temperature) to the reservoir mixing conditions. Data are given on Fig. 3 for the wood chip washing operation. In the thermodynamic representation isothermal mixing is assumed, all the process streams entering the mixer having first been heated to the mixing temperature.

224

PROBLEM DEFINITION

Fig. 3. Thermodynamic (reference case)

Stream Comp. T (K) P (bar) m (kg/s)

1 WW 278 2 3.6

2 Steam 351 1 3.6

3 Steam 351 1 3057.3

4 Chips 278 1 15.7

5 WW 350 1 3040

Exchanger

Q (kW)

EX 1 1086

EX 2 2243

EX 3 6390

225

PROBLEM DEFINITION

Paper machine drying

There are two thermodynamic requirements for the drying section of the paper machine: preheating the humid sheet, and evaporating its water content which is reduced from 58% at the inlet of the drying section to 8% in the exiting paper.

Primary and secondary refiners

Since the steam produced by evaporation of the white water in the refiners is not returned in the steam network, the thermodynamic requirements are identically defined as a hot stream to be condensed and cooled to the ambient temperature. 226

PROBLEM DEFINITION

Table 1 gives the characteristics of the hot and cold streams for thermodynamic requirements of each of the major energy consuming operations in the process shown on Fig.1. Steam consumption for soot blowing and general heating has been assimilated to process requirements and the consumption for deaeration is treated as part of the steam network model. The secondary refiner steam will be recovered.

227

TABLE 1

Representation Stream type Tin (K) Tout (K) m Cp (kW/K) Q (MW) P (bar)

Wood chip washing

Thermo. (chips) Cold 278 351 31 2.2 –

Thermo. (WW) Cold 350 351 13,595 6.4 –

Thermo. (makeup) Cold 278 351 15 1.1 –

Preheat before primary refiners

Thermo. 351 388 251 9.4 –

Preheat before secondary refiners


Thermo. (pulp) Cold 324 362 60 2.3 –

TMP whitewater tank

Thermo. (FW) Cold 278 321 591 25.7 –


Thermo. (WW) Hot 324 321 2576 6.5 –

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TABLE 1 (CONTINUED)


Deinking whitewater tank

Thermo. (FW) Cold 308 313 70 0.3 –

Thermo. (WW) Cold 313 313 950 0.2 –


Paper machine whitewater

Thermo. (FW) Cold 288 308 1004 20.2 –


Thermo. (WW) Hot 309 308 4768 5.8 –

Drying section

Thermo. (heating) Cold 309 363 42 25.7 –

Thermo. (drying) Cold 309 373 Water 1.4 –

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TABLE 1 (CONTINUED)


Conventional representation

Primary refiners Cold 421 298 Water 73.7 4.46

Secondary refiners Cold 373 298 Water 14.3 1.00

Secondary refiners Hot 388 298 Water 7.5 1.70

Heating Cold 323 417 Water 30.1 3.43

Soot blowing Cold 278 540 Water 6.0 16.52

Effluent treatment Cold 278 417 Water 1.5 3.43

Saw mill Cold 278 417 Water 5.1 3.43

Boilers Cold 323 417 Water 8.3 3.43

Deareator Cold 323 408 Water 3.8 1.70

LP level Cold 323 417 Water 47.6 3.43

MP level Cold 323 421 Water 8.7 4.46

HP level Cold 323 540 Water 10.7 16.52

LP level Hot 394 323 Water 10.2 2.03

MP level Hot 407 323 Water 2.3 3.06

HP level Hot 472 323 Water 3.5 15.12

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Perform a complete Thermal Pinch Analysis

Using the hot and cold streams from the process flowsheet reported in the table 1, determine QH,min, QC,min , the minimum consumption of external utilities (energy targets), and construct the grand composite curves.

Propose a ΔTmin using Introduction to Pinch Technology, 1998.of Linnhoff, M., (disponible at www.linnhoffmarch.com) or using the experience ΔTmin presented in the first tier - basic concepts.

Propose a heat exchanger network for the chosen ΔTmin and respecting the energy targets.

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module 12: “heat and mass exchange networks optimization”

Documents

relevant heat

designedthe basic process

mass networks optimization

pinch analysis71

structure of module

role of pinch technology

overall process design

basic conceptstier i4tier