process synthesis and optimization of an … · process synthesis and optimization of an integrated...

PROCESS SYNTHESIS AND OPTIMIZATION OF AN INTEGRATED

CHILLED AND COOLING WATER SYSTEM FOR RESOURCES

CONSERVATION

LEONG YIK TEENG

DEGREE OF DOCTOR OF PHILOSOPHY

A thesis submitted for the degree of Doctor of Philosophy at

Monash University in 2016

School of Engineering (Chemical Engineering)

ii

Copyright notice

Notice 1

© Leong Yik Teeng (2016). Except as provided in the Copyright Act 1968, this thesis may not

be reproduced in any form without the written permission of the author.

iii

Abstract

Globalization, economic development and population growth have led to a sustained upward

trend in world energy demand. The increasing level of energy consumption, especially in the

industrial sector, has also contributed to adverse environmental impact via carbon emissions.

Water chillers, which are used in many industrial processes for heating, ventilating and air

conditioning (HVAC) and process cooling, are among the major energy consumers in many

industrial facilities. Energy sources depletion and the increasing greenhouse gas pollutions have

driven the worldwide effort to reach the highest possible level of energy efficiency. One of the

strategies to improve energy efficiency is by having multiple plants located in a close proximity

known as eco-industrial park (EIP); cooperate in a joint effort to achieve a greater overall energy

savings. Forming an EIP which is operated by independent entities requires the consensus from

all parties, thus there exists a need for a strategic decision-making tool. Moreover, periodical

circumstances such as seasonal and market demand changes by each participating plant would

result in different mode of process operation in an EIP. Thus, there is a need to study explicitly

the effect of such periodical operations due to the high level of connectivity within an inter-plant

network. In this research, we have developed four different approaches for EIP by integrating

both chilled and cooling water systems (CCWS). First contribution in this work is the

introduction of free cooling in an integrated superstructure for CCWS. It is found that the

interaction between both systems could enhance the overall resource conservation beyond those

achievable by individual system alone. Second contribution is the adoption of fuzzy analytic

hierarchy process (FAHP) approach in the development of decision-making framework for the

synthesis of inter-plant chilled and cooling water network (IPCCWN). This approach considers

all the participating plants‘ interest for the establishment of an EIP so as to reach the consensus

of cooperation. Third contribution is the development of a systematic stepwise approach for

obtaining a flexible multi-period IPCCWN that could accommodate for the variation of cooling

utility flow rate and temperature. Lastly, we proposed an integrated analytic hierarchy process

(IAHP) approach to the development of multi-objective optimization of IPCCWN that embeds

multiple design criteria simultaneously. In future work, we suggest extending the aforementioned

approaches to CCWS with waste heat recovery scheme through absorption chilling process.

iv

Declaration

This thesis contains no material which has been accepted for the award of any other degree or

diploma at any university or equivalent institution and that, to the best of my knowledge and

belief, this thesis contains no material previously published or written by another person, except

where due reference is made in the text of the thesis.

Signature:

Print Name: Leong Yik Teeng

Date: 13/4/2016

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Publications during enrolment

1. Leong, Y. T., Tan, R. R., Aviso, K. B., Chew. I. M. L., 2015, Fuzzy Analytic Hierarchy

Process and Targeting for Inter-Plant Chilled And Cooling Water Network Synthesis, Journal

of Cleaner Production, 110, 40-53.

2. Leong, Y. T., Lee, J.-Y., Chew. I. M. L., 2016, Incorporating Timesharing Scheme in Eco-

industrial Multi-period Chilled and Cooling Water Network Design, Industrial &

Engineering Chemistry Research, 55(1), 197-209.

3. Leong, Y. T., Tan, R. R., Chew. I. M. L., 2015, Superstructural Approach to the Synthesis of

Free-Cooling System through an Integrated Chilled and Cooling Water Network, Process

Safety and Environmental Protection. (In press) DOI:

http://dx.doi.org/10.1016/j.psep.2015.10.017.

4. Leong, Y. T., Tan, R. R., Chew. I. M. L., 2014, Optimization of Chilled and Cooling Water

Systems in a Centralized Utility Hub, Energy Procedia, 61. 846-849.

5. Leong, Y. T., Tan, R. R., Balan, P., Chew. I. M. L., 2015, Synthesis of Mixed Strategy

Games in Eco-Industrial Park using Integrated Analytic Hierarchy Process, Chemical

Engineering Transactions, 45, 1651-1656.

http://dx.doi.org/10.1016/j.psep.2015.10.017

vi

Thesis including published works General Declaration

I hereby declare that this thesis contains no material which has been accepted for the award of

any other degree or diploma at any university or equivalent institution and that, to the best of my

knowledge and belief, this thesis contains no material previously published or written by another

person, except where due reference is made in the text of the thesis.

This thesis includes three original papers published in peer reviewed journals and one

unpublished publications. The core theme of the thesis is process synthesis and the optimization

of chilled and cooling water system for resources conservation. The ideas, development and

writing up of all the papers in the thesis were the principal responsibility of me, the candidate,

working within the chemical engineering under the supervision of Dr. Irene Chew Mei Leng.

(The inclusion of co-authors reflects the fact that the work came from active collaboration

between researchers and acknowledges input into team-based research.)

In the case of four chapters my contribution to the work involved the following:

Thesis

chapter

Publication title Publication

status*

Nature and

extent (%)

of students

contribution

3 Superstructural approach to the synthesis of free-cooling

system through an integrated chilled and cooling water

network

in press 85

4 Fuzzy analytic hierarchy process and targeting for inter-

plant chilled and cooling water network synthesis

published 75

5 Incorporating Timesharing Scheme in Ecoindustrial

Multiperiod Chilled and Cooling Water Network Design

published 85

6 Multi-objective optimization of inter-plant chilled and

cooling water network using integrated analytic hierarchy

process

submitted

to journal

75

* e.g. ‘published’/ ‘in press’/ ‘accepted’/ ‘returned for revision’/‘submitted to journal’

vii

I have renumbered sections of submitted or published papers in order to generate a consistent

presentation within the thesis.

Student signature: Date: 13/4/2016

The undersigned hereby certify that the above declaration correctly reflects the nature and extent

of the student and co-authors‘ contributions to this work.

Main Supervisor signature: Date: 13/4/2016

viii

Acknowledgements

First, I would like to express my gratitude to my supervisor, Dr. Irene Chew Mei Leng and my

co-supervisor, Prof. Raymond R. Tan, for their guidance during my Ph.D study. Also, my

appreciation goes to the research collaborators, Dr. Lee Jui-Yuan and Dr. Kathleen B. Aviso.

I would like to acknowledge my financial support from Monash University Malaysia (Higher

Degree by Research Scholarships) and the Ministry of Higher Education

(FRGS/2/2014/TK05/MUSM/03/1).

Sincere thanks to my family and my friend, Wern Wei, for their support and motivation during

my Ph.D study. Lastly, thanks to my colleague, Siu Hoong.

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TABLE OF CONTENTS

Page

CHAPTER 1 INTRODUCTION 1

1.1 Background 1

1.2 Research objectives and scopes 3

CHAPTER 2 LITERATURE REVIEW 5

2.1 Process integration – process system engineering 5

2.2 Total site/Inter-plant Integration 6

2.3 Chilled Water System 7

2.3.1 Vapor-compression refrigeration system 8

2.3.2 Absorption refrigeration system 9

2.4 Process synthesis and optimization of chilled water system 11

2.5 Cooling Water System 13

2.6 Process synthesis and optimization of cooling water system 16

CHAPTER 3 SUPERSTRUCTURAL APPROACH TO THE SYNTHESIS OF

FREE-COOLING SYSTEM THROUGH AN INTEGRATED CHILLED AND

COOLING WATER NETWORK

20

3.1 Introduction 20

3.2 Problem statement 22

3.3 The optimization model 23

3.3.1 Base scenario 24

3.3.1.1 Mass and energy balance of process sources and sinks 25

3.3.1.2 Design of the cooling tower 25

3.3.1.3 Design of the chiller 27

3.3.1.4 Total annual power consumption of a chilled and cooling water

system

28

3.3.1.5 Total annual cost of a chilled and cooling water system 29

3.3.2 Scenario 1 29

x

3.3.3 Scenario 2 30

3.3.4 Scenario 3 32

3.4 Case studies 34

3.4.1 Example 1 37

3.4.1.1 Single chiller and cooling tower 37

3.4.1.2 Multiple chillers and cooling towers 43

3.4.2 Example 2 44

3.4.2.1 Single chiller and cooling tower 44

3.4.2.2 Multiple chillers and cooling towers 50

3.5 Conclusion 51

CHAPTER 4 FUZZY ANALYTIC HIERARCHY PROCESS AND

TARGETING FOR INTER-PLANT CHILLED AND COOLING WATER

NETWORK SYNTHESIS

52

4.1 Introduction 52

4.2 Problem Statement 54

4.3 Methodology: stage 1 - optimization model for generating alternative IPCCWN

designs

55

4.4 Methodology: stage 2 - fuzzy analytic hierarchy process (FAHP) approach 59

4.5 Case Study 61

4.6 Conclusion 79

CHAPTER 5 INCORPORATING TIMESHARING SCHEME IN ECO-

INDUSTRIAL MULTI-PERIOD CHILLED AND COOLING WATER

NETWORK DESIGN

81

5.1 Introduction 81

5.2 Problem Statement 83

5.3 Design methodology 85

5.3.1 Step 1: Multi-period single plant CCWN 85

5.3.2 Step 2: Preliminary multi-period IPCCWN 86

5.3.3 Step 3: Pareto optimal multi-period IPCCWNs 89

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5.3.3.1 Pareto optimal solution 1 (POS 1): Global minimum-cost network

design approach

89

5.3.3.2 Pareto optimal solution 2 (POS 2): Fuzzy optimization approach 89

5.3.4 Step 4: Timesharing scheme for multi-period IPCCWN 90

5.4 Case study 90

5.4.1 Four-step design methodology 93

5.4.1.1 Step 1: Determining upper limit cost for each participating plant 93

5.4.1.2 Step 2: Determining lower limit cost for each participating plant 94

5.4.1.3 Step 3: Obtaining Pareto optimal EIPs 96

5.4.1.4 Step 4: Applying timesharing scheme on the Pareto optimal EIPs 99

5.5 Conclusion 104

CHAPTER 6 MULTI-OBJECTIVE OPTIMIZATION OF INTER-PLANT

CHILLED AND COOLING WATER NETWORK USING INTEGRATED

ANALYTIC HIERARCHY PROCESS

105

6.1 Introduction 105

6.2 Problem statement 107

6.3 Steps of IAHP approach to the establishment of an EIP 107

6.3.1 Step 1: Determining the criteria for the establishment of EIP 108

6.3.1.1 Economic performance 108

6.3.1.2 Environmental impact 109

6.3.1.3 Connectivity 110

6.3.1.4 Network reliability 111

6.3.2 Step 2: Pairwise comparison of the criteria 112

6.3.3 Step 3: Embedding criteria weightings in the EIP optimization model -

IAHP

113

6.4 Case study 114

6.4.1 The mathematical formulation of the criteria 115

6.4.1.1 Criterion – Economic performance 115

6.4.1.2 Criterion – Environmental impact 116

6.4.1.3 Criterion – Connectivity 118

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6.4.1.4 Criterion – Network reliability 119

6.4.2 Scenario 1 (Different weighting for the criteria) 120

6.4.3 Scenario 2 (Same weighting for the criteria) 128

6.5 Conclusion 132

CHAPTER 7 FUTURE RECOMMENDATION 133

NOMENCLATURE 134

REFERENCES 140

APPENDICES 151

Appendix 1: LINGO ver13 mathematical modelling codes in chapter 3 151




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LIST OF FIGURES

Page

Figure 2.1: Vapor-compression chiller system 8

Figure 2.2: Vapor-compression chiller cycle 8

Figure 2.3: Absorption refrigeration cycle 10

Figure 2.4: Schematic diagram of cooling water system 14

Figure 2.5: Graphical representation of cooling tower characteristic 15

Figure 3.1-a: Conventional chilled water system 21

Figure 3.1-b: Proposed scheme with a free-cooling structure 22

Figure 3.2: Schematic of CCWS without free-cooling (Base scenario) 23

Figure 3.3: Schematic of CCWS with free-cooling (Scenario 1) 23

Figure 3.4: Schematic of CCWS with free-cooling plants (Scenario 2) 24

Figure 3.5: Schematic of CCWS with free cooling (Scenario 3) 24

Figure 3.6: results for Base scenario, Scenario 1, Scenario 2 and Scenario 3

(Example 1)

38

Figure 3.7: CCWS for Example 1 (Base scenario) 39

Figure 3.8: CCWS for Example 1 (Scenario 1) 40



Figure 3.11: Overall for Example 1 43

Figure 3.12: results for Base scenario, Scenario 1, Scenario 2 and Scenario 3

(Example 2)

45

Figure 3.13: CCWS for Example 2 (Base scenario) 46




Figure 3.17: Overall for Example 2 50

Figure 4.1: Satisfaction level based on fuzzy goal 56

Figure 4.2: A depiction of a triangular fuzzy number 60

Figure 4.3: Network structure of preliminary IPCCWN 67

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Figure 4.4: Network structure of alternative IPCCWN in Strategy 1 70



Figure 4.7: Hierarchy for selecting optimum IPCCWN design 74

Figure 4.8: Final average weights of the criteria for selecting the optimum IPCCWN

design

76

Figure 4.9: Design methodology of optimum IPCCWN 79

Figure 5.1: Flowchart of the proposed design methodology 84

Figure 5.2: Superstructure for single plant CCWN in any time period 86

Figure 5.3: Superstructure for the inter-plant CCWN in any time period 88

Figure 5.4: Percentage network cost savings for all the plants with different objective

function

95

Figure 5.5: Multi-period inter-plant CCWN of POS 1 (indicated streams , ,

and in kg/h)

98

Figure 5.6: Multi-period inter-plant CCWN of POS 2 (indicated streams , ,

and in kg/h)

99

Figure 5.7: Multi-period inter-plant CCWN of POS 1with timesharing scheme

(indicated streams , , and in kg/h)

101

Figure 5.8: Alternative sharing of multi-period cross-plant pipelines for POS 1


102

Figure 5.9: Multi-period inter-plant CCWN POS 2 with timesharing scheme (indicated

streams , , and in kg/h)

103

Figure 5.10: Alternative sharing of multi-period cross-plant pipelines for POS 2


104

Figure 6.1: Decision hierarchy for the establishment of EIP using the proposed IAHP 114

Figure 6.2: Main criteria proposed for the establishment of EIP 115

Figure 6.3: IPCCWN for Scenario 1(a) 124

Figure 6.4: IPCCWN for Scenario 1(b) 127

Figure 6.5: IPCCWN for Scenario 2(a) 129

Figure 6.6: Inter-plant CCWN for Scenario 2(b) 131

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LIST OF TABLES

Page

Table 3.1: Process data for Example 1 35

Table 3.2: Process data for Example 2 35

Table 3.3: Parameter values in the optimization model 36

Table 4.1: Linguistic terms and the corresponding TFNs 59

Table 4.2: Water characteristic of design coil in Plant A (Foo et al., 2014a) 62

Table 4.3: Water characteristic of design coil in Plant B 63

Table 4.4: Water characteristic of design coil in Plant C 63

Table 4.5: Final water limiting data 64

Table 4.6: Parameter values for the case study 65

Table 4.7: Fresh chilled and cooling water requirement for Plant A, Plant B and Plant C

in Base case

65

Table 4.8: Comparison of total network cost between base case and preliminary

IPCCWN

66

Table 4.9: Cost saving allocation of Strategies 1, 2 and 3 68

Table 4.10: Fuzzy Optimization results of Strategies 1, 2 and 3 73

Table 4.11: The comparison matrix of criteria for Plant A, Plant B and Plant C 75

Table 4.12: The average matrix comparison of criteria 75

Table 4.13: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to

participants satisfaction (C1)

76


fresh cost (C2)

77


piping cost (C3)

77

Table 4.16: The comparison of Strategy1, Strategy 2 and Strategy 3 with respect to

reliability (C4)

77

Table 4.17: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to cost

savings allocation strategy (C5)

77

Table 4.18: Scores of Network Design 1, Network Design 2 and Network Design3 with 78

xvi

respect to participant‘s satisfaction (C1), fresh cost (C2), piping cost (C3), reliability

(C4) and cost savings allocation strategy (C5)

Table 5.1: Temperatures and flow rate of sinks and sources 92

Table 5.2: Parameter values for the case study 93

Table 5.3: Total network cost and fresh chilled and cooling water consumption for base

case

94

Table 5.4: Results for preliminary multi-period inter-plant CCWNs of EIP 95

Table 5.5: Results for POS 1 and POS 2 96

Table 6.1: Scale of relative importance 113

Table 6.2: Rankings of economic performances for participating plants 116

Table 6.3: Rankings of environmental impact for participating plants 117

Table 6.4: Rankings of connectivity for participating plants 118

Table 6.5: The value (indicated value in kg/h) 119

Table 6.6: Rankings of network reliability for participating plants 120

Table 6.7: Pairwise comparison matrix of the criteria for the establishment of EIP based

on Plant 1

121


on Plant 2

121


on Plant 3

122

Table 6.10: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 1(a) 125

Table 6.11: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 1(b) 128

Table 6.12: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 2(a) 130

Table 6.13: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 2(b) 132

1

CHAPTER 1 INTRODUCTION

1.1 Background

Economic growth is the main factor considered in the projection of world energy consumption. It

is projected that the world‘s gross domestic product (GDP) growth averages 3.6% per year (EIA,

2013). World energy consumption will then grow by 56% between 2010 and 2040. Worldwide

energy-related carbon emissions are projected to be risen from about 31 billion metric tons in

2010 to 45 billion metric tons in 2040, a 46% increase. The world industrial sector will still

consume the largest of global delivered energy in 2040. The environmental concern issues, such

as global warming, will be worsen due to the gradually increasing greenhouse gas emissions

from the energy production. If no action taken to mitigate carbon dioxide emissions before 2017,

all the allowable carbon dioxide would be locked-in by energy infrastructure at that time (IEA,

2012).

In Malaysia, four main energy sources contribute to the overall power generation in decreasing

order are natural gas, coal, hydropower and oil. The overall carbon footprint for the power

generation in Malaysia is estimated at average 0.662 kg CO2/kWh (Lim, 2009). Chillers are by

far the major electric energy user among the facilities in office, commercial and institutional

building for air-conditioning (Saidur, 2009). Also, chillers are commonly used in industries for

process cooling purposes. It is found that 27.2% of the total power are consumed by chiller

plants in a semiconductor fabrication (Hu and Chuah, 2003). In a typical blow moulding factory

(Tangram, 2001), chillers use 14% of the total electricity for plastic processing. Chillers account

for 54-67% of the total energy in fresh fruit and vegetable processing plants (Hackett et al.,

2005). Enhancing the chillers‘ system could save a very substantial amount of the electric energy

and reduce the associated emissions released to the atmosphere. These make them the excellent

candidate for improvements to its efficiency (Saidur et al., 2011).

Over the last 30 years, the coefficient of performance (COP) of water-cooled chillers has been

improved from 4 to 7 (Jayamaha, 2006). Many research works have been carried out focusing on

the study of individual chiller units with particularly finding the optimal chiller loading. Various

2

methods include the use of Lagrangian (Chang, 2004), genetic algorithm (Chang, 2005), particle

swarm algorithm (Lee and Lin, 2009), and differential evolution algorithm (Lee et al., 2011)

were presented to optimize the chiller‘s performance. Although improving the energy

performance of chillers provides the greatest energy savings, additional opportunities remain,

which can potentially be explored to reduce the overall energy consumption.

An integrated approach such as system optimization is desired to improve the overall cost

savings. Trane (2000) proposed system optimization to examine the entire units of operation

including chiller, water pumps, piping, cooling tower, and global controls with the goal of

simultaneously reducing capital costs and operating costs. Three strategies are proposed for

energy and capital cost reduction; (1) reduce condenser design flow rates which can be done by

using a smaller water pump, cooling tower or pipe size; (2) reduce chilled water flow rate and

temperature and (3) control condenser water temperature. Graves (2003) presented

thermodynamic model of chiller and cooling tower system in the process control for improving

the overall energy efficiency. Furlong and Morrison (2005) analysed the combination of water-

cooled chiller and cooling tower performance by considering the design load, load profile, and

local ambient conditions in the system optimization.

Process integration (PI) techniques are a useful strategy that facilitates the integration of a system

considering the interaction among the unit operations and supply chain networks for energy

conservation. They have been widely applied on the optimization of both chilled and cooling

water systems (CCWS) separately. The combination of two PI techniques, namely pinch analysis

and mathematical optimization, have been proposed in the design of cooling water system (Feng

et al., 2005; Majozi and Nyathi, 2007; Kim and Smith, 2003). The former technique is usually

applied to target the minimum cooling water flow rate before precedes the design of cooling

water network using the latter techniques. Various superstructural approach to the synthesis of

optimal cooling water systems with the minimum total annual cost (Ponce-Ortega et al., 2010;

Rubio-Castro et al., 2013) and cooling water flow rate were determined (Majozi and Moodley,

2008). Only a few works have been reported using PI techniques in the optimization of chilled

water network (Lee et al., 2013; Foo et al., 2014b).

3

In addition, chilled and cooling water are common utilities of various petrochemical and

chemical industries. Sharing of these utilities through the synthesis of symbiotic network among

multiple plants would able to enhance the energy conservation based on the concept of industrial

symbiosis (IS) (Chertow, 2007). This symbiotic relationship among different entities is

encouraged by the proximity of geography where different plants are co-located to establish an

eco-industrial park (EIP) (Chiu, 2003). An example for the first realization of IS is Kalundborg

EIP (Jacobsen, 2006) where multiple companies collaborate and share their resources. This has

motivated the research presented in this study to develop systematic frameworks for the

synthesis of chilled and cooling water system in an EIP using process integration techniques.

1.2 Research objectives and scopes

This research focuses on the development of chilled and cooling water system (CCWS) in an EIP

via PI. The main outcomes from this research are to attain robust and optimum decision-making

frameworks for the development of inter-plant chilled and cooling water network (IPCCWN)

The optimum frameworks consist of systematic approaches such as superstructural approach to

enhance the overall energy conservation, game theory to reach to the consensus of cooperation

from different companies, timesharing scheme to deal with the network uncertainties and

integrated analytical hierarchy process (IAHP) to address multiple objectives simultaneously in

the optimization so as to obtain a resilient CCWS. Four main objectives have been identified in

this work to achieve the aforementioned. The objectives and their respective scopes are listed as

follow:

Synthesis and optimization of CCWS with free-cooling structure:

Free cooling could reduce energy consumption through evaporative cooling mechanism

as it is less energy intensive as compared to water chiller. It is proposed to integrate free-

cooling structure in CCWS to enhance the overall energy conservation. Single objective

superstructural approach is adopted in this study to explore all the possible topological

arrangements of CCWS.

4

Development of decision-making framework for IPCCWN design:

Fuzzy analytic hierarchy process (FAHP) is a systematic decision-making tool in solving

complex decision problem involving multi-objective for an IPCCWN. This study is to

develop a decision-making framework from the stage of the synthesis of alternative inter-

plant network designs to the stage of the selection process. Decision makers from

different companies would be able to select an optimal solution based on the criteria

given using FAHP.

Synthesis of multi-period IPCCWN:

Periodical changes in cooling demands would affect the network feasibility if it is

configured under single period assumption. To solve this, cooling demands for all the

time periods should be considered during the stage of network design. This study

develops a systematic design methodology to determine Pareto optimality for multi-

period IPCCWN. Fuzzy optimization approach is adopted to synthesize the IPCCWN

considering individual plants‘ goals. Timesharing scheme is then presented to efficiently

share the pipelines for all time periods.

Multi-objective optimization of IPCCWN:

Multiple design criteria such as economic performance, sustainability, connectivity and

network reliability are identified as the main objectives concerned for the establishment

of EIP. This study proposes an IAHP with mathematical optimization approach that

embeds the aforementioned objectives for the synthesis of an optimum IPCCWN.

5

CHAPTER 2 LITERATURE REVIEW

2.1 Process integration – process system engineering

Process integration (PI) is a holistic approach to process design, retrofitting, and operation which

emphasizes the unity of process (El-Halwagi, 1997). It offers a systematic and integrative

framework for a process to determine its attainable performance targets, select the design options

leading to the realization of these targets, and understand the global insights of the process.

Three vital elements of PI include synthesis, analysis and optimization. Rudd (1968) defined

process synthesis as the discrete decision making activities of conjecturing (1) which of the many

available components parts one should use, and (2) how they should be interconnected to

structure the optimal solution to a given design problem. A flow sheet which represents the

interconnection of various pieces of equipment is the result of process synthesis. Process

synthesis and process analysis supplement each other in a process design. Process analysis is

aimed at decomposing the whole process into its constituent elements for individual study.

Through process analysis, the detailed characteristics (e.g flow rates, temperatures, and pressure)

can be obtained. Once the process has been synthesized and analysed, it might not necessarily

meet the design objectives. Therefore, it is important to optimize the process in order to obtain

the optimum design among the set of candidate solutions. In process optimization, objective

function (e.g cost, profit, power consumption, etc) which will be minimized or maximized

represents how optimal is the design.

There exist two distinct PI techniques: insight-based pinch analysis and mathematical

optimization techniques. The insight-based techniques, includes graphical and algebraic

methods, provides useful insight for problem analysis. The earliest successful attempt in

graphical technique is the synthesis of heat exchanger network for minimum hot and cold utility

targeting (Linnhoff and Flower, 1978; Linnhoff and Hindmarsh, 1983). Subsequently, the

analogy between heat and mass transfer led to the evolution of mass integration (El-Halwagi and

Manousiouthakis, 1989), from which water network synthesis has become a widely studied area

(Kuo and Smith, 1998; Foo, 2009). In the graphical approach, pinch diagram is created by

plotting a hot and cold composite stream on the same diagram. The point where both composite

streams touch is termed as the thermal pinch point. Using the pinch diagram, one can determine

6

the minimum heating and cooling utility requirements. However, graphical techniques have low

accuracy and tedious solution for complex problem. In such cases, an algebraic technique is

recommended. Although this technique has less insight for designers compare to graphical

technique, it is more computationally effective especially for large and complex problems.

Mathematical optimization techniques, on the other hand, are powerful in handling many

practical constraints such as capital cost function and sustainability. Although it does not provide

good insights for designers, it can handle multiple quality constraints simultaneously.

Superstructural approach is the most commonly used mathematical optimization technique to the

synthesis of resource conservation networks.

2.2 Total site/Inter-plant Integration

The concept of industrial ecology which promotes cooperation among companies has been

widely adapted in the field of process integration to generate greater overall material and energy

savings as compared to unilateral initiatives. Frosch and Gallopoulos (1989) proposed that

resource consumption and waste generation may be further minimized by allowing the waste

material and energy streams from one industry serve as inputs for another. The existence of

resource exchange among the industrial plants within a specific geographical zone will then form

an eco-industrial park (EIP).

Considerably amount of works in process integration were extended to include multiple

networks. Total site/Inter-plant integration can be defined as a network consisting of plants of

different kinds directly or indirectly using process streams. Dhole and Linnhoff (1993) and Hu

and Ahmad (1994) studied on total site heat integration to determine levels of generation of

steam to indirectly integrate different processes. Since the generation and use of steam has to be

performed at a fixed temperature, opportunities for integration are lost. Olesen and Polley (1996)

decomposed the overall plant into individual zones and determined the interzonal spent water

that can be transferred by using ―Load Table‖ and ―Capacity Diagram‖. Rodera and Bagajewicz

(1999) developed targeting procedures for direct and indirect integration in a special case of two

plants. Bagajewicz and Rodera (2000) extend the results originally developed for two plants

(Rodera and Bagajewicz, 1999) to the case of multiple plants. Foo (2008) presented plant-wide

integration by using water cascade analysis technique.

7

On the other hand, mathematical optimization techniques for the inter-plant integration have also

been reported. One of these is the superstructural-based optimization techniques by Lovelady et

al. (2007) for an integrated pulp and paper mill. Liao et al. (2007) considered the multi-period

problem by solving a mixed integer nonlinear programming (MINLP) model to locate minimum

inter-plant water targets. Chew et al. (2008) proposed two different IPWI schemes which is

direct and indirect integration. Water is reused directly in different plants via inter-plant pipelines

in the direct scheme and a mixed integer linear program (MILP) model is formulated and solved

to attain the water flow rates; whereas in the indirect scheme a centralized utility hub exists to

collect water before it is reused in other plants. Chew and Foo (2009) proposed an automated

targeting method which is formulated as a linear programming model for inter-plant water

integration. In their work, the developed model aids in determining the minimum flow rate or

cost targets before detailed network design. Lovelady and El-Halwagi (2009) presented a source-

interception-sink structural approach where the interception units account for the possibilities of

direct recycle, material exchange, mixing and segregation of different streams, separation and

treatment to manage the water resources in an EIP.

2.3 Chilled Water System

Chilled water is common utility often used to cool building‘s air and is indispensable in such

industries as plastic industries, semiconductor fabrication, chemical processing, food and

beverage processing, and pharmaceutical industry, among others. It provides cooling at

temperatures (between 2°C to 7°C) below that which cannot be achieved using cooling water.

Systems that employ chilled water to perform cooling duty are known as chilled water system.

Chilled water system can be centralized, where single chiller serves multiple cooling purposes

with cooling capacities ranging from ten tons to thousands of tons, or decentralized where each

application has its own chiller with cooling capacities ranging from 0.2 to 10 short tons.

Chillers can be water-cooled, air-cooled, or evaporative cooled. Water–cooled chillers are cooled

by a separate condenser water loop and connected to cooling towers to remove heat to the

atmosphere. Air-cooled and evaporative cooled chillers need no cooling tower, the former are

8

directly cooled by ambient air while the latter implement a mist of water over the condenser coil

to aid in condenser cooling.

There are two types of chiller technology: vapor-compression chiller and absorption chiller.

Vapor-compression chiller are by far the most commonly used while absorption chiller only

applied in special circumstances where waste heat is available or where heat is derived from

solar collectors.

2.3.1 Vapor-compression refrigeration system

Vapor-compression refrigeration system typically consists of a compressor, a condenser, an

evaporator and a thermal expansion device (also called throttle valve) (Figure 2.1). It uses

electrically powered compressor to drive the refrigeration process. Various design for vapor-

compression refrigeration technologies have been reviewed in (Park et al., 2015). Most vapor-

compression refrigeration system use chlorofluorocarbon refrigerant (CFCs) as the working

fluid.

Compressor

Thermal

expansion

valve

(Throttle valve)

Condenser

Evaporator

Figure 2.1: Vapor-compression chiller system Figure 2.2: Vapor-compression chiller cycle

Figure 2.2 depicts the thermodynamics of the vapor-compression refrigeration cycles (Perry et

al., 1997) on a temperature versus entropy diagram. As shown in Figure 2.2, refrigerant enters

the compressor as a saturated vapor at point 1 and exit the compressor as superheated vapor at

point 2. From point 1 to point 2, refrigerant is compressed to a higher pressure at constant

entropy. After the compressor, the refrigerant enters condenser through a coil or tubes for waste

Throttling

4 Tem

pera

ture

(T)

Specific entropy (s)

1

2

3

Saturated

vapour

Saturated

liquid

Superheated vapour

Liquid +

Vapour

Condensation

Evaporation

Compression

9

heat removal by either cooling water or cooling air flowing across the coil or tubes. The

condensation process occurs at essentially constant pressure. Refrigerant then leaves the

condenser as saturated liquid at point 3. From point 3 to point 4, liquid refrigerant is partially

vaporized through the expansion valve and undergo an abrupt decrease of pressure. Cold and

partially vaporized refrigerant provide cooling effect at the evaporator. The mixture of vapor and

liquid refrigerant from the evaporator is again a saturated vapor and enter compressor to

complete the refrigeration cycle.

The coefficient of performance (COP) of a vapor-compression refrigeration system is a ratio of

cooling duty performed to input power required, given in Eq. 2.1 (Smith, 2005). The power input

includes the compressor drive motor, condenser water pump drive motor, cooling tower fan drive

motor, and chiller control system feeder circuit.

(2.1)

2.3.2 Absorption refrigeration system

In contrast to vapor-compression refrigeration system, absorption refrigeration system uses heat

sources (e.g. waste heat, solar heat, etc) as the energy to drive the refrigeration process. Various

designs for absorption refrigeration technologies have been reviewed in Srikhirin et al. (2001).

Figure 2.3 shows the principle of absorption refrigeration process (Ameen, 2006). The

absorption refrigeration cycle combines refrigerant separation and absorption processes. The

absorption process is carried out in the absorber where the vapor refrigerant from the evaporator

is absorbed in a solution and heat is rejected to the surrounding during this process. The

refrigerant separation process is then carried out when the refrigerant is saturated in the

absorption process. Heat is applied to the generator in the refrigerant separation process. The

high pressure refrigerant vapor enters to a condenser, transferring its heat to the surrounding, and

condenses. The liquid refrigerant is throttled through a valve to a low pressure and is partially

vaporized and its temperature decreases. The low temperature refrigerant is then fed to an

evaporator, providing refrigeration process.

10

Generator Condenser

Absorber Evaporator

QLQH

QL QL

Refrigerant separation

process

Absorption process

Replace compressor

Figure 2.3: Absorption refrigeration cycle

The of the absorption refrigeration system can be evaluated from:

(2.2)

Note that the work input for the pump is often assumed negligible for the purposes of analysis.

There are many refrigerants available to run absorption refrigeration system, particularly water/

ammonia and lithium bromide/water are the most commonly used working fluids (Danny

Harvey, 2006). Ammonia absorption chillers can be applied to low temperature cooling process,

as the freezing point of ammonia is -77°C. Ammonia is used as refrigerant while water is used as

absorbent. Both ammonia and water are volatility thus requiring a rectifier in the refrigeration

system to remove water vapor which carried with ammonia before entering the condenser. This

is to avoid the water accumulate in the evaporator and offset the system performance. Ammonia

absorption chillers usually provide low cooling capacity of 3 to 5 tons and generally have a low

COP of about 0.5. It operates under very high pressure (485kPa in evaporator and 1500kPa in

condenser). Although ammonia and water are environmentally friendly, there are other

disadvantages such as its high pressure, toxicity, and corrosive to some metal.

Lithium bromide absorption chillers on the other hand, have limitation to the low temperature

application to that above 0°C. Such chillers use water as refrigerant and lithium bromide as

11

absorbent and must be operated under vacuum conditions. It has a higher COP as compared to

ammonia absorption chillers. Since lithium bromide is non-volatility absorbent, rectifier is no

needed in the refrigeration system. Lithium bromide has a very high affinity for water thus has a

very high absorption rate for water. It is also corrosive to some metals so requiring some additive

like lithium hydroxide and lithium chromate to avoid the corrosion.

2.4 Process synthesis and optimization of chilled water system

In the aspect of the chilled water system, many works have been reported on the optimization of

the individual chiller unit. Chang (2004) maximized the COP of a chiller for energy

conservation. The author determined the flow rate, supply and return temperature of chilled

water to estimates chiller output refrigerating capacity. Using COP-part load ratio (PLR) curve as

a concave function, results show larger power savings were obtained using Lagrangian method

as compared to the conventional method (equal loading rate). Chang (2005) later proposed

genetic algorithm in place of the Lagrangian method in the modelling to minimize the chilled

water system power consumption. In this work, genetic algorithm solved Lagrangian method's

problem of not being able to deal with a system with non-convex kW-PLR function.

Lee and Lin (2009) applied particle swarm algorithm to develop a model for optimal chiller

loading problem in multi-chiller system. The loading ratio of each chiller was considered as the

optimum parameter to minimize the energy consumption. Results showed that particle swarm

algorithm outperforms the genetic algorithm by overcoming the divergence of Lagrangian

method occurring at low demands. Lee et al. (2011) used differential evolution algorithm method

to solve the optimal chiller loading problem. From the results, the proposed method found the

same optimal solution as the particle swarm algorithm, but obtained better average solutions.

Lee and Cheng (2012) devised a hybrid optimization algorithm to identify the optimal settings

and minimize the energy consumption of the chilled water system. Particle swarm optimization

algorithm and Hooke-Jeeves algorithm were combined to form the hybrid optimization

algorithm. From the optimized results, optimal chilled temperature set-points can significantly

reduce the energy consumed by water chillers. However, the optimal temperature obtained for

chilled water is higher than the conventional setting; more water must be supply to consume

12

more energy. The optimized settings reduced the total energy consumed by the chilled water

system by 9.4% in summer and 11.1% in winter compared to conventional settings.

Apart from the optimization of the individual chiller unit, waste heat recovery technology using

absorption chiller is an alternative way to reduce the energy consumption in chilled water

system. Kalinowski et al. (2009) modeled and analyzed natural gas process with propane

refrigeration system and absorption refrigeration system by using Engineering Equation Solver

as modeling platform. In the modelling, few important assumptions were made: (i) only waste

heat from gas turbine is used to power the absorption refrigeration system, (ii) saturated vapor at

the outlet of rectifier with 0.99 ammonia concentration. The absorption refrigeration system

implementation reduces 1.9MW electricity used to operate conventional vapor compression

refrigeration cycle in conventional natural gas plant.

Popli et al. (2013) investigated the utilization of waste heat recovered from the gas turbine to

generate steam in waste heat recovery steam generator and to power single-effect water/LiBr

absorption refrigeration system. Under worst-case summer conditions, three waste heat powered

single-effect water/LiBr absorption chillers recovered 17MW from gas turbine exhaust gas and

this provides 12.3MW of cooling. Since absorption refrigeration system can provide same

amount of cooling as conventional vapor compression refrigeration cycle, the basis of thermo-

economic feasibility is justified.

Kaynakli et al. (2015) evaluated the effect of evaporator temperature on the exergy destruction of

high pressure generator in double effect absorption refrigeration system, which uses various heat

sources. The exergy destruction value is the highest in hot air applications and followed by, in

order, steam and hot water, under same operating conditions except the mass flow rate of heat

carrier.

On the other hand, optimization of chilled water network could also enhance the overall energy

conservation. Chew et al. (2007) developed a chilled water cascade analysis to determine the

minimum fresh chilled water requirement. Chilled water network that achieved the minimum

chilled water flow rate was then designed based on nearest neighbour algorithm (Prakash and

13

Shenoy, 2005). A dual saving of water and energy were achieved in this chilled water network

synthesis.

Lee et al. (2013) developed two different scheme, namely direct (without intermediate mains)

and indirect (with intermediate mains) integration, in the chilled water network model. The

design problem is formulated as MINLP models and applied to two industrial case studies.

Different network configurations achieving significant chilled water reduction were presented as

alternatives for practical implementation. The author also suggested studying a detailed work for

chilled water system design including the individual system components such as chiller units,

cooling towers and chilled water network as well as the case of multiple chilled water sources in

the future work.

Foo et al. (2014a) adopted a pinch analysis technique to identify the minimum water flow rate

requirement in chilled water network. In addition, an integrated chilled and cooling water

network was proposed in the study by Foo et al. to reduce operating costs and it is then compared

with the stand-alone chilled water network integration. The integration of both chilled and

cooling water network allows the mixing of both cooling sources in the process sink and so are

their return streams.

2.5 Cooling Water System

In cooling water system, cooling towers are used to reject waste heat to the ambient atmosphere.

Figure 2.4 shows a basic feature of a cooling water system. The hot water from the cooling water

network flow down through the packing of cooling tower counter currently or in cross-flow with

air. The packing inside the cooling towers provide a large interfacial area for heat and mass

transfer between air and water. Water is cooled by approximately 80 percent of latent heat

transfer owing to evaporation of the water and 20 percent of sensible heat transfer owing to the

difference in temperature of water and air. Water is lost through evaporation and drift. Drift is

droplet of water entrained in the air leaving the top of the tower. In Figure 2.4, blowdown is

necessary to prevent the build-up of contamination in the circulation while makeup water is

required to compensate for the loss of water from evaporation, drift and blowdown.

14

Cooling Tower

Cooling Water

Network

Cooling Water

Recirculation Water

Makeup

Drift/Windage Evaporation

Blowdown

Figure 2.4: Schematic diagram of cooling water system

Cooling towers mainly comprise of the frame and casing, fill, cold-water basin, drift eliminators,

air inlet, louvers, nozzles and fans. There are two main types of cooling towers: the natural draft

and mechanical draft cooling towers. The main difference between both cooling towers is the

former do not have fan and the latter have a large fan to force air through circulated water.

Natural draft cooling towers are usually constructed in concrete and mostly used for large heat

duties due to the expensive large concrete structure. Mechanical draft cooling tower for large

duties often consist of two or more cooling towers in order to achieve the desired capacity.

Merkel developed a most generally accepted theory of the cooling tower heat transfer process

based upon the analysis of enthalpy potential difference as the driving force. Gharagheizi et al.

(2007) and Lemouari et al. (2007) studied the thermal performance of a cooling tower with the

used of Merkel equation given in Eq 2.3 to evaluate the cooling tower performance.

∫

(2.3)

where = mass-transfer coefficient; = contact area/tower volume; = active cooling

volume of plan area; = circulating cooling water flow rate; = enthalpy of saturated air

at water temperature; = enthalpy of air stream; = inlet water temperature of cooling

tower and = outlet water temperatures of cooling tower.

The performance of cooling tower can be determined by evaluating the actual level of cooling

towers approach and range against the design values (Perry et al., 1997). Figure 2.5 presents the

15

En

tha

lpy

dri

vin

g

forc

e

Range

B

Air operating

line

Water Operating

Line

A

C

D

Approach

𝑯𝒂 𝒊𝒏

𝑯𝒂 𝒐𝒖𝒕

𝑯𝒘 𝒊𝒏

𝑯𝒘 𝒐𝒖𝒕

𝑻𝒘𝒃 𝒊𝒏 𝑻𝒘 𝒊𝒏 𝑻𝒘 𝒐𝒖𝒕 𝑻𝒘𝒃 𝒐𝒖𝒕

cooling tower approach and range. The higher deviation between the actual and design cooling

towers approach and ranges the lower the cooling tower performance. Cooling towers range is

measured by the difference between the cooling tower water inlet temperature and outlet

temperature . The larger the cooling tower range the better the cooling tower

performance since it able to reduce the water temperature effectively. On the other hand, the

difference between the cooling tower outlet cold water temperature and inlet ambient

wet bulb temperature gives the cooling tower approach. Cooling tower approach is

mainly used to determine the degree of unsaturation of the inlet air. Highly unsaturated inlet air

is able to transfer more heat from water and result in a high performance of cooling tower.

Therefore, the lower the cooling tower approach the better the cooling tower performance.

Cooling towers effectiveness is determined by the ratio between the range and the ideal range

(e.g summation of range and approach).

Figure 2.5: Graphical representation of cooling tower characteristic

Crozier (1980) suggested that the cooling tower performance can be improved by increasing the

return water temperature due to the higher thermal driving force between warm water and cold

air. Kim and Smith (2001) maximized the cooling tower performance by maximizing the inlet

temperature for a fixed flow rate to the cooling tower, and minimizing the inlet flow rate for a

fixed inlet temperature. However, higher return water temperature will result in higher

evaporation rate in cooling tower and consequently increase the makeup water and blowdown

16

flow rates. Eqs 2.4 to 2.6 given by Perry et al. (1997) presenting the determination of

evaporation, makeup water and blowdown flow rate respectively.

(2.4)

(2.5)

(2.6)

where = Flow rate of evaporation; = flow rate of makeup water; = cycles of

concentration and = flow rate of cooling tower blow down.

In evaluating the power consumption of cooling water system, fan and pump horsepower

requirement are the significant factors. Cooling tower fan horsepower can be reduced as the

ambient wet-bulb temperature decreases while pump horsepower can be reduced by decreasing

the tower height which subsequently reduces the static lift. The static air horsepower and

pump horsepower requirement are given in Eqs 2.7 and 2.8 respectively (Perry et al.,

1997).

(2.7)

(2.8)

where = air volume, m3/s; = static head, m; = density of water at ambient temperature,

kg/m3; = flow rate of water entering pump, m

3/s; = total head, m and = pump efficiency.

2.6 Process synthesis and optimization of cooling water system

As heat and water utilities are often associated with each other in process industry operations, the

optimum synthesis of cooling water system is gaining much attention from researchers to

achieve simultaneous water and energy savings. Castro et al. (2000) formulated an optimization

model for a cooling water system that minimizes the operating cost. The model was developed

by considering the pressure drop through the lines and the heat exchangers. This model was

applied to study the influence of climatic changes on the cooling tower performance. Results

showed that during the month with highest humidity and lower temperatures, the highest

operating cost was obtained. From this observation, the humidity affects the cooling tower

performance more than the air temperature.

17

Kim and Smith (2001) presented a mathematical model for cooling water system by exploring

the opportunities for cooling water reuse. The outlet condition of water from the cooling tower

was predicted from the cooling towel model and the cooling water network was developed by

using the principles of pinch analysis. The limiting cooling water profile was produced using the

concept of the limiting water profile by Wang and Smith (1994). Besides, the procedure of Kuo

and Smith (1998) for the design of water re-use networks was also adapted for cooling water

network design. A number of design options for debottlenecking cooling systems were presented

to enhance cooling tower performance and cooling water network. However, their work was

limited to one cooling source which is not practical in most of the case.

Kim et al. (2001) presented an approach to distributed cooling water systems for effluent

temperature reduction. Aqueous effluent with a high temperature is sent to the cooling water

system so as to meet the permitted level of temperature before discharge. The targeting for pinch

temperature is done by plotting the composite curve for all effluent streams in a cooling water

system. The distributed cooling system was then designed using the grouping rules (Wang and

Smith, 1994): (1) all effluent streams exceed pinch temperature must go to the cooling source;

(2) all effluent streams at pinch temperature are partially cooled and bypassed and; (3) all

effluent streams below pinch temperature must bypass the cooling. Also, the effect of

evaporation loss from the cooling tower is considered when targeting for the cooling line.

Kim and Smith (2003) later developed a mixed integer non-linear programming (MINLP) model

for cooling water networks considering the pressure-drop constraints, complexity of networks,

and performance of cooling tower. The objective in this work is to obtain cooling water network

with minimum pressure drop. The starting point for MINLP model was solved by linearized the

problem through setting the outlet temperature of each heat exchanger to maximum value and

used linear correlation equation for pressure drop estimation.

Kim and Smith (2004) designed a cooling water system that allowed the cooling tower to take

wastewater as makeup. A high-density polyethylene plant was demonstrated in the case study.

Two wastewater streams (channel water and washer tank) from the units were mixed together

18

with recirculated cooling water. Result showed that substituting makeup with wastewater can

yield water savings and aqueous emissions reduction. The water savings identified a potential to

reduce 45% of the cooling water makeup, 98% of water makeup for the operation units, and 58%

of the wastewater. However, modification of the cooling water network is needed as the inlet

temperature and flow rate to the tower increase.

Feng et al. (2005) proposed a MINLP problem for cooling water networks synthesis using

superstructural approach. The objective of the model is to minimize the circulating water flow

rate from heat exchanger to the cooling tower. The superstructure was divided into three mains:

supply main, intermediate main and return main. The energy balance across the intermediate

main was the most important feature in the model as the temperature of this main was an

optimization variable which must be lower than the cooling water using operation maximum

outlet temperature. In this work, the authors did not address the attempt to linearize the problem

as the globally optimal solution is often difficult to obtain when solving MINLP problem.

Ponce-Ortega et al. (2007) presented a MINLP problem for cooling water networks synthesis

based on a stage wise superstructural approach. The number of stage in this case was equivalent

to the number of hot streams to be cooled. The objective function of this model is to minimize

the annual cost including annualized capital cost for cooling water. The main setback for this

method was the global optimal solution cannot be guaranteed. This formulation was later

improved by Ponce-Ortega et al. (2010) by presenting a MINLP model for cooling water systems

that gives the global optimal solution.

Cortinovis et al. (2009a) proposed a cooling water system model which considers the cooling

tower performance, and hydraulic and thermal performance of the heat exchanger network. The

heat exchanger network mass balance and mechanical energy balance were included in hydraulic

model while the enthalpy balance across each heat exchanger was included in thermal model.

This cooling water system model was developed to validate with the experimental data. The

setback of this model was not able to predict the evaporation, makeup and blowdown flow rate.

Besides, the minimum temperature approach between the process and the cooling water was not

considered in the model. This work was then extended by Cortinovis et al. (2009b) considering

19

the previous mentioned process condition. The model was also used to study the effect of change

in heat load, makeup water temperature and the air temperature on the total operating cost. From

the results, higher heat load of the process requires optimum performance of the cooling tower

which can be achieved by having higher air flow rate or higher forced hot blowdown flow rate.

In practice, large scale of industrial systems requires multiple cooling towers to remove the

waste heat from the process. Majozi and Nyathi (2007) developed a methodology for cooling

water system consisting of multiple cooling sources. Minimum cooling water flow rate was

obtained using graphical approach and the cooling water network was synthesized using

mathematical optimization technique. In this work, all possible water reuse and recycle

opportunities are exploited. Two case studies proposed in this work were linearized to obtain

global optimal solution. This mathematical formulation was adapted by Majozi and Moodley

(2008) to develop cooling water system consisting at least two cooling towers. Four operational

cases were considered with the main objective of debottlenecking the overall cooling water

supply for the cooling water network.

Rubio-Castro et al. (2013) developed a stage-wise superstructure for heat exchanger network in

cooling water system that consists of multiple cooling towers. The objective function was to

minimize the total annual cost including the investment costs of the operation units and the

operating costs of utilities. In this work, the most important design variable was the number of

cooling water sources for removing heat from several hot process streams at different

temperature ranges. From the results, cooling water systems consisting of multiple cooling

towers with different supply temperature yield significant better results than traditional systems

with single cooling tower.

20

CHAPTER 3 SUPERSTRUCTURAL APPROACH TO THE SYNTHESIS OF FREE-

COOLING SYSTEM THROUGH AN INTEGRATED CHILLED AND COOLING

WATER NETWORK

This chapter presents superstructural approach to the optimization of chilled and cooling water

system (CCWS) with the integration of free-cooling structure. Free-cooling structure is

integrated in CCWS to reduce the energy consumption. It is an economical method that uses

mechanical devices such as cooling tower to assist chiller on producing chilled water with lower

energy consumption.

3.1 Introduction

Free cooling can be designed into chilled water system to reduce the energy consumption. It is

commonly known as economizer cycle that uses mechanical devices such as cooling tower to

reduce energy consumption of chiller (BAC, 2012). It is an economical method that uses external

surrounded air to assist chiller on producing chilled water with lower energy consumption. Water

economizer (Trane, 2008) has been developed into different types such as strainer cycle, indirect

evaporative precooling, evaporative cooling with air-cooled chiller, dry cooler with air-cooled

chiller, plate-and-frame heat exchanger and so on. Series arrangement between cooling tower

and chiller is known as strainer cycle type economizer (Petchers, 2003; Shehabi et al., 2010).

This type of economizer uses a strainer or filter to minimize the contamination of water in order

to reduce the risk of fouling in chilled water system. It can be used for process cooling in various

industries, district cooling networks or air conditioning system in buildings. Most of the research

works on free cooling mainly focus on studying the configuration features and cooling

performances. Des Champs and Ashrae (2011) studied the overall system cooling performance

using indirect evaporative cooling. Oranski and Mayes (2012) analyzed the performance of free

cooling with different types of filtration. Zhang et al. (2014) has present a literature review to

provide the basic background knowledge on free cooling of data centre due to the high cooling

energy consumption.

Though cooling towers consume less energy to remove the same amount of heat load compared

with chillers, temperature of cooling water is inconsistent and the minimum temperature can only

21

reach the ambient wet bulb temperature. Many studies have been performed on the optimization

of cooling water systems (Cortinovis et al., 2009a; Cortinovis et al., 2009b), cooling water

network (Kim and Smith, 2003; Feng et al., 2005; Ponce-Ortega et al., 2007; Ponce-Ortega et al.,

2010) and cooling towers (Castro et al., 2000) respectively to improve the energy efficiency.

Several studies on cooling water systems with multiple cooling towers (Majozi and Nyathi,

2007; Majozi and Moodley, 2008; Rubio-Castro et al., 2013) have also been reported. Significant

improvements in energy savings are found in cooling water systems consisting of multiple

cooling towers.

The conventional chilled water system configuration is shown in Figure 3.1-a, which depicts the

network between the chiller and the ancillary equipment. There is lack of attention given to

optimization of free-cooling chilled and cooling water system (CCWS) using process integration

(PI) techniques. This chapter explores the potential for further cost and energy saving by

optimizing free-cooling CCWS. Free cooling using a cooling tower is applied in conjunction

with a chiller, so as to reduce the overall power consumption in the CCWS (Figure 3.1-b).

Several scenarios of free-cooling superstructures for CCWS are presented. Two examples are

used to illustrate the proposed scenarios for CCWS. The comparison of power consumption and

total annual cost between the free-cooling and the conventional structure of CCWS are

performed in the case studies. This chapter also analyses the power consumption of the proposed

scenario of free-cooling CCWS for cases involving single and multiple chillers and cooling

towers.

Valve Compressor

Condenser

Evaporator

Cooling

LoadSupply chilled

water

Returned chilled water

Figure 3.1-a: Conventional chilled water system

22

Valve Compressor

Condenser

Evaporator

Cooling

LoadSupply chilled water

Cooling

tower

Returned chilled

waterMake-up water

Evaporation

Blow-down

Figure 3.1-b: Proposed scheme with a free-cooling structure

3.2 Problem statement

The formal problem statement is as follows:

Given a number of industrial plants which are interested in reducing the power

consumption and the incurred cost through the integration of CCWS with free-cooling

structure.

Each plant has its own set of process sources and sinks with known

temperature and heat capacity flow rates.

Given are also the operating data of cooling tower, vapour-compression chiller, as well

as the cost data.

The objective is to analyse superstructures for different scenarios of CCWS with free cooling.

Several free-cooling structures based on Figure 3.1-b are proposed to explore the potential of

energy and cost savings on CCWS. However, no attempt is made to analyse the quality (i.e.,

purity) of chilled and cooling water in this chapter. To address this problem, this chapter

proposes to formulate superstructures for different scenarios of CCWS with free cooling by

including chiller and cooling tower model. The proposed superstructures are modelled as MINLP

problems. The solution of the problem addressed in this work should provide the information as

follows:

(a) The chilled and cooling water network that maximize the overall total annual cost.

23

(b) The effect of a free-cooling structure of CCWS.

(c) The total annual power consumption of single and multiple chillers and cooling towers.

3.3 The optimization model

In this section, the mathematical model for the Base scenario (Figure 3.2) and the proposed

scenarios with a free-cooling structure of CCWS is developed. In Scenario 1, a free-cooling

structure of CCWS is integrated within an individual plant (Figure 3.3). Next, Scenario 2

proposes a free-cooling structure with a centralized chiller among the integrated plants (Figure

3.4). Later, Scenario 2 is extended into Scenario 3 (Figure 3.5) in which a free-cooling structure

with a centralized chiller and cooling tower among the integrated plants is proposed.

Plant

Cooling

tower

Returned cooling water

Supply cooling water


Supply chilled water

Chiller

Figure 3.2: Schematic of CCWS without free-cooling (Base scenario)

Plant

Cooling

tower





Chiller

Free-cooling

water

Figure 3.3: Schematic of CCWS with free-cooling (Scenario 1)

24

Plant 1

Cooling

tower

Returned

cooling water

Supply

cooling water

Returned

chilled water


Centralized

chiller

Free-cooling

water

Plant 2

Cooling

tower

Returned

cooling water

Returned

chilled water

Supply

cooling waterFree-cooling

water


Figure 3.4: Schematic of CCWS with free-cooling plants (Scenario 2)

Plant 1

Centralized

Cooling

tower





Free-cooling

water

Centralized

chiller

Plant 2





Figure 3.5: Schematic of CCWS with free cooling (Scenario 3)

3.3.1 Base scenario

The Base scenario (Figure 3.2) is the conventional CCWS within individual plants. The

mathematical modelling code for this scenario is shown in Appendix 1(a). This scenario is

subject to water and energy constraints (Eqs. 3.1-3.3), cooling tower model (Eqs. 3.4-3.19),

chiller model (Eqs. 3.20-3.27), total annual power consumption (Eqs. 3.28-3.33) and cost

25

constraints (Eqs. 3.34-3.37). In Base scenario, the free-cooling structure is not considered. As

shown in Figure 3.2, the returned chilled and cooling water is sent to the chiller and cooling

tower for regeneration, respectively. The regenerated chilled and cooling water is then directly

integrated into the plant.

3.3.1.1 Mass and energy balance of process sources and sinks

The available water flow rate of source can be reused in other sinks and/or sent for

regeneration through the chiller and/or cooling tower, as follows:

∑ (3.1)

The required water flow rate in sink is sourced from reused streams and/or

regenerated chilled and cooling water , as follows:

∑ (3.2)

where = flow rate of the return stream from source to the chiller; and = flow rate of

the returned stream from source to the cooling tower

The corresponding energy balance of process sinks is expressed as follows:

∑ (3.3)

where = temperature of source ; = temperature of regenerated chilled water;

= temperature of regenerated cooling water; and = water temperature requirement in sink .

3.3.1.2 Design of the cooling tower

This section describes the mathematical model for single unit cooling tower. The inlet stream of

the cooling tower ( is equal to the sum of the returned stream from source ,

∑ (3.4)

and the outlet stream of the cooling tower is given as follows:

(3.5)

where = blow-down water; = evaporation rate of water; and = flow rate of drift.

The energy balance for the cooling tower is described as follows:

∑ (3.6)

where = inlet water temperature of the cooling tower.

26

The make-up water ( ) for the cooling tower replaces the water loss due to evaporation ( ,

drift ( and blow-down (Smith, 2005), as follows:

(3.7)

, (3.8)

(3.9)

(3.10)

where = air mass flow rate of the cooling tower; = mass-fraction humidity of air

entering the cooling tower; = mass-fraction humidity of air leaving the cooling tower; =

percent loss of circulating water in cooling tower; and = cycle of concentration.

To determine the existence of a cooling tower, the inlet water flow rate of the cooling tower is

formulated as follows:

(3.11)

(3.12)

where = upper limit for the inlet water flow rate of the cooling tower;

= lower limit

for the inlet water flow rate of the cooling tower; and = binary variable used to determine the

existence of the cooling tower.

The mass transfer coefficient ( and Merkel‘s number ( (Robert et al., 1997; Costelloe

and Finn, 2009) can be obtained using the correlation equations described as follows:

(3.13)

(3.14)

where = area of mass transfer of the cooling tower.

The cooling tower fill volume ( can be obtained using the following equation:

. (3.15)

To avoid fouling and corrosion, the inlet water temperature of the cooling tower should not be

higher than the upper limit and lower than lower limit

:

(3.16)

The regenerated cooling water temperature is constrained as follows:

(3.17)

27

where = lower limit for the regenerated cooling water temperature that takes the value of;

and = upper limit for the regenerated cooling water temperature that takes the value.

The inlet water temperature of the cooling tower must be higher than the regenerated cooling

water:

(3.18)

The cooling tower is designed to operate at the

ratio (Singham, 1983) as:

(3.19)

where = ratio of inlet water mass flow rate of cooling tower to air mass flow rate of cooling

tower.

3.3.1.3 Design of the chiller

This section describes the mathematical model for single unit chiller. The inlet stream of the

chiller is equal to the sum of the returned stream from source , as follows:

∑ (3.20)

The outlet stream of the chiller is given as

∑ (3.21)

The energy balance of the chiller is given as follows:

∑ , (3.22)

where = inlet water temperature of the chiller.

The inlet water temperature of the chiller and the regenerated chilled water temperature are

constrained as follows:

(3.23)

(3.24)

(3.25)

where = lower limit for the inlet water temperature of the chiller;

= upper limit for the

inlet water temperature of the chiller; = lower limit for the regenerated chilled water

temperature; and = upper limit for the regenerated chilled water temperature.

To determine the existence of a chiller, the power consumption of the chiller is

constrained as follows:

28

(3.26)

(3.27)

where

= upper limit of chiller power consumption;

= lower limit of chiller

power consumption; and = the binary variable that determines the existence of a chiller.

3.3.1.4 Total annual power consumption of a chilled and cooling water system

The power consumption of a tower fan ( and water pump for a cooling water

system is described as follows (Rubio-Castro et al., 2013):

(3.28)

(3.29)

where = coefficient of cooling tower performance; = specific heat capacity of water;

= fill height of cooling tower; = acceleration due to gravity; and = pump efficiency of the

cooling water system.

The power consumption of the chiller ( and water pump ( ) of a chilled water

system is described as follows (Shan et al., 2000):

(3.30)

(3.31)

where = chiller‘s coefficient of performance; = height of chiller; and = pump

efficiency of the chilled water system.

The cooling capacity of a chiller in is written as (Shan et al., 2000):

(3.32)

The total annual power consumption of an individual plant is described as

(3.33)

29

3.3.1.5 Total annual cost of a chilled and cooling water system

The objective function is to minimize the total annual cost of CCWS (Eq. 3.34) consisting

of the investment cost of the cooling tower (Eq. 3.35), the investment cost of the

chiller (Eq. 3.36) and the operating cost (Eq. 3.37).

Min (3.34)

( ) (3.35)

(3.36)

(3.37)

where = annualized factor; = initial investment cost of the cooling tower; = fixed

cost parameter of the cooling tower based on the fill volume; = fixed cost parameter of the

cooling tower based on the air mass flow rate; = initial investment cost of the chiller;

= incremental cost of the chiller based on the cooling capacity; = annual operating time; =

unit cost of electricity; and = unit cost of make-up water.

3.3.2 Scenario 1

In Scenario1 (Figure 3.3), the introduction of a free-cooling structure of CCWS for individual

plants is proposed. The mathematical model in this scenario (see Appendix 1(b)) is subject to

water and energy constraints (Eqs. 3.1-3.3), cooling tower model (Eqs. 3.4, 3.5-3.19, and 3.38),

chiller model (Eqs. 3.21, 3.23-3.27, and 3.39-3.40), total annual power consumption (Eqs. 3.28-

3.33) and cost constraints (Eqs. 3.34-3.37). The mass balance at the outlet of the cooling tower is

described in Eq. 3.38. The outlet stream for the individual plant cooling tower (Eq. 3.38) is

integrated into the process sinks and chillers of the individual plants. The mass and energy

balances at the inlet of the chiller are described in Eqs. 3.39 and 3.40, respectively. The inlet

stream for individual plant chillers (Eq. 3.39) are the return stream from source and the free-

cooling stream.

∑ (3.38)

∑ (3.39)

∑ (3.40)

where = flow rate of the free-cooling stream from the cooling tower to the chiller.

30

3.3.3 Scenario 2

In Scenario 2 (Figure 3.4), a centralized chiller is integrated into independent plants in a

proximity zone. The mathematical model in this scenario (see Appendix 1(c)) is subject to water

and energy constraints (Eqs. 3.41-3.43), cooling tower model (Eqs. 3.4, 3.5-3.19, and 3.38),

chiller model (Eqs. 3.25-3.27, and 3.44-3.50), total annual power consumption (Eqs. 3.28-3.33)

and cost constraints (Eqs. 3.35, 3.37, and 3.51-3.53). Each plant contains its individual cooling

tower, and the regenerated cooling water is integrated back into its respective plant and

centralized chiller. The available water flow rate of source in plant can be reused in

other sinks and/or sent for regeneration through the centralized chiller and/or the cooling tower

in plant , as follows:

∑ (3.41)

where = flow rate of the returned stream from source to the centralized chiller.

The required water flow rate of sink in plant is sourced from a reused stream

and/or regenerated chilled water from the centralized chiller and/or regenerated cooling water

from the cooling tower in plant .

∑ (3.42)

where = flow rate of regenerated chilled water from the centralized chiller to sink .

The corresponding energy balance of the process sinks is expressed as follows:

∑ (3.43)

where = temperature of regenerated chilled water from the centralized chiller.

The inlet and outlet stream of the cooling tower are described by Eq. 3.4 and Eq. 3.38,

respectively. The energy balance of the cooling tower in plant is described by Eq. 3.6. The

mathematical model of the cooling tower is described by Eqs 3.7-3.19.

The inlet and outlet stream of the centralized chiller are given in Eqs. 3.44

and 3.45, respectively.

∑ ∑ ∑ (3.44)

∑ ∑ (3.45)

To determine the existence of pipelines between the centralized chiller and plant , the stream

constraints and are formulated as follows:

∑ ∑

(3.46)

31

∑ ∑

(3.47)

∑ ∑

(3.48)

∑ ∑

(3.49)

where ∑

= upper limit for the water flow rate from plant to the centralized chiller;

∑

= lower limit for the water flow rate from plant to the centralized chiller;

∑

= upper limit for the water flow rate from the centralized chiller to plant ;

∑

= lower limit for the water flow rate from the centralized chiller to plant ; =

binary variable to determine the existence of a pipeline from plant to the centralized chiller;

and = binary variable to determine the existence of a pipeline from the centralized chiller

to plant .

The energy balance of the centralized chiller is written as

∑ ∑ ∑ (3.50)

where = inlet water temperature of the centralized chiller.

The inlet water temperature of the centralized chiller and the regenerated chilled water

temperature ( are constrained according to Eqs 3.23-3.25.

The investment cost of the centralized chiller is given in Eq. 3.51.

(3.51)

where = binary variable to determine the existence of a centralized chiller; and =

cooling capacity of the centralized chiller.

The piping cost within the individual plant is considerably less than the pipeline cost between the

centralized chiller and each plant. Therefore, the intra-plant piping cost is assumed to be

negligible. The incurred piping cost of each participant plant in this scenario is given as follows:

[

(∑ ∑ ) ( )]

(3.52)

where = investment cost of pipelines between the centralized chiller and plant ; =

distance between participating plant and the centralized hub; = fixed cost parameter based on

the cross-sectional area of the pipelines; = fixed cost parameter for building one pipeline; =

density of water; and = streamvelocity.

32

Note that the (Eq. 3.53) in this scenario is described as follows:

Min ∑ ∑ ∑

(3.53)

3.3.4 Scenario 3

Scenario 3 (Figure 3.5) proposes centralized CCWS with a free-cooling structure. The

mathematical model (see Appendix 1(d)) in this scenario is subject to water and energy

constraints (Eqs. 3.54-3.56), cooling tower model (Eqs. 3.7-3.10, 3.13-3.19, and 3.57-3.63),

chiller model (Eqs. 3.25-3.27, 3.45-3.49, and 3.64-3.65), total annual power consumption (Eqs.

3.28-3.33) and cost constraints (Eqs. 3.51-3.52, and 3.66-3.68). The regenerated cooling water

from the centralized cooling tower is integrated with the plant and the centralized chiller. The

available water flow rate of source can be reused on other sinks and/or sent for

regeneration through the centralized chiller and cooling tower.

∑ (3.54)

where = flow rate of the return stream from source to the centralized cooling tower.

The required water flow rate of sink in plant is sourced from a reused stream

and/or regenerated chilled and cooling water from the centralized hub.

∑ (3.55)

where = flow rate of regenerated cooling water from the centralized cooling tower to sink

.

The corresponding energy balances of the process sinks are as follows:

∑ (3.56)

where = temperature of regenerated cooling water from the centralized cooling tower.

The inlet stream of the centralized cooling tower is equal to the sum of the return

stream from source of all of the plants ,

∑ ∑ (3.57)

and the outlet of the centralized cooling tower is written as

∑ ∑ (3.58)

33

where = water flow rate of the free-cooling stream from the centralized cooling tower to the

centralized chiller; = blow-down water flow rate of the centralized cooling tower; and

= make-up water flow rate of the centralized cooling tower.

To determine the existence of pipelines between the centralized cooling tower and plant , the

constraints of streams and are formulated as follows:

∑ ∑

(3.59)

∑ ∑

(3.60)

∑ ∑

(3.61)

∑ ∑

(3.62)

where ∑

= upper limit of water flow rate from plant to the centralized cooling tower;

∑

= lower limit of water flow rate from plant to the centralized cooling tower;

∑

= upper limit of regenerated cooling water from the centralized cooling tower to

plant ; ∑

= lower limit of regenerated cooling water from the centralized cooling

tower to plant ; = binary variable to determine the existence of a pipeline from plant to

the centralized cooling tower; and = binary variable to determine the existence of a

pipeline from the centralized cooling tower to plant .

The energy balance of the centralized cooling tower is described as follows:

∑ ∑ (3.63)

where = inlet water temperature of the centralized cooling tower.

The inlet stream of the centralized chiller is given as

∑ ∑ (3.64)

The outlet stream of the centralized chiller is described in Eq. 3.45. The energy balance of the

centralized chiller is given as

∑ ∑ (3.65)

The investment cost of the centralized cooling tower is described as follows:

( ) (3.66)

34

where = binary variable to determine the existence of a centralized cooling tower; =

centralized cooling tower film volume; and = air mass flow rate of the centralized cooling

tower.

The piping cost between the centralized cooling tower and plant is described as

follows:

[

(∑ ∑ ) ( )]

(3.67)

The in this scenario is given as

Min ∑

∑ (3.68)

3.4 Case studies

The proposed superstructures of three different scenarios of CCWS with free cooling are

formulated as MINLP models. The MINLP formulation takes into account the interaction among

cooling tower, chiller and the process sinks of industrial plants. Two examples are used to

demonstrate the proposed CCWS superstructures. The stream data for process sinks and sources

of the examples are given in Tables 3.1 and 3.2. From both examples, the chilled and cooling

water characteristics, such as water flow rate and temperature, are given. The proposed MINLP

models were implemented in the software LINGO v13.0 with an integral branch-and-bound

Global Solver (Gau and Schrage, 2003) in a 8.0 GB RAM desktop computer with Intel Core I7

CPU at 3.4 GHz and a Windows 8 operating system. The parameter values given in Table 3.3 are

used to solve the MINLP models for both examples. Note that, each example was solved to

demonstrate the proposed superstructures for CCWS and to establish a comparison among these

scenarios.

35

Table 3.1: Process data for Example 1

Table 3.2: Process data for Example 2

Plant, Sink, Flow rate,

(kg/s)

Temperature,

(oC)

Source, Flow rate,

(kg/s)

Temperature,

(oC)

Example 1

Pla

nt

A SK-A1 360 5 SR-A1 250 11

SK-A2 400 12 SR-A2 280 20

SK-A3 120 20 SR-A3 340 35

SK-A4 320 25 SR-A4 80 58

SR-A5 200 65

SR-A6 50 70

Pla

nt

B SK-B1 210 5 SR-B1 100 10

SK-B2 260 17 SR-B2 160 28

SK-B3 300 24 SR-B3 280 48

SR-B4 230 65

Pla

nt

C SK-C1 400 8 SR-C1 200 12

SK-C2 380 16 SR-C2 100 35

SR-C3 480 45

Total 2750 Total 2750

Plant, Sink, Flow rate,

(kg/s)

Temperature,

(oC)

Source, Flow rate,

(kg/s)

Temperature,

(oC)

Example 2

Pla

nt

A SK-A1 360 6 SR-A1 270 19

SK-A2 250 15 SR-A2 300 40

SK-A3 280 22 SR-A3 320 45

Pla

nt

B SK-B1 220 5 SR-B1 180 16

SK-B2 200 14 SR-B2 150 48

SK-B3 170 19 SR-B3 260 50

Pla

nt

C SK-C1 320 7 SR-C1 200 17

SK-C2 250 15 SR-C2 180 42

SR-C3 190 55

Total 2050 Total 2050

36

Table 3.3: Parameter values in the optimization model

Parameter Value Parameter Value Parameter Value

0.2983 year-1 250

1000 kW

1246000 US$ 7200 0.0105

200 US$/tons 1 ms-1 0.002

1097.5 US$/

(kg dry air/s)

0.005 kg-

water/kg-dry-air

1.2

31185 US$ 0.02 kg-

water/kg-dry-air

0.82

1606.15

US$/m3

∑

750 kg/s 0.82

0.03 US$/kW h ∑

0.5 kg/s 8 °C

5.75 10-5

US$/kg

∑

750 kg/s 5 °C

4 ∑

0.5 kg/s 25 °C

4 ∑

750 kg/s 15 °C

4.2 kJ/kg °C ∑

0.5 kg/s 25 °C

7920 h/year ∑

750 kg/s 15 °C

10 m ∑

0.5 kg/s 75 °C

10 m 750 kg/s

35 °C

100 m 100 kg/s 1 kg/m

3

9.8 ms-2

15000 kW

37

3.4.1 Example 1

3.4.1.1 Single chiller and cooling tower

The proposed scenarios of integrated superstructure for CCWS described in Section 3.3 are

formulated as MINLP models with the objective of minimizing . In this example, the

MINLP problem for Base scenario involves: 165 continuous variables, 6 integer variables and

145 constraints; Scenario 1: 168 continuous variables, 6 integer variables and 145 constraints;

Scenario 2: 168 continuous variables, 10 integer variables and 145 constraints and Scenario 3:

151 continuous variables, 14 integer variables and 125 constraints. The CPU time to solve the

Base scenario, Scenario 1, Scenario 2 and Scenario 3 for Example 1 are 204s, 20s, 45s, and 2s,

respectively. Figure 3.6 summarizes the results of Example 1. The Base scenario has the

highest overall among the integrated plants, followed by Scenario 1, Scenario 2 and

Scenario 3. The of the individual plants is in descending order from the Base scenario to

Scenario 3, except for Plant C, which has a slightly higher individual in Scenario 3 than in

Scenario 2. Scenario 1, Scenario 2 and Scenario 3 with a free-cooling structure show a

significant reduction in as compare to the Base scenario. Although Scenario 3 has the least

overall , it is not the individual best result for all the plants. Figure 3.6 also shows that

Scenario 2 and Scenario 3 are comparable in terms of the individual plant and the

overall . Scenario 2 proposed a centralized chiller with a free-cooling structure, while

Scenario 3 proposed centralized CCWS with a free-cooling structure.

The configurations of CCWS with the Base scenario, Scenario 1, Scenario 2, and Scenario 3 for

Example 1 is shown in Figures 3.7-3.10, respectively. In Figure 3.7, the overall inlet water flow

rate to the individual plant chiller in the Base scenario is 970 kg/s and the overall inlet water

temperature is 17.14°C. Scenario 1 (Figure 3.8), Scenario 2 (Figure 3.9) and Scenario 3 (Figure

3.10) have the same overall inlet water flow rate (818.6 kg/s) and temperature (15°C).

Meanwhile, the overall inlet water flow rates of the cooling tower in Scenario 1 (1567 kg/s),

Scenario 2 (1557.2 kg/s) and Scenario 3 (1564.7 kg/s) are higher than the Base scenario (1405.5

kg/s). Note that, Scenario 1 with the highest inlet water flow rate of the cooling tower has the

highest overall among the proposed scenarios of CCWS with free-cooling structure.

Scenario 2 (1557.2 kg/s, 50.71°C) has a lower overall inlet water flow rate of the cooling tower

38

but a slightly higher overall inlet water temperature of the cooling tower compared with Scenario

3 (1564.7 kg/s, 50.55°C). All the proposed scenarios have the same outlet water temperature for

the cooling tower (15°C) and chiller (5°C). The overall make-up water flow rates of the Base

scenario, Scenario 1, Scenario 2, and Scenario 3 for Example 1 are 21.8 kg/s, 24.6 kg/s, 24.5 kg/s

and 7.1 kg/s, respectively. The inlet water flow rate and the temperature of the chiller and

cooling tower appear to reflect the economic results of the proposed scenarios for Example 1.

Apparently, the optimization runs the formulated MINLP model in the way to reduce the inlet

water flow rate and the temperature to the chiller but increase them for cooling tower. This is due

to the relatively low energy consumption of cooling tower to the chiller.

Figure 3.6: results for Base scenario, Scenario 1, Scenario 2 and Scenario 3 (Example 1)

0

1

2

3

4

5

6

Base scenario Scenario 1 Scenario 2 Scenario 3

𝑇𝐴𝐶

(x10

6 U

S$/y

ear)

Plant A

Plant B

Plant C

Overall TAC

39

Figure 3.7: CCWS for Example 1 (Base scenario)

40

Figure 3.8: CCWS for Example 1 (Scenario 1)

41


42


43

3.4.1.2 Multiple chillers and cooling towers

This section analyzes the total annual power consumption of CCWS for cases involving

single and multiple chillers and cooling towers. To establish the comparison between both cases,

the optimization model for Base scenario (section 3.3.1), Scenario 1 (section 3.3.2), Scenario 2

(section 3.3.3) and Scenario 3 (section 3.3.4) are repeated. The objective function is set to

minimize the total annual power consumption of the CCWS. Figure 3.11 compares the

overall of each scenario considering single (blue column) and multiple (red column) chillers

and cooling towers. The overall for single and multiple chillers and cooling towers cases

were identical in each scenario, except for the Base scenario. Base scenario does not have a free-

cooling structure, and the overall in this scenario was reduced significantly by introducing

multiple chillers and cooling towers. However, the overall for both cases in the Base

scenario remained higher than the proposed scenario of CCWS with free-cooling structure. The

conventional method that increases the number of operational unit to enhance the energy

efficiency in CCWS appears unfavourable because the investment cost for the multiple operation

units is apparently higher than the cost of a single operation unit. The proposed scenarios for

CCWS with a free-cooling structure could reduce the investment cost for energy savings.

Although the piping networks for CCWS with free cooling are more complex compared to the

Base scenario, it reduces the overall as well as the overall .

Figure 3.11: Overall for Example 1

0

2000

4000

6000

8000

10000

12000

14000

16000

Basescenario

Scenario 1 Scenario 2 Scenario 3

Ove

rall 𝑇𝐴𝑃

(kW

)

Single chiller and cooling tower

Multiple chillers and coolingtowers

44

3.4.2 Example 2

3.4.2.1 Single chiller and cooling tower

In this example, the MINLP problem for Base scenario involves: 135 continuous variables, 6

integer variables and 139 constraints; Scenario 1: 138 continuous variables, 6 integer variables

and 139 constraints; Scenario 2: 138 continuous variables, 10 integer variables and 139

constraints; Scenario 3: 117 continuous variables, 14 integer variables and 119 constraints. The

required CPU times to solve the formulated MINLP models for integrated superstructures of

CCWS in Base scenario, Scenario 1, Scenario 2 and Scenario 3 for Example 2 using LINGO

v13.0 software with global solver are 2s, 55s, 6s and 4s, respectively. The results of each

scenario in this example are summarized in Figure 3.12. The overall and individual plant

for each scenario is in descending order from the Base scenario to Scenario 3. Scenario 3

with the least overall is the best individual result for all of the individual plants. Note

that, of Plant A is same to Base Scenario and Scenario 1 (totalling to 2,201,271 US$/year).

The configurations of CCWS in the Base scenario, Scenario 1, Scenario 2, and Scenario 3 for

Example 2 are shown in Figures 3.13-3.16, respectively. It is worth to note that the chilled and

cooling water network in Plant A for both Base scenario (Figure 3.13) and Scenario 1 (Figure

3.14) are the same after the superstructural optimization. In this example, Plant A has no free-

cooling structure within its individual plant in Scenario 1 and thus it has the same as the

Base scenario. Plant A in Example 1 has higher source water temperature (up to 70°C) than

Example 2 (up to 45°C). This explained that free-cooling structure is favoured for cases with

large water temperature difference between sinks and sources. Identical to the results from

Example 1, Scenario 1, Scenario 2 and Scenario 3 have a higher overall inlet water flow rate of

the cooling tower than the Base scenario. The overall inlet water flow rate and temperature of the

cooling tower are as follows: Base scenario (1131 kg/s, 46.94°C); Scenario 1 (1451.7 kg/s,

42.67°C); Scenario 2 (1574.1 kg/s, 42.07°C); and Scenario 3 (1574.1 kg/s, 42.07°C). In this

example, all of the scenarios have the same inlet water flow rate of the chiller (820 kg/s), except

for Scenario 3, which has a slightly higher flow rate (822.6 kg/s). Note that the overall inlet

water temperature of the chiller descends in order from the Base scenario to Scenario 3. The

overall inlet water temperatures of the chiller in the Base scenario, Scenario 1, Scenario 2 and

Scenario 3 are 22.93°C, 18°C, 15.03°C and 15°C, respectively. The outlet water temperatures of

45

the cooling tower (15°C) and chiller (5°C) are the same in all of the proposed scenarios. The

overall make-up water flow rates of the Base scenario, Scenario 1, Scenario 2 and Scenario 3 are

25.8 kg/s, 33.9 kg/s, 37 kg/s and 7.1 kg/s, respectively.

Figure 3.12: results for Base scenario, Scenario 1, Scenario 2 and Scenario 3 (Example 2)

0

1

2

3

4

5

6

7

Base scenario Scenario 1 Scenario 2 Scenario 3

𝑇𝐴𝐶

(x10

6 U

S$/y

ear)

Plant A

Plant B

Plant C

Overall TAC

46

Figure 3.13: CCWS for Example 2 (Base scenario)

47


48


49


50

3.4.2.2 Multiple chillers and cooling towers

Figure 3.17 shows the overall of the two cases, involving single and multiple chillers and

cooling towers in Base scenario, Scenario 1, Scenario 2 and Scenario 3 with the objective

function of minimizing the overall . The overall of a single chiller and cooling tower

descends in order from the Base scenario to Scenario 3. The overall of multiple chillers and

cooling towers in the Base scenario and Scenario 1 is lower than the case with single chiller and

cooling tower. Multiple chillers and cooling towers could reduce the overall total power

consumption when free cooling structure is not applied. Plant A has no free-cooling structure in

Scenario 1, therefore the power consumption in Plant A is reduced significantly in the case with

multiple chillers and cooling towers. Hence, the overall for the case of multiple chillers and

cooling towers get better in Scenario 1 for this example than Example 1. Although the

investment cost for multiple chillers and cooling towers is not included in this section, this

conventional method to enhance the energy efficiency by increasing the number of operation unit

is apparently not economically favourable than the single operation unit.

Figure 3.17: Overall for Example 2

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Basescenario

Scenario 1 Scenario 2 Scenario 3

Ove

rall 𝑇𝐴𝑃

(kW

)

Single chiller and cooling tower

Multiple chillers and coolingtowers

51

3.5 Conclusion

In this chapter, we have developed integrated superstructures for three different scenarios of

CCWS with free-cooling. The proposed integrated superstructures for CCWS have been

formulated as MINLP models. Two examples were then solved to demonstrate the proposed

superstructures for CCWS. From the case study results, it has been shown that the inlet flow rate

and temperature to chiller are reduced while the flow rate to the cooling tower is increased. The

model seeks the optimal solution by exploring the opportunity to increase the recycled water

flow rate in cooling tower due to the relative low energy consumption of cooling tower relative

to the chiller. It is observed in the examples that the synergy between the chiller and cooling

tower optimized using superstructural approach could enhance the overall system performance.

Superstructural approach explores the potential of interaction in CCWS that produces greater

energy savings than the sum of its individual parts, as shown in Base scenario. Although this

synergy results in a more complex piping network, it is feasible in practice to introduce the

added complexity in the pipeline structure to enhance energy conservation. Alternatively, the

binary variables may be used to reduce network complexity, with a consequent trade off in

performance. This chapter also analyses the power consumption for cases involving single and

multiple cooling towers and chillers. CCWS with free-cooling structure could improve the

overall energy efficiency without investing in a new chiller and/or cooling towers.

52

CHAPTER 4 FUZZY ANALYTIC HIERARCHY PROCESS AND TARGETING FOR

INTER-PLANT CHILLED AND COOLING WATER NETWORK SYNTHESIS

In recent years, the concept of industrial symbiosis has led to improvements in resource

efficiency that may not be possible with individual industrial plants acting independently. One

has a specific aspect is to achieve economies of scale by having multiple companies located in

close proximity in order to share common utilities, such as chilled and cooling water, in an eco-

industrial park (EIP). Together, these industrial plants may form an inter-plant chilled and

cooling water network (IPCCWN) to achieve greater overall cost savings. Some issues faced by

an IPCCWN include network reliability problems due to the consistency of sources‘ availability,

and cost savings allocations for IPCCWN synthesis due to the subjectivity of human preference

on decision making. This chapter develops decision making framework for the synthesis of

IPCCWN to determine a feasible solution that will satisfy all industrial plants.

4.1 Introduction

Synthesis of IPCCWN requires strategic decision-making approach to ensure a fair distribution

of benefits among the participants. There are several approaches to perform decision-making

analysis, such as game theory and fuzzy optimization. Game theory is a study of mathematical

models of optimization involving decision-makers (von Neumann and Morgenstern, 1944). In

general, a decision-maker (also known as player) may either act unilaterally (in a non-

cooperative game) or cooperate with other players (in a cooperative game) to reach to an optimal

outcome (Roger, 1991; Colin, 2003). Thus, the synthesis of IPCCWN lends itself to the use of

game theoretic techniques as it involves more than one decision-maker to reach an outcome.

Previously, game theory has been used in water conflict resolution studies (Parrachino, 2006;

Zara, 2006; Madani, 2010) by forming a game-theoretic framework. Lou et al. (2004) assessed

the environmental and economic sustainability of participants in an industrial ecosystem using

game theoretic emergy based analysis whereas Chew et al. (2011) assessed the payoff of

different inter-plant water network designs through cooperative and non-cooperative approaches.

Recently, Cheng et al. (2014) developed a game theory based optimization model to configure an

optimal inter-plant heat exchanger network.

53

The concept of fuzzy optimization on the other hand, was first proposed by Bellman and Zadeh

(1970). Fuzzy optimization aims at solving the fuzzy model optimally based on their

membership functions (Zimmermann, 1978). Aviso et al. (2010) used a variable, λ, to measure

the satisfaction level of a participants‘ goal to minimize fresh water consumption of an inter-

plant network on a dimensionless scale ranging from 0 to 1. This satisfaction level is bound by

fuzzy logic constraints to ensure that individual goals are achieved in the optimized network.

One main advantage of this approach is that it allows each player to independently set goals for

cost savings, prior to negotiations with other parties. Furthermore, Aviso et al. (2011) proposed

fuzzy optimization of topologically constrained inter-plant network due to the issues that there

may be incomplete or variable process data given by participating plants. In the later works by

Tan et al. (2011), fuzzy bi-level optimization approach for the design of inter-plant water

exchange networks with a centralized hub was proposed. Note that, the bi-level structure used in

their models is equivalent to Stackelberg (i.e., leader-follower) (Stackelberg, 1952; Simaan and

Cruz, 1973) games with continuous decision domains.

All the above-mentioned works dealt with quantitative objective functions in decision-making

such as minimizing operating cost, freshwater flow rate, etc. It is important to note that apart

from setting an objective function using quantitative criteria, there may be other criteria that are

subjective, or otherwise difficult to quantify (e.g., reliability), which could be an important

consideration while building a new network structure. Thus a decision-making tool that takes

into account both the quantitative and qualitative criteria is needed in the development of an

inter-plant network. Furthermore, such criteria cannot be integrated directly into optimization

models, but may nevertheless reflect major concerns of the parties involved in the network. One

of the useful decision-making tools that deal with both quantitative and qualitative criteria is the

analytic hierarchy process (AHP) (Saaty, 1977). Cheng et al. (1999) reported that the AHP

enables decision makers to model a complex problem into a simple hierarchy and to evaluate a

large number of quantitative and qualitative criteria in a systematic manner through a unified

problem decomposition strategy.

Although AHP can handle both qualitative and quantitative criteria, the ranking of the AHP is

rather not precise since arbitrary values are used in pairwise comparisons (Mon et al., 1994).

54

Fuzziness and vagueness (Bouyssou et al., 2000) existing in decision-making problems should be

accounted for and works done show that the fuzzy analytic hierarchy process (FAHP), an

extension of AHP, gives a better description of the decision-making process as compared to the

conventional AHP methods (Cheng and Mon, 1994; Mon et al., 1994; An et al., 2011; Liao,

2011). Fuzziness is usually represented by membership functions which reflect the decision

maker's subjectivity and preference on the objects while vagueness deals with the situation of

making sharp or precise distinctions. van Laarhoven and Pedrycz (1983) first proposed FAHP by

representing fuzziness and vagueness using triangular fuzzy numbers (TFNs) in the pairwise

comparisons and the priority vectors were obtained based on logarithmic least squares method.

Buckley (1985) employed the geometric mean method to derive the final fuzzy weights for each

fuzzy matrix. The final fuzzy weights are used to rank the alternatives from highest to lowest.

Chang (1996) used the extent analysis method to derive the synthetic extent value of the pairwise

comparison. More recently, Tan et al. (2014) proposed an FAHP methodology for comparing

process engineering alternatives. This methodology generates crisp scores and weights from

scaled fuzzy judgments. Thengane et al. (2014) used AHP and FAHP to perform cost-benefit

analysis for different hydrogen production technologies.

This chapter focuses on the development of a methodology for synthesizing an optimum

IPCCWN in enhancing water and energy recovery. A sequential two-stage optimization and

decision-making approach is proposed in this work. In the first stage of this approach, fuzzy

optimization technique is used to synthesize alternative IPCCWNs in consideration of three

different cost savings allocation strategies. In the second stage of this work, FAHP is adopted as

a decision making tool in selecting the optimum IPCCWN design by including the qualitative

criteria (e.g. network reliability). The optimal choice thus reflects the ideal compromise based on

both quantitative and qualitative criteria. We then illustrate this methodology with a case study.

Finally, conclusions are given at the end of this chapter.

4.2 Problem Statement

This chapter considers the design of chilled and cooling water exchange network between plants

which are located in neighbouring zones. As a motivating example, we consider three plants

(Plant A, Plant B and Plant C) which are operated independently in a hypothetical inter-plant

55

network. Given is a set of chilled and cooling water sinks and sources characteristics consisting

of (1) flow rate, (2) heat capacity flow rate and (3) temperature. Fresh chilled and cooling water

are available from the central facility to supplement the plants in performing the cooling duty

when the available chilled and cooling water sources are exhausted (these streams are analogous

to fresh water in inter-plant water networks). It is desired to synthesize an overall cost optimal

IPCCWN. The participating plants in the IPCCWN intend to meet their individual fuzzy cost

goals.

4.3 Methodology: stage 1 - optimization model for generating alternative IPCCWN designs

As mentioned earlier, each participating plant operates as a different entity; thus, a successful

establishment of an IPCCWN depends on the cooperation of all participants. In this case, the

satisfaction level of each participating plant (fuzzy cost goal) is a function of their total

network cost . A variable ( is introduced to represent the satisfaction level of each

participating plant in the IPCCWN. The objective is to maximize the overall satisfaction as given

by Eq. 4.1. Since each plant will have an associated degree of satisfaction, which has to be

maximized simultaneously, the best compromising solution is obtained by maximizing the

satisfaction level of the least satisfied participant ( ). This is known as max-min aggregation

(Zimmermann, 1978; Czogala and Zimmermann, 1986), as defined in Eq. 4.2. The satisfaction

level of each participant is described by Eq. 4.3 and illustrated in Figure 4.1. If the

incurred by a plant is greater than or equal to the upper limit , the degree of satisfaction

is at its minimum level of zero. Conversely, if the is less than or equal to the lower

limit , the plant has achieved its goal and achieves the maximum satisfaction level of

one. Meanwhile, if the cost falls between and

, the degree of satisfaction for the

individual plant ( will take a value between zero to one.

Objective function: max (4.1)

(4.2)

Degree of satisfaction of each plant:

{

(4.3)

56

To find the optimal solution (see Appendix 2) for the case study, the objective function in Eq. 4.1

is solved subject to water balance constraints (Eqs. 4.4-4.5) and energy balance constraints (Eq.

4.6). Note that, Eqs. 4.5-4.6 are solved subject to the fixed water flow rate and fixed water

temperature requirement for all the sinks.

Source flow rate balance:

∑ (4.4)

Sink flow rate balance:

∑ (4.5)

Energy balance:

∑ (4.6)

where = flow rate of water from source i to sink j; = return stream from source i; =

available water flow rate of source i; = flow rate of fresh chilled water entering sink ;

= flow rate of fresh cooling water entering sink ; = water flow rate requirement in

sink j; = outlet temperature of source i; = temperature of fresh chilled water; =

temperature of fresh cooling water; and = water temperature requirement in sink .

Figure 4.1: Satisfaction level based on fuzzy goal

The total network cost incurred in each participating plant k is given in Eq. 4.7, which

consists of the annualized costs for: (1) return stream ; (2) fresh chilled and cooling water

( ; (3) reused streams ( and; (4) inter-plant piping . Return stream is analogous

to waste water stream that is not reused or recycled in any plant. They are sent to an external

utility plant for fresh chilled and cooling water regeneration with a constant unit cost of return

stream regardless of the water temperature, as shown in Eq. 4.8. The fresh chilled and

𝑇𝐴𝐶𝑘𝐿

𝜆

1

0

Satisfied Partially Satisfied Not Satisfied

𝑇𝐴𝐶𝑘 𝑇𝐴𝐶𝑘𝑈

𝑇𝐴𝐶

57

cooling water from the external utility plant will be sent back to the industrial plants for further

reuse. The synthesized close-loop regeneration-reuse of CCWNs possesses more environmental

benefits, as compared to the conventional practice where the return streams are discharged to the

nearby environment as waste streams which would cause thermal pollution (Nędzarek et al.,

2013). This would be a win-win situation for both industrial plants and the external utility plant

because the industrial plants could avoid the higher cost for structural intake and release than the

constant unit cost of return stream in order to comply with the environmental legislation

(Environmental Protection Agency, 2014), while the external utility plant could make profit

through selling the fresh chilled and cooling water to the industrial plants. On the other hand, the

operating cost for fresh chilled and cooling water consumption is referred to the unit costs of

fresh chilled water denoted as and fresh cooling water denoted as in Eq 4.9. Each

participating plant may serve as exporter or receiver of reused water. The cost associated with

the reused streams in plant , given in Eq. 4.10, embeds the revenue of sources selling

to another plant . Note that, the unit cost of reused streams from all sources is also assumed to

be the same regardless of the temperature so as to promote inter-plant water exchange. Note that,

unless flow rates are given on annual basis, an appropriate conversion factor (yearly

operating time) must be inserted in Eqs 4.8-4.10 to ensure consistency of all cost components. As

both receiver and exporter, the cross-plant flow rate in Eq. 4.10 indicates the cumulative flow

rate that sinks in plant receive from sources in plant and also the cumulative flow rate

that sources in plant export to sinks in plant . The total cost associated with reused stream

in plant is given in Eq. 4.11. Cost for reused stream is accounted because it encourages the

industrial symbiosis by reducing the fresh chilled and cooling water consumption.

(4.7)

∑ (4.8)

∑ ∑

(4.9)

∑ ∑ ∑ ∑

(4.10)

∑ (4.11)

58

It must be noted that an inter-plant piping will be needed and the cost incurred is shared equally

between the exporter and the receiver. Since each participating plant acts as both exporter and

receiver of the reused water, the incurred cross-plant piping cost accounts for both the cross-

plant flow rate that each participating plant receives and exports from and to plant . Same in

chapter 3, parameter is the incremental cost based on the cross-sectional area of pipelines and

is the cost parameter for building one pipeline. indicates the distance for all pipelines

between two plants. Note that the cost for building internal pipelines within individual plant is

relatively small because of the considerably small distance as compared to the cross-plant

pipelines and hence assumed to be negligible (Chew et al., 2008). As for the internal pipelines,

many industrial plants have used flexible hoses instead of building fixed pipes. There are many

types of flexible industrial hoses available and many of them can withstand high temperature and

pressure. Furthermore, flexible hoses can be easily removed when not needed and their

reusability in other sub-processes for other time periods makes the internal piping cost

insignificant compared to the cross-plant piping cost. Eq. 4.12 describes the upper and lower

bounds of the cross-plant flow rates and the binary variable ( in the equation indicates the

existence of cross-plant pipeline. As the exporter of reused stream to plant , the cross-plant

piping cost of participating plant is described in Eq. 4.13. As the receiver of reused

water from plant , the cross-plant piping cost of participating plant is described in

Eq. 4.14. The total inter-plant piping cost of participating plant is given in Eq. 4.15.

(4.12)

∑ ∑ ∑ ∑

(4.13)

∑ ∑

∑ ∑

(4.14)

∑ ∑ (4.15)

where = stream velocity, ms-1

; = water density, kg·m-3

; = annualized factor; = binary

variable for cross-plant piping; = lower limit of cross-plant flow rate; and = upper limit

of cross-plant flow rate.

59

4.4 Methodology: stage 2 - fuzzy analytic hierarchy process (FAHP) approach

FAHP is applied in this work to select the optimum network design based on qualitative and

quantitative criteria. Using this approach, triangular fuzzy ratings are utilized instead of the

conventional singular values in AHP. FAHP employs fuzzy set theory to handle uncertainty and

is capable of capturing a human‘s appraisal of ambiguity when complex multiple attribute

decision making problems are considered. This ability comes to exist when the crisp judgments

are transformed into fuzzy judgments.

The first step in the FAHP is to model the decision-making process as a hierarchy containing the

goal to be achieved at the top hierarchy, followed by the criteria to achieve the goal and finally

the alternatives to be assessed in decision making. Upon establishing the hierarchy, pairwise

comparison is performed to compare the importance of each criterion relative to others. These

pairwise comparisons are carried out using linguistic terms (Büyüközkan et al., 2004) with the

original TFNs slightly modified to represent the case study (see Table 4.1). Figure 4.2 further

illustrates the TFN, which is represented by a set of values: the lower value ( , modal value

, and upper value . As shown in Figure 4.2, the corresponding fuzzy membership

function aids in classifying a judgment using linguistic term. In order to conduct the pairwise

comparison, a questionnaire is developed and distributed to the decision makers. The questions

asked are with respect to criteria that have been pre-defined earlier.

Table 4.1: Linguistic terms and the corresponding TFNs

Linguistic Terms TFNs Reciprocal TFNs

Equally important (1, 1, 1) (1, 1, 1)

Moderately more important (2.5, 3, 3.5) (0.29, 0.33, 0.40)

Strongly more important (4.5, 5, 5.5) (0.18, 0.20, 0.22)

Very strongly more important (6.5, 7, 7.5) (0.13, 0.14, 0.15)

Extremely more important (9, 9, 9) (0.11, 0.11, 0.11)

60

Figure 4.2: A depiction of a triangular fuzzy number

Next, a fuzzy comparison matrix that represents the fuzzy relative importance of each pair

criteria is established with:

(4.16)

In Eq. 4.16, are TFN of criteria over criteria denoted by . and represent a

fuzzy degree of judgment. The greater the difference between , the fuzzier the degree;

when , the judgment is a non-fuzzy number. If strong importance of element over

element holds, then the pairwise comparison scale can be represented by the fuzzy number as

below (Eq. 4.17):

(4.17)

The steps of Chang (1996) extent analysis method are then used to estimate the relative weights

of the decision elements. The value of fuzzy synthetic extent with respect to criteria is

defined as (Eq. 4.18):

∑ ∑ ∑ (4.18)

In order to obtain a single representative number, these values must be defuzzified. One method

of doing this is to obtain the integral value, (Eq. 4.19) of those corresponding synthetic values.

The index of optimism shown in Eq. 4.19 represents the degree of optimism of a decision

maker. For a moderate decision maker, .

Fuzz

y m

ember

ship

funct

ion

1

0

𝑙

Linguistic

term

𝑚 𝑢

61

(4.19)

where = lower values of fuzzy synthetic values; = medium values of fuzzy synthetic value;

and = upper values of fuzzy synthetic values.

Via normalization, the normalized weight of each criterion is calculated as follows (Eq. 4.20):

∑ (4.20)

4.5 Case Study

The water stream data of Plant A (Foo et al., 2014a), Plant B and Plant C are shown in Table 4.2,

Table 4.3 and Table 4.4 respectively. In this case study, each process sink and source is assumed

to have a fixed temperature and flow rate. Each process stream shown in Tables 4.2-4.4

represents the water characteristic in each unit. The streams are characterized with their entering

water temperature (EWT), leaving water temperature (LWT) and their respective flow rates. The

mathematical model is then simplified by grouping streams with similar temperatures. The final

water limiting data of Plant A, Plant B and Plant C are simplified in Table 4.5. This case study

was solved using the parameters given in Table 4.6.

Synthesis of base case and preliminary IPCCWN are necessary prior to generate alternative

IPCCWN designs. Base case refers to the optimal network for each plant without implementing

IPCCWN. The objective function of the base case is to independently minimize the total network

cost of each participating plant. The total network cost consists of cost associated with return

stream and fresh chilled and cooling water costs ( (Eq. 4.21), subject to water balance

constraints (Eqs. 4.4-4.5) and; energy balance constraints (Eq. 4.6). Table 4.7 shows the base

case fresh chilled and cooling water requirement for Plant A, Plant B and Plant C.

Objective function: min (4.21)

Next, the preliminary IPCCWN is synthesized by solving the objective function in Eq. 4.22,

subject to water balance constraints (Eqs 4.4-4.5); energy balance constraint (Eq. 4.6); and

incurred costs including cost associated with return stream , fresh chilled and cooling

water costs ( , overall cost associated with reused streams ( and overall inter-plant

piping cost (Eqs. 4.7-4.15).

Objective function: min ∑ (4.22)

62

Table 4.2: Water characteristic of design coil in Plant A (Foo et al., 2014a)

Stream in Plant A EWT, (oC) LWT, (

oC) Flow rate, kg/h Flow rate heat

capacity, (kJoC

-1h

-1)

A-1 6.67 17.70 228.66 955.80

A-2 6.67 16.67 19.27 80.55

A-3 6.67 16.67 32.39 135.39

A-4 6.67 17.56 12.62 52.75

A-5 6.67 16.67 13.14 54.93

A-6 10.00 17.74 6.83 28.55

A-7 8.00 17.35 9.98 41.72

A-8 10.00 20.88 35.15 146.93

A-9 6.67 10.00 224.82 939.75

A-10 6.67 11.11 16.18 67.63

A-11 6.67 10.50 31.24 130.58

A-12 6.67 11.11 15.14 63.29

A-13 15.00 19.71 18.20 76.08

A-14 15.00 18.90 13.40 56.01

A-15 15.00 19.24 10.10 42.22

A-16 15.00 18.76 8.30 34.69

A-17 15.00 19.65 6.20 25.92

A-18 6.67 16.67 2.80 11.70

A-19 6.67 16.67 2.80 11.70

A-20 6.67 16.67 2.80 11.70

A-21 6.67 16.67 1.50 6.27

A-22 6.67 16.67 1.50 6.27

A-23 17.00 22.60 6.40 26.75

A-24 17.00 24.01 25.80 107.84

5601.20

63

Table 4.3: Water characteristic of design coil in Plant B

Stream in Plant B EWT, (oC) LWT, (


capacity, (kJoC

-1h

-1)

B-1 6.67 11.67 50.00 209.00

B-2 6.67 17.67 100.00 418.00

B-3 8.00 20.00 30.00 125.40

B-4 15.00 20.00 30.00 125.40

B-5 15.00 21.00 30.00 125.40

B-6 17.00 23.00 20.00 83.60

B-7 17.00 24.00 110.00 459.80

B-8 20.00 40.00 200.00 836.00

B-9 30.00 40.00 250.00 1045.00

B-10 30.00 75.00 220.00 919.60

B-11 55.00 75.00 300.00 1254.00

5601.20

Table 4.4: Water characteristic of design coil in Plant C

Stream in Plant B EWT, (oC) LWT, (


capacity, (kJoC

-1h

-1)

C-1 6.67 8.67 119.81 500.81

C-2 9.67 19.00 154.43 645.52

C-3 16.67 8.67 77.29 50.95

C-4 16.67 19.00 72.94 323.07

C-5 16.67 26.67 12.19 304.89

1825.24

64

Table 4.5: Final water limiting data

Sink, Flow

rate,

(kg/h)

Flow rate

heat

capacity,

(kJoC

-1h

-1)

Temperature,

(oC)

Source, Flow

rate,

(kg/h)

Flow rate

heat

capacity,

,

(kJoC

-1h

-1)

Temperature,

(oC)

Pla

nt

A

1 604.86 2528.31 6.67 1 224.82 939.75 10.00

2 9.98 41.72 8.00 2 31.24 130.58 10.50

3 41.98 175.48 10.00 3 31.32 130.92 11.11

4 56.20 234.92 15.00 4 76.20 318.51 16.67

5 32.20 134.59 17.00 5 258.09 1078.82 17.70

6 21.70 90.70 19.00

7 34.50 144.22 20.00

8 35.15 146.93 20.88

9 6.40 26.75 22.60

10 25.80 107.84 24.01

3115.02 3115.02

Pla

nt

B

6 150.00 627.00 6.67 11 50.00 209.00 11.67

7 30.00 125.40 8.00 12 100.00 418.00 17.67

8 60.00 250.80 15.00 13 60.00 250.80 20.00

9 130.00 543.40 17.00 14 30.00 125.40 21.00

10 200.00 836.00 20.00 15 20.00 83.60 23.00

11 470.00 1964.60 30.00 16 110.00 459.80 24.00

12 300.00 1254.00 55.00 17 450.00 1881.00 40.00

18 520.00 2173.60 75.00

5601.2 5601.2

Pla

nt

C

13 119.81 500.81 6.67 19 132.00 551.76 8.67

14 154.43 645.53 9.67 20 231.72 968.58 19.00

15 162.42 678.90 16.67 21 72.94 304.90 26.67

1825.24 1825.24

65

Table 4.6: Parameter values for the case study

Parameter Value Parameter Value

0.231 0.05 US$/kg

7920 hour/year 0.1 US$/kg

100 m 0.5

6.67 °C 2000

19.8 °C 250

0.754 US$/kg 1 ms-1

0.23 US$/kg 1000 kgm-3

Table 4.7: Fresh chilled and cooling water requirement for Plant A, Plant B and Plant C in Base

case

Plant Fresh chilled water flow rate heat

capacity, (kJoC

-1h

-1)

Fresh cooling water flow rate heat

capacity, (kJoC

-1h

-1)

A 2553.37 0.00

B 750.04 1169.03

C 655.30 0.00

Total 3958.71 1169.03

Table 4.8 shows the total network cost of the base case and the preliminary IPCCWN. The

optimal network structure of the preliminary IPCCWN with four inter-plant pipelines is shown in

Figure 4.3. Note that, only chilled water needs to be supplied from the central facility. From

Table 4.8, the cost savings allocation is Pareto optimal meaning no other allocation can be made

where at least one individual plant will be better off without making another plant worse off. In

this case study, there must be at least one participating plant that reduces its cost savings in order

to improve other plants cost savings. Since the preliminary IPCCWN does not incorporate fuzzy

cost goal limits set by each participating plant, Plant B and Plant C might refuse the

collaboration due to lower cost savings (4.7 % and 3.9%, respectively) as compared to Plant A

66

(19.8 %). In this case study, the formation of IPCCWN is solely dependent on the participating

plants themselves. Therefore, Plant A with the highest cost savings needs to bear part of the cost

of Plant B and Plant C. However, Plant A might also refuse to subsidize the other two partners.

Unless there is an external subsidy (e.g., from government), the formation of IPCCWN cannot

proceed. Using the fuzzy optimization with max-min strategy, each participating plant can get

the cost savings based on their fuzzy cost goal limits and at the same time maximize the

satisfaction level of the least satisfied participant. Also, no cross-subsidy among the three partner

plants is needed. Therefore, fuzzy optimization with max-min strategy is used to generate

alternative IPCCWNs in the next step with three different strategies as shown in Table 4.9.

Table 4.8: Comparison of total network cost between base case and preliminary IPCCWN

Base case Preliminary IPCCWN

Total network cost,

($/y)

Total network cost,

($/y)

Cost saving, ($/y)

[%Cost saving]

Plant A 1,712,637 1,373,238 339,399 [19.8%]

Plant B 835,333 796,255 39,078 [4.7%]

Plant C 439,532 422,566 16,966 [3.9%]

Total 2,987,502 2,592,059 395,443 [13.2%]

67

Figure 4.3: Network structure of preliminary IPCCWN

68

Table 4.9: Cost saving allocation of Strategies 1, 2 and 3

Plant Targeted lower limit of

total network cost,

($/y)

Targeted cost saving, ($/y)

[Targeted cost saving, (%)]

Str

ate

gy 1

A 1,563,262 149,375 [8.7%]

B 685,958 149,375 [17.9%]

C 290,157 149,375 [34.0%]

Total 2,539,377 448,125 [15.0%]

Str

ate

gy 2

A 1,455,742 256,895 [15.0%]

B 710,033 125,300 [15.0%]

C 373,602 65,930 [15.0%]

Total 2,539,377 448,125 [15 .0%]

Str

ate

gy 3

A 1,361,545 351,090 [20.5%]

B 791,042 44,291 [5.3%]

C 386,788 52,744 [12.0%]

Total 2,539,377 448,125 [15.0%]

In order to get the best solution for each strategy, one should set an ambitious goal for the overall

. Using the overall of the preliminary IPCCWN as the reference point, the lower

boundary of the overall targeted which either equal to or lower than $2,592,059/y is

considered an ambitious goal. In this optimization problem, the overall is derived from

15% targeted cost saving from the overall of Base case. Thus, the overall is equal to

$2,539,377/y which is lower than the cost derived from preliminary IPCCWN. In addition, all

strategies should have the same overall ($2,539,377/y) in order to make the alternative

IPCCWN designs comparable for the selection process. Three types of cost saving allocation

strategies are proposed to generate the alternative IPCCWNs. Strategy 1 pertains to equal

targeted cost savings ($149,375/y) among the participating plants while equal targeted

percentage cost savings (15%) among the participating plants is proposed in Strategy 2. Strategy

3 is an arbitrary cost savings allocation. Note that, the proposed strategies are adapted from

typical game theoretical approaches, known as common payoff game (Strategies 1 and 2) and

constant sum game (Strategy 3). In common payoff games, all participating plants have either the

same cost saving or percentage cost saving. In constant sum games, high cost saving in one

69

participating plant is obtained by lowering other plants targeted cost savings. In each strategy,

for the participating plants are set as the value shown in the base case ($1,712,637/y for

Plant A; $835,333/y for Plant B; $439,532/y for Plant C).

Utilizing the cost savings allocation strategy shown in Table 4.9, the alternative IPCCWNs are

generated by solving the objective function in Eq. 4.1, subject to constraints in Eqs. 4.2-4.15.

The alternative IPCCWNs for Strategy 1, Strategy 2 and Strategy 3 are shown in Figures 4.4-4.6

respectively. As shown in the figures, there are eight inter-plant pipelines (indicated as bold

lines) for Strategy 1 (Figure 4.4), six inter-plant pipelines for Strategy 2 (Figure 4.5) and five

inter-plant pipelines for Strategy 3 (Figure 4.6). Also, all designs require only external chilled

water supply. The satisfaction level of the individual plants, are then summarized in Table

4.10. The percentage cost savings shown in Table 4.10 is defined as the percentage cost

difference between base case and the alternative IPCCWN. In a game theoretic situation where

each agent (plant) has self-interest, the total payoff will be less than if they act in unison as a

single decision maker (Aviso et al., 2011). From Table 4.10, Strategy 3 has the highest

satisfaction level 0.87) while Strategy 1 has the least satisfaction level ( 0.46). It is

observed that, the overall in Strategy 3 is closer to the Preliminary IPCCWN. Apparently,

Strategy 3 will be chosen in the first stage of this work due to its highest satisfaction level.

However, subjectivity preference on the strategies selection based on human behaviour is not

considered in this stage. Therefore, FAHP is conducted in the next stage to make a decision on

IPCCWN design selection considering both qualitative and quantitative criteria.

70

Figure 4.4: Network structure of alternative IPCCWN in Strategy 1

71


72


73

Table 4.10: Fuzzy Optimization results of Strategies 1, 2 and 3

Plant Total network cost,

($/y)

Cost saving, ($/y)

[Cost saving, (%)]

Piping

cost, ($/y)

Fresh cost,

($/y)

Str

ate

gy 1

A

0.46

1,644,004 68,633 [4.0%] 52,470 1,320,462

B 766,700 68,633 [8.2%] 29,770 329,996

C 370,899 68,633 [15.6%] 31,557 263,731

Total 2,781,603 205,899 [6.9%] 113,797 1,914,189

Str

ate

gy 2

A

0.55

1,571,923 140,714 [8.2%] 41,481 1,268,770

B 766,700 68,633 [8.2%] 29,770 329,996

C 403,419 36,113 [8.2%] 20,568 302,807

Total 2,742,042 245,460 [8.2%] 91,819 1,901,573

Str

ate

gy 3

A

0.87

1,408,426 304,211 [17.8%] 34,609 1,230,053

B 796,956 38,377 [4.6%] 34,596 329,996

C 393,831 45,701 [10.4%] 19,862 241,017

Total 2,599,213 388,289 [13%] 89,067 1,801,066

In the second stage of this work, all three alternative IPCCWN designs are further analysed using

FAHP approach based on a set of pre-defined quantitative and qualitative criteria. Figure 4.7

shows the hierarchy in the selection of optimum network design. The criteria include:

participants satisfaction, (C1); fresh cost, (C2); piping cost, (C3); reliability, (C4); and cost

savings allocation strategy, (C5). The synthesis of inter-plant chilled and cooling water network

treats all the participant plants as a whole. Note that, the reliability (C4) and cost savings

allocation strategy (C5) are deemed as qualitative (subjective) criteria. To assess the reliability of

alternatives IPCCWN, the respective network structure is evaluated based on the capability of

their counterpart to supply consistent water sources. This is due to the potential penalties or risks

which result from the interdependencies among the participating plants (Benjamin et al., 2014a).

Other related reliability issues include technology lock-in (i.e., options for future process

modifications are constrained by agreements with partner companies). The same is true for cost

savings allocation strategy, which is also a subjective criterion depending on the preference of

individual plants when collaborating in IPCCWN. To evaluate these subjective criteria, financial

manager and process engineers are the suitable personnel for judgment.

74

Selecting the Optimum

IPCCWN design

Participants

Satisfaction

(C1)

Cost Savings

Allocation

Strategy

(C5)

Reliability

(C4)

Strategy 1

Strategy 2

Strategy 3

Fresh Cost

(C2)

Piping Cost

(C3)

Figure 4.7: Hierarchy for selecting optimum IPCCWN design

The questions asked to candidates for criteria comparison is given in the standard AHP form

(e.g., ―How important is C1 relative to C2‖). Table 4.11 shows the comparison matrix of criteria

for Plant A, Plant B and Plant C. The average comparison matrix of criteria is then summarized

in Table 4.12. Using Eqs. 4.18-4.20, the final average weight of each criterion, , is shown in

Figure 4.8. From Figure 4.8, criterion C5, which is cost savings allocation strategy, is the most

important criteria when selecting an IPCCWN design, whereas criterion C3, which corresponds

to piping cost, is the least important criterion.

75

Table 4.11: The comparison matrix of criteria for Plant A, Plant B and Plant C

C1 C2 C3 C4 C5

C1 (1,1,1) (2.5,3,3.5)

(1,1,1)

(2.5,3,3.5)

(4.5,5,5.5)

(2,5,3,3.5)

(2.5,3,3.5)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

(0.18,0.20,0.22)

(0.11,0.11,0.11)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

C2 (0.29,0.33,0.40)

(1,1,1)

(0.29,0.33,0.40)

(1,1,1)

(2.5,3,3.5)

(2.5,3,3.5)

(4.5,5,5.5)

(2.5,3,3.5)

(2.5,3,3.5)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

C3 (0.18,0.20,0.22)

(0.29,0.33,0.40)

(0.29,0.33,0.40)

(0.29,0.33,0.40)

(0.29,0.33,0.40)

(0.18,0.20,0.22)

(1,1,1)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

(0.13,0.14,0.15)

(0.11,0.11,0.11)

(0.11,0.11,0.11)

(0.13,0.14,0.15)

C4 (6.5,7,7.5)

(6.5,7,7.5)

(4.5,5,5.5)

(0.29,0.33,0.40)

(0.29,0.33,0.40)

(6.5,7,7.5)

(6.5,7,7.5)

(6.5,7,7.5)

(6.5,7,7.5)

(1,1,1)

(0.29,0.33,0.40)

(0.18,0.20,0.22)

(1,1,1)

C5 (9,9,9)

(6.5,7,7.5)

(6.5,7,7.5)

(6.5,7,7.5)

(6.5,7,7.5)

(6.5,7,7.5)

(9,9,9)

(9,9,9)

(6.5,7,7.5)

(2.5,3,3.5)

(4.5,5,5.5)

(1,1,1)

(1,1,1)

Table 4.12: The average matrix comparison of criteria

C1 C2 C3 C4 C5

C1 (1,1,1) (2.00,2.33,2.67) (3.17,3.67,4.17) (0.15,0.16,0.17) (0.12,0.13,0.14)

C2 (0.53,0.55,0.60) (1,1,1) (3.17,3.67,4.17) (1.71,2.05,2.38) (0.13,0.14,0.15)

C3 (0.25,0.29,0.34) (0.25,0.29,0.34) (1,1,1) (0.13,0.14,0.15) (0.12,0.12,0.12)

C4 (5.83,6.33,6.83) (2.36,2.55,2.77) (6.50,7.00,7.50) (1,1,1) (0.49,0.51,0.54)

C5 (7.33,7.67,8.00) (6.50,7.00,7.50) (8.17,8.33,8.50) (2.67,3.00,3.33) (1,1,1)

76

Selecting the Optimum

IPCCWN design

Participants

Satisfaction

(w1=0.12)

Cost Savings

Allocation

Strategy

(w5=0.44)

Reliability

(w4=0.29)

Strategy 1

Strategy 2

Strategy 3

Fresh Cost

(w2=0.12)

Piping Cost

(w3=0.03)

Figure 4.8: Final average weights of the criteria for selecting the optimum IPCCWN design

The assessors from each plant then evaluate the criteria of each alternative network design. The

comparisons of Network Design 1, Network Design 2 and Network Design 3 with respect to the

predefined criteria are given in Tables 4.13-4.17. The criteria scores of alternative network

designs, as shown in Table 4.18 can be obtained using the same method as that used for the

weight of criteria calculation using Eqs. 4.18-4.20. Eq. 4.23 describes the final score of each

alternative network design ( .

∑ (4.23)

e.g:

Table 4.13: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to participants

satisfaction (C1)

Strategy 1 Strategy 2 Strategy 3

Strategy 1 (1,1,1) (0.29,0.33,0.40) (0.18,0.20,0.22)

Strategy 2 (2.5,3,3.5) (1,1,1) (0.29,0.33,0.40)

Strategy 3 (4.5,5,5.5) (2.5,3,3.5) (1,1,1)

77

Table 4.14: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to fresh cost

(C2)


Strategy 1 (1,1,1) (0.29,0.33,0.40) (0.18,0.20,0.22)

Strategy 2 (2.5,3,3.5) (1,1,1) (0.29,0.33,0.40)

Strategy 3 (4.5,5,5.5) (2.5,3,3.5) (1,1,1)

Table 4.15: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to piping cost

(C3)


Strategy 1 (1,1,1) (0.18,0.20,0.22) (0.18,0.20,0.22)

Strategy 2 (4.5,5,5.5) (1,1,1) (0.29,0.33,0.40)

Strategy 3 (4.5,5,5.5) (2.5,3,3.5) (1,1,1)

Table 4.16: The comparison of Strategy1, Strategy 2 and Strategy 3 with respect to reliability

(C4)


Strategy 1 (1,1,1) (0.18,0.20,0.22) (0.13,0.14,0.15)

Strategy 2 (4.5,5,5.5) (1,1,1) (0.29,0.33,0.40)

Strategy 3 (6.5,7,7.5) (2.5,3,3.5) (1,1,1)

Table 4.17: The comparison of Strategy 1, Strategy 2 and Strategy 3 with respect to cost savings

allocation strategy (C5)


Strategy 1 (1,1,1) (0.13,0.14,0.15) (6.5,7,7.5)

Strategy 2 (6.5,7,7.5) (1,1,1) (9,9,9)

Strategy 3 (0.13,0.14,0.15) (0.11,0.11,0.11) (1,1,1)

78

Table 4.18: Scores of Network Design 1, Network Design 2 and Network Design3 with respect

to participant‘s satisfaction (C1), fresh cost (C2), piping cost (C3), reliability (C4) and cost

savings allocation strategy (C5)

Scores of alternative network designs,


Participants satisfaction 0.10 0.30 0.61

Fresh cost 0.10 0.30 0.61

Piping cost 0.08 0.39 0.55

Reliability 0.07 0.34 0.59

Cost savings allocation strategy 0.31 0.64 0.05

The final score of alternative network designs are; Network Design 1 (FS1 = 0.18); Network

Design 2 (FS2 = 0.46) and; Network Design 3 (FS3 = 0.36). Using the final scores shown above,

Network Design 2 is ranked as the highest and represents the best option one should choose. It is

worth noting that without performing Stage 2; Network Design 3 will be selected based solely on

the result of the optimization model. In general, mathematical programming methods are not able

to account for human subjectivity on the decision making process. Thus, FAHP is used in stage 2

to quantify those subjective criteria which would otherwise not be accounted for in a purely

optimization-based model, and thus facilitates the selection of an optimum solution among the

alternatives. Figure 4.9 shows the process flow of design methodology for identifying the

optimum IPCCWN. The proposed design methodology in stage 2 is applicable in any case study

which takes into consideration both qualitative and quantitative criteria in making the final

decision among the alternatives.

79

Figure 4.9: Design methodology of optimum IPCCWN

4.6 Conclusion

A sequential two-step methodology for IPCCWN synthesis and selection among alternative

IPCCWN designs has been developed. The first step used fuzzy optimization to generate

alternative IPCCWN designs in consideration of different cost savings allocation strategies. The

second step proposed FAHP to select the optimum network design considering both qualitative

and quantitative criteria. In synthesizing an optimum IPCCWN formed by different entities,

Base case synthesis of Plant A, Plant B and Plant C

individual plant process integration

objective function: minimize 𝑇𝑁𝐶𝑘

reference for 𝑇𝑁𝐶𝑘𝑈

Preliminary IPCCWN synthesis

objective function: minimize ∑ 𝑇𝑁𝐶𝑘𝑘 𝐾

reference for ∑ 𝑇𝑁𝐶𝑘𝐿

𝑘 𝐾

Generating alternative IPCCWN strategy

objective function: maximize overall satisfaction level 𝜆

∑ 𝑇𝑁𝐶𝑘𝐿

𝑘 𝐾 of the alternative IPCCWN strategies are same

Optimum IPCCWN selection using FAHP approach

Qualitative and quantitative criteria are predefined

Subjective criteria are considered in the selection

80

results from the case study show that the benefits may not be distributed equitably among the

participants. Selecting an optimum IPCCWN to facilitate the collaboration among participating

plants is one of the pivotal steps to the success of the implementation of IPCCWN as a whole.

Thus, finding a compromise between participants in IPCCWN is very important or one will

rather choose to quit the collaboration. On the other hand, the conventional AHP method does

not take into account the uncertainty associated with the mapping of one's judgement to a

number. It creates and deals with a very unbalanced scale of judgement. FAHP utilizes triangular

fuzzy ratings with crisp boundaries that provide sharp transition for judgments made from one

class to another. Therefore, FAHP approach gives a more precise judgment as compared to the

traditional AHP, which utilizes the conventional singular values. Although this chapter proposed

a design methodology to derive an optimum network that achieves the best balance of

performance for the predefined decision criteria, the solution obtained is not the global minimum

cost that can be obtained via a fully cooperative approach; this is a consequence of the self-

interested behaviour of the individual plants.

81

CHAPTER 5 INCORPORATING TIMESHARING SCHEME IN ECO-INDUSTRIAL

MULTI-PERIOD CHILLED AND COOLING WATER NETWORK DESIGN

The establishment of an EIP that originates from the concept of industrial symbiosis allows

individual plants to cooperate with each other so as to achieve greater water and energy recovery

through inter-plant chilled/cooling water reuse/recycle. However, periodical circumstances such

as variation of market demands and plant shut-down schedules, which are common in different

business operations, have not been well considered in designing an EIP. Thus, there is a need to

study explicitly the effect of such periodical operations due to the high level of connectivity

within an EIP. This chapter presents a design methodology to develop a robust EIP by

integrating a set of multi-period chilled and cooling water networks (CCWNs). The proposed

design methodology aids in developing an EIP, taking into account network flexibility in

multiple period operations.

5.1 Introduction

Industrial production can be divided into batch and continuous processes. Various process

integration techniques have been developed for water conservation in batch and continuous

processes. These include limiting composite curve (Wang and Smith, 1994), mass problem

table (Castro et al., 1999), evolutionary table (Sorin and Bedard, 1999), water surplus diagram

(Hallale, 2002), material recovery pinch (El-Halwagi et al., 2003), water cascade analysis (Foo

et al., 2005) and load interval diagram (Almutlaq et al., 2005). In practice, both batch and

continuous processes are influenced by process- and market-related uncertainties including

seasonal product demand, scheduled plant shut-down and expansion plans of plant capacity. In

adaptation to the above transient scenarios, several methods such as Petri-net based (Ghaeli et

al., 2005), timed automata (Panek et al., 2008), S-graph (Hegyháti and Friedler, 2011), strip

packing (Castro and Grossmann, 2012) and mathematical programming techniques (Lee et al.,

2014) have been proposed to achieve an optimum scheduling plan for the transient production.

These scheduling plans would result in the change of the process demand as the total demand

could be increased, be decreased or remain unchanged.

82

Chilled and cooling water are common utilities widely used to perform cooling duty in various

industries. Looking at the high investment costs and the long-term nature of large-scale utility

systems that require long-term planning perspectives, sometimes extending over many

decades, chilled and cooling water networks (CCWNs) configured under the single period

assumption may not be able to accommodate with periodical changes of the future process

demand. There is a lack of attention given to the synthesis of multi-period CCWNs. A closely

related area of work to design multi-period CCWNs is referred to heat exchanger network

(HEN) design. Various design methods have been developed to consider HENs flexibility for

multi-period operation. Floudas and Grossmann (1986) first introduced sequential strategies to

develop flexible HENs by separately optimizing the network for each time period. Though the

sequential approach reduces the computation load, its global optimality is often questioned

since the trade-offs (such as those between cost and sustainability) could not be fully

addressed. Many works have developed simultaneous strategies for multi-period HEN

synthesis (Aaltola, 2002; Ma et al., 2008; Isafiade and Fraser, 2010). However, simultaneous

approaches may not get convergence easily in optimization runs especially when the model is

highly nonlinear. In their works, the more flexible a network is, the more pipelines required.

Hence, forming a high-flexibility network would normally be associated with higher

investment cost since more cross-plant pipelines are required to ensure the feasibility of the

network for all the time periods. Sadeli and Chang (2012) proposed timesharing schemes to

efficiently utilize heat exchangers so as to reduce the overdesign of the heat exchanger units in

different time periods. The authors presented four heuristic rules to overcome the

aforementioned shortcoming: Rule 1 divides the matches of heat exchanger units shared in

different time periods into two groups, one with the largest area required for the match and the

other requires an auxiliary heat exchanger unit to facilitate the match; Rule 2 entails the

overdesign margin that should not exceed 15% of that actual required or the larger heat

exchanger unit; Rule 3 identifies the base heat exchanger units that could be used for more than

one period of time; Rule 4 states that the remaining heat duties yet to be satisfied are

considered one at a time in ascending order. Jiang and Chang (2013) addressed the issue of

unexpected deviation from nominal operating conditions by designing multi-period HENs

separately for each time period after applying the timesharing scheme.

83

Recently, multi-period planning has been proposed for direct water reuse within industrial city

(Bishnu et al., 2014). They have considered future expansion of plants‘ capacities and the

changes of process sinks and sources over the time horizon. In their work, they did not

minimize the total number of inter-plant piping connections that result in a complex network

structure for plants‘ capacities expansion. This chapter proposes a design methodology for the

synthesis of an optimal multi-period IPCCWN. The proposed design methodology takes into

account network flexibility and complexity, and individual plant cost goals in this work. A

four-step design methodology is presented to achieve the aforementioned objective. Figure 5.1

shows the design framework of the proposed methodology. Multi-period single plant CCWN is

first developed to determine the upper bound of cost for each participating plant (this is taken

as the base case). The global lower bound of cost is then identified in the following step. Two

Pareto optimal multi-period IPCCWNs is then synthesized in the third step. The resulting

multi-period IPCCWNs from the preceding step are further simplified by incorporating the

timesharing at last. The proposed design approach will be demonstrated through an illustrative

example.

5.2 Problem Statement

The formal problem statement is as follows. Given a set of industrial plants , which

operate independently in an EIP; each of those uses chilled and cooling water, which can be

reused/recycled within the inter-plant network. It is intended to maximize the water and energy

conservation by having an IPCCWN for the participating plants. Note that, periodical operation

modes in component units vary the demand of cooling utilities. Each participating plant has a

set of chilled and cooling water sources and sinks characterized by their water

temperatures and flow rates for all time periods . The objective in this work is to develop

a design methodology for the synthesis of a multi-period IPCCWN with optimized cost savings

allocation among the participating plants. This chapter presents a four-step design

methodology to optimize cost goals and network flexibility and complexity. Since the

establishment of an EIP involves multiple decision makers from each participating plant, it is

important to know each of their goals (i.e. cost) to form the IPCCWN network. In order to

design an optimum network, it is important to set the upper and lower limits of their goals.

Knowing each participating plant‘s upper limit cost aids in the integration of the symbiotic

84

network so that each plant would achieve at least the same or lower cost as compared to its

base case without implementing the EIP. On the other hand, the desired cost of each

participating plant is indicated as the lower limit cost.

Figure 5.1: Flowchart of the proposed design methodology

Step 4: Timesharing scheme for multi-period CCWN of EIP

Reduce the network complexity and ensure the network feasibility for all

time periods

EIP Modeling

Construct a case study for the execution of the stepwise approach

Step 1: Multi-period single plant CCWN

Identify the upper limit cost for each participating plant

Step 2: Preliminary multi-period CCWN of EIP

Identify the lower limit cost for each participating plant

Step 3: Pareto optimal multi-period CCWN of EIP

To arrive compromise in an EIP when Pareto optimality of the solution is

reached

85

5.3 Design methodology

This section describes the four-step design methodology to integrate chilled and cooling water

sources and sinks of the participating plants. The formulations in the first three steps synthesize

a direct inter-plant integration network among the participating plants. However, direct inter-

plant water integration results in a complex network, especially when considering multi-period

operation (Bishnu et al., 2014). Hence, Step 4 presents the heuristic rule to simplify the multi-

period inter-plant network. The mathematical model for multi-period IPCCWN synthesis is

formulated by taking into account the economic, water flow rate and energy balance

constraints.

5.3.1 Step 1: Multi-period single plant CCWN

To identify the base case, each participating plant is assumed to operate independently in a multi-

period operation mode for CCWN synthesis. Single plant CCWNs are first to be optimized with

the objective function given in Eq. 5.1, subject to the costs constraints (Eqs. 5.2-5.4), water flow

rate balance constraints (Eqs. 5.5 and 5.6), and energy balance constraints (Eq. 5.7). Note that,

the optimal results obtained for the individual plants in this step are the upper limit costs for

forming an EIP in a later step. This is to ensure that the cost of the individual plant could be

better off by building an EIP as compared to the base case. The total network cost given

in Eq. 5.2 consists of the operating costs of return streams and fresh chilled and cooling

water . The cost for return stream and fresh chilled and cooling water are given in

Eqs. 5.3 and 5.4 respectively. Same in Chapter 4, the unit cost of return stream is assumed

to be the same regardless of the water temperature. Note that, the operational time for period

is inserted in both Eqs. 5.3-5.4 to shown the cost for the respective period. The water flow

balances for sources and sinks are described in Eqs. 5.5 and 5.6 respectively. The plant sources

could be reused within the internal process sinks, and/or sent to the external utility plant as return

streams, while the process sinks could reuse the process sources from the sink outlet, and/or

receive fresh chilled and cooling water. The energy balance for sinks given in Eq. 5.7 ensures

that the inlet temperature does not exceed its maximum limit. The superstructure for the

synthesis of single plant CCWN for any time period is shown in Figure 5.2.


86

∑ ∑ (5.2)

∑ (5.3)

(∑ ∑ ) (5.4)

∑ (5.5)

∑ (5.6)

∑ (5.7)

Figure 5.2: Superstructure for single plant CCWN in any time period

5.3.2 Step 2: Preliminary multi-period IPCCWN

After identifying the upper limit costs of all the participating plants in the preceding step, a

preliminary EIP is obtained in this step by solving the model comprised of Eqs. 5.8-5.17 for each

participating plant individually to determine their lower limits costs (or targeted/desired costs).

87

The objective function is to minimize the total network cost of each participating plant as given

in Eq. 5.8. The total network cost of each participating plant for all time periods , given in Eq.

5.9, consists of the operating cost for return stream , fresh chilled and cooling water

consumption , and reused stream and the investment cost for cross-plant piping

installation . The operating cost for the return stream and fresh chilled and cooling water

consumption are given in Eqs. 5.10 and 5.11 respectively. The cost associated with the reused

water of plant with another plant accounts for the revenue of selling source (Eq.

5.12). Note that, each participating plant may serve as both exporter and receiver of the sources.

With the formation of an EIP, the source exporter could benefit from selling its sources to other

plants, while the source receiver could reduce the cost for fresh chilled and cooling water

consumption. The unit cost of reused streams is assumed to be the same regardless of the

water temperature. The total cost associated with reused stream in plant is given in Eq. 5.13.

To find the optimal solution, this model is subjected to water balance constraints (Eqs. 5.5 and

5.6) and energy balance constraints (Eq. 5.7). The superstructure for the IPCCWN for any time

period is shown in Figure 5.3.


(5.9)

∑ ∑ (5.10)

∑ ∑

∑ ∑

(5.11)

∑ ∑ ∑ ∑

(5.12)

∑ ∑ (5.13)

Same in Chapter 4, internal piping cost of each participating plant is considerably small as

compared to the cross-plant piping cost and thus assumed to be negligible. To determine the

existence of a cross-plant pipeline, Eq. 5.14 describes the upper and lower bounds

of the cross-plant flow. Note that, the cross-plant piping cost is shared equally between the

exporter and receiver of the reused water as both parties benefit in this symbiotic industrial

relationship. As the source exporter for plant , the cross-plant piping cost of plant

88

is given in Eq. 5.15. As the source receiver for plant , the cross-plant piping cost of

plant is given in Eq. 5.16. The total inter-plant piping cost of plant is given in Eq. 5.17.

(5.14)

∑ ∑ ∑ ∑

(5.15)

∑ ∑

∑ ∑

(5.16)

∑ ∑ ∑ ∑

(5.17)

Figure 5.3: Superstructure for the inter-plant CCWN in any time period

89

5.3.3 Step 3: Pareto optimal multi-period IPCCWNs

A Pareto optimal outcome is achieved when no party could be better off without causing any

other worse off by changing resource allocation. Assuming ‗selfish‘ behaviour of the

participating plants where none of them is willing to reduce their own benefits (in this case cost

savings); hence, Pareto optimal solution is presented to arrive at a compromise in an EIP. This

compromise is the mutual consensus of opinion among the participating plants that no one could

individually improve its benefit when Pareto optimality is arrived. Note that the problem

addressed in this work entails multi-objective optimization to consider all the participating

plants‘ cost goals for two Pareto optimal solutions; each approach comes with its pros and cons

which will be discussed in the following subsections. The mathematical modelling codes for

Pareto optimal multi-period IPCCWNs using LINGO ver13 software are shown in Appendix 3.

5.3.3.1 Pareto optimal solution 1 (POS 1): Global minimum-cost network design approach

POS 1 identifies the global minimum cost for the formation of EIP with the objective function as

given in Eq. 5.18. To find an optimal solution, this model is solved subjected to water balance

constraints (Eqs. 5.5 and 5.6), energy balance constraints (Eq. 5.7) and costs (Eqs. 5.9-5.17).

Objective function: min ∑ (5.18)

5.3.3.2 Pareto optimal solution 2 (POS 2): Fuzzy optimization approach

In game theory, the max-min strategy is a low risk strategy to maximize the minimum gain for

one participant to achieve. This section presents POS 2 using a fuzzy optimization approach to

implement max-min strategy in mathematical programming. Since an EIP consists of multiple

plants from different entities, the establishment of an EIP may be hindered if failing to satisfy

any of the participating plants‘ objectives. To realize Pareto optimality, the objective function in

this case is to maximize the overall satisfaction level of participating plants for all time

periods (Eq. 5.19). The minimum gain of the least satisfied participating plant is to be

maximized, as given in Eq. 4.2. To find an optimal solution, this model is solved subjected to

water balance constraints (Eqs. 5.5 and 5.6), energy balance constraints (Eq. 5.7) and costs (Eqs.

5.9-5.17). The satisfaction level of each participating plant is defined same in Chapter 4 (Eq. 4.3)

90

Objective function: Max (5.19)

5.3.4 Step 4: Timesharing scheme for multi-period IPCCWN

The proposed timesharing scheme in this work is to efficiently share common cross-plant

pipelines between two plants for all time periods in order to get the maximum cost savings of

each participating plant. The delivered sources are then transferred to the respective process

sinks within individual plant through flexible hoses which can be easily removed or changed in

different periods. Since from the optimization run in the preceding step takes into account

the investment cost of all the cross-plant flows/pipelines for all time periods, there are potentially

extra cost savings for each participating plant by introducing the timesharing scheme. The main

aims in this step are to enhance the cost savings of each plant and to reduce network complexity.

The following heuristic rules are presented to implement the proposed timesharing scheme for

multi-period IPCCWNs:

Rule 1: For each set of connecting plants, identify all the possible cross-plant flows of

different time periods to share a common pipeline.

Rule 2: The cross-sectional area of the common cross-plant pipeline must be sized based on

the maximum cross-plant stream flow rate so as to ensure network feasibility;

Rule 3: Arrange the cross-plant streams to share in a common pipeline in descending order

based on the flow rate. (e.g. both the highest and the second highest cross-plant flow

rate in different periods should be arranged to share in the same common pipeline).

5.4 Case study

A typical EIP could have many different plants but not all of them are major chilled and cooling

water consumers. Therefore, an EIP that involves three or more industrial plants should suffice to

represent the industrial symbiosis. In addition, the case study considered may be simplified by

merging plants that are similar and close to each other so as to reduce the number of plants. A

case study on a hypothetical EIP which consists of three plants (Plant 1, Plant 2, and Plant 3) is

used to demonstrate the proposed design methodology. Each plant has its own set of water

limiting data for three operational time periods. The characteristics of sources and sinks for each

participating plant include water flow rates and temperatures are given in Table 5.1. It is

91

observed that some of the plants‘ source temperatures are low enough to be direct reused in sinks

of the other plants. This present the opportunities for chilled and/or cooling water recovery

through inter-plant network. It is intended to optimize the multi-period CCWN between these

plants in order to form an EIP. The formulated LP (Step 1) and MILPs (Steps 2 and 3) are solved

using LINGO v13.0 software in a 8.0 GB RAM desktop computer with Intel Core i7 CPU at 3.4

GHz and a Window 8 operating system. This case study was solved using the parameters given

in Table 5.2.

92

Table 5.1: Temperatures and flow rate of sinks and sources

Period 1 Period 2 Period 3

(kg/h)

(oC)

(kg/h)

(oC)

(kg/h)

(oC)

(kg/h)

(oC)

(kg/h)

(oC)

(kg/h)

(oC)

Pla

nt

1

1 604.86 6.67 1 224.82 10.00 1 250.00 6.00 1 200.00 10.00 1 650.00 7.00 1 470.00 10.00

2 9.98 8.00 2 31.24 10.50 2 150.00 9.00 2 250.00 13.50 2 110.00 8.00 2 290.00 12.00

3 41.98 10.00 3 31.32 11.11 3 300.00 12.00 3 160.00 15.00 3 250.00 10.00 3 130.00 14.00

4 56.20 15.00 4 76.20 16.67 4 200.00 15.00 4 180.00 17.00 4 320.00 17.00 4 120.00 17.00

5 32.20 17.00 5 258.09 17.70 5 180.00 20.00 5 90.00 19.50 5 470.00 21.00 5 50.00 23.00

6 21.70 19.00 6 150.00 24.50 6 70.00 25.00

7 34.50 20.00 7 50.00 36.00 7 90.00 28.00

8 35.15 20.88 8 230.00 30.00

9 6.40 22.60 9 150.00 39.00

10 25.80 24.01 10 200.00 55.00

Pla

nt

2

6 150.00 6.67 11 50.00 11.67 8 150.00 6.00 8 50.00 10.00 6 200.00 6.00 11 90.00 12.00

7 30.00 8.00 12 100.00 17.67 9 200.00 7.00 9 580.00 14.50 7 70.00 9.00 12 180.00 15.00

8 60.00 15.00 13 60.00 20.00 10 280.00 10.00 10 170.00 20.00 8 280.00 12.00 13 280.00 18.00

9 130.00 17.00 14 30.00 21.00 11 170.00 17.00 11 110.00 30.00 9 150.00 13.00 14 150.00 20.00

10 200.00 20.00 15 20.00 23.00 12 180.00 20.00 12 70.00 32.00 10 170.00 19.00 15 170.00 25.00

11 470.00 30.00 16 110.00 24.00 11 640.00 22.00 16 290.00 32.00

12 300.00 55.00 17 450.00 40.00 17 350.00 40.00

18 520.00 75.00

Pla

nt

3

13 119.81 6.67 19 132.00 8.67 13 260.00 6.00 13 190.00 11.50 12 500.00 8.00 18 80.00 14.00

14 154.43 9.67 20 231.72 19.00 14 380.00 9.00 14 450.00 12.50 13 180.00 13.00 19 420.00 16.00

15 162.42 16.67 21 72.94 26.67 15 120.00 17.00 15 120.00 23.60 14 110.00 15.00 20 290.00 21.00

16 90.00 20.00 16 90.00 29.80 15 460.00 22.00 21 70.00 30.00

22 270.00 36.00

23 120.00 40.00

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Table 5.2: Parameter values for the case study

Parameter Value Parameter Value

0.231 0.05 US$/kg

100 m 0.1 US$/kg

2640 hours/period 2000

6 °C 250

20 °C 1 ms-1

0.754 US$/kg 1000 kgm-3

0.23 US$/kg

5.4.1 Four-step design methodology

5.4.1.1 Step 1: Determining upper limit cost for each participating plant

In the first step of the proposed design methodology, multi-period individual plant CCWNs (base

case) are synthesized for determining the upper limit cost of each participating plant in the EIP

formation. The total network cost and fresh chilled/cooling water consumption derived from in-

plant water integration with multi-period CCWNs of individual plants are given in Table 5.3.

From Table 5.3, upper limit costs of Plant 1, Plant 2, and Plant 3 are 3.19, 2.73 and 2.39

million US$/y, respectively. These upper limit costs are the baseline to derive cost savings for

the participating plants in the following sections. In the base case, the total fresh chilled and

cooling water consumption is found to be 42500 and 6048 tons/y, respectively.

94

Table 5.3: Total network cost and fresh chilled and cooling water consumption for base case

Plant Fresh chilled water

flow rate (tons/y)

Fresh cooling water

flow rate (tons/y)

Total network cost

(million US$/y)

Plant 1 17760 0 3.19

Plant 2 12075 6048 2.73

Plant 3 12665 0 2.39

Total 42500 6048 8.31

5.4.1.2 Step 2: Determining lower limit cost for each participating plant

The preliminary multi-period inter-plant CCWNs are synthesized to obtain the lower limit cost

for each participating plant. The

of each plant is derived by minimizing their total

network cost separately. This is to find the maximum cost savings for each plant by exploiting

sources from other plants. As shown in Table 5.4, the of Plant 1, Plant 2, and Plant 3 are

2.61, 1.68, and 1.63 million US$/y, respectively. From the preliminary EIP results as shown in

Table 5.4, there is significant reduction in total fresh chilled and cooling water consumption as

compared to the base case (in Table 5.3). To minimize the cost individually for each plant is a

self-interest act that only explores the opportunity to reuse water (with cheaper cost) from the

other plants in order to reduce its own consumption of fresh cold utilities (with higher cost).

Figure 5.4 further illustrates the cost saving of each participating plants derived from the

objective function of minimizing individual plant . It is observed that negative cost savings

are found in plants that are not involved in the objective function, e.g. minimizing for Plant

1 results in negative cost savings in Plant 2 and Plant 3. These negative cost savings represent the

increases in total network cost for individual plants as compared to their base case in Table 5.3.

Thus, a systematic approach to ensure a compromising solution is required for the establishment

of an EIP, so that no participant would be disadvantaged in this EIP effort.

95

Table 5.4: Results for preliminary multi-period inter-plant CCWNs of EIP

Objective

function

Plant Fresh chilled water

flow rate (tons/y)

Fresh cooling water

flow rate (tons/y)

Total network cost

(million US$/y)

min Plant 1 11412 0 2.61

Plant 2 12271 0 4.38

Plant 3 13347 0 4.01

Total 37030 0 11.00

min Plant 1 19794 371 5.87

Plant 2 5787 0 1.68

Plant 3 12726 0 4.05

Total 38307 371 11.6

min Plant 1 15953 182 4.80

Plant 2 11243 0 3.93

Plant 3 6216 0 1.63

Total 33412 182 10.36

Figure 5.4: Percentage network cost savings for all the plants with different objective function

Minimize total networkcost of Plant 1



Plant 1 18.2 -84 -50.5

Plant 2 -60.4 38.5 -44

Plant 3 -50.5 -44 31.8

-100

-80

-60

-40

-20

0

20

40

60

% T

ota

l ne

two

rk c

ost

sav

ing

96

5.4.1.3 Step 3: Obtaining Pareto optimal EIPs

The results for POS 1 and POS 2 are summarized in Table 5.5. From Table 5.5, both Pareto

solutions have the same total fresh chilled and cooling water consumption. Significant reduction

in fresh chilled and cooling water consumption is observed by forming a Pareto optimal EIP. It is

observed that all the participating plants obtain positive cost savings in the Pareto optimal inter-

plant network configurations that distribute reusable water in the way to reach the compromising

solution among the plants. The satisfaction levels of Plant 1, Plant 2, and Plant 3 in POS 1 are

found to be 0.33, 0.31 and 0.25. Under this circumstance, conflicts among the participating

plants might arise due to the lower satisfaction level found in Plant 3. Consensus on the

cooperation might fail to be reached if the least satisfied participants refuse the collaboration.

POS 2 proposes a max-min strategy to maximize the satisfaction level of the least satisfied

participating plant. Though the overall total network cost in POS 2 (7.61 million US$/y) is

slightly higher than POS 1 (7.6 million US$/y), it fairly distribute the benefits by ensuring the

same satisfaction level (0.3) among the participating plants.

Table 5.5: Results for POS 1 and POS 2

Plant Fresh chilled

water flow rate

(tons/y)

Fresh cooling

water flow

rate (tons/y)

Total network

cost (million

US$/y)

% Total

network cost

saving

Satisfaction

level,

Pareto Optimal solution 1

Plant 1 11563 0 3.02 5.3 0.33

Plant 2 7234 561 2.42 11.4 0.31

Plant 3 7953 0 2.17 9.2 0.25

Total 26750 561 7.6 8.4*

Pareto Optimal Solution 2

Plant 1 11563 0 3.00 5.96 0.30

Plant 2 7234 561 2.40 12.09 0.30

Plant 3 7953 0 2.20 7.95 0.30

Total 26750 561 7.61 8.7*

* mean values

97

The corresponding multi-period IPCCWN in POS 1 is shown in Figure 5.5. The inlet streams

such as fresh chilled and cooling water and the outlet return streams for each participating plant

are drawn as dotted line with the arrow showing the stream flow direction. Eight cross-plant

pipelines (solid line) are observed in the global minimum-cost network design. There are four

cross-plant streams (F1,9,1, F1,14,1, F5,11,1, and F19,7,1) in period 1, two cross-plant streams (F14,9,2

and F14,10,2) in period 2, and two cross-plant streams (F2,8,3 and F19,11,3) in period 3. Among them,

there are three cross-plant flows from Plant 1 to Plant 2, one from Plant 1 to Plant 3, and four

from Plant 3 to Plant 2. In this EIP network, Plant 1 and Plant 3 are the main source exporters

because their sources‘ temperature is low enough to be reused in other plants. Figure 5.6 shows

the corresponding multi-period inter-plant CCWN in POS 2. Nine cross-plant pipelines (solid

line) are observed in this Pareto optimal EIP. There are five cross-plant streams (F1,9,1, F1,14,1,

F5,11,1, F19,7,1, and F20,11,1) in period 1, two cross-plant streams (F14,9,2 and F14,10,2) in period 2, and

three cross-plant streams (F2,8,3 and F19,11,3) in period 3. Among them, there are three cross-plant

flows from Plant 1 to Plant 2, one from Plant 1 to Plant 3, and five from Plant 3 to Plant 2.

Similar to POS 1, Plant 1 and Plant 3 are the main source exporters. The sink and source

temperatures appear to be the main factor to forge the IP CCWN symbiosis because the

temperature of sources in one plant could be low enough to be reused in the sinks of other plants.

98

Plant 1

Plant 2

Plant 3

F1,14,1=73.01

F14,9,2=28.57

F14,10,2=131.43

F19,7,1=15.96

F1,9,1=101.36

Fchw Fcw

W

1460.02

913.38

1004.20

70.83

1084.92

1537.77

825.75

F5,11,1=122.96

F19,11,3=75.5

F2,8,3=77.78

Figure 5.5: Multi-period inter-plant CCWN of POS 1 (indicated streams , , and

in kg/h)

99

Plant 1

Plant 2

Plant 3

F2,8,3=77.77

F1,14,1=73.01

F20,11,1=94.24

F14,9,2=28.57

F19,7,1=15.96

F1,9,1=101.36

Fchw Fcw

W

F14,10,2=131.43

1460.02

913.38

1004.20

70.83

1142.09

1574.83

731.51

F5,11,1=65.78

F19,11,3=75.5

Figure 5.6: Multi-period inter-plant CCWN of POS 2 (indicated streams , , and

in kg/h)

5.4.1.4 Step 4: Applying timesharing scheme on the Pareto optimal EIPs

To reduce the number of cross-plant pipelines for further cost savings, timesharing scheme is

implemented in this step to reduce the number of cross-plant pipelines for all time periods. From

POS 1, stream (in Period 3) could be shared with either stream (in Period 1) or

(in Period 1) using a common cross-plant pipeline connecting Plant 1 and Plant 2 according to

Rule 1. Looking at the cross-plant flows between Plant 1 and Plant 3, there is only one cross-

plant pipeline from Plant 1 to Plant 3 (stream ). On the other hand, the possible cross-plant

flows to share the common pipelines between Plant 3 and Plant 2 are: (1) streams (in

Period 2) with (in Period 1);(2) streams (in Period 2) with (in Period 3); (3)

stream (in Period 2) with (in Period 1); and (4) steam (in Period 2) with

(in Period 3). Next, base on Rule 2, common cross-plant pipeline is selected for each set

100

of connecting plant based on the maximum cross-plant stream flow. For example, one of the

common pipelines from Plant 1 to Plant 2 for both stream and sharing in different

periods (in Figure 5.7) is built based on the maximum stream flow . This is to ensure the

pipeline feasibility for all time period. From Rule 3, the cross-plant streams are arranged to share

with the common pipelines in descending order based on the flow rate. The alternative

arrangement for cross-plant streams sharing in the common pipelines without following Rule 3

(as shown in Figure 5.8) would results in a higher investment cost for the pipeline as compared

to Figure 5.7 due to the larger total cross-sectional area. With the timesharing scheme, the

number of cross-plant pipelines in POS 1 is reduced from eight (in Figure 5.5) to five (in Figure

5.7). The cross-plant pipelines are reduced from four to three in Plant 1, seven to four in Plant 2

and five to three in Plant 3. Each participating plant could thus obtain additional cost savings

with lower investment cost for cross-plant pipelines. The total network cost of Plant 1, Plant 2,

and Plant 3 are further reduced to 2.99, 2.15, and 2.19 million US$/y respectively.

101

Plant 1

Plant 2

Plant 3

F5,11,1=122.96

F1,14,1=73.01

F19,7,1=15.96;

F14,9,2=28.57

F1,9,1=101.36;

F2,8,3=77.78

Fchw Fcw

W

F14,10,2=131.43;

F19,11,3=75.5

1460.02

913.38

1004.20

70.83

1084.92

1537.77

825.75

Figure 5.7: Multi-period inter-plant CCWN of POS 1with timesharing scheme (indicated streams

, , and in kg/h)

102

Plant 1

Plant 2

Plant 3

F5,11,1=122.96

F1,14,1=73.01

F14,9,2=28.57;

F19,11,3=75.5

F1,9,1=101.36;

F2,8,3=77.78

Fchw Fcw

W

F19,7,1=15.96;

F14,10,2=131.43

1460.02

913.38

1004.20

70.83

1084.92

1537.77

825.75

Figure 5.8: Alternative sharing of multi-period cross-plant pipelines for POS 1 (indicated streams

, , and in kg/h)

Likewise for POS 2, stream (in Period 3) could be shared with either stream (in

Period 1) or (in Period 1) in a common pipeline between Plant 1 to Plant 2. There is one

cross-plant pipeline from Plant 1 to Plant 3 (stream ) and the possible cross-plant flows

such as streams , , and could be shared with either stream or

in the common pipelines from Plant 3 to Plant 2. Next, total five common cross-plant

pipelines are built as shown by stream flows , , , and (see Figure

5.9). The alternative arrangement for cross-plant stream sharing in the common pipelines without

following Rule 3 is shown in Figure 5.10. Implementing the timesharing scheme reduces the

overall cross-plant pipelines for the multi-period inter-plant CCWN of POS 2 from nine (in

Figure 5.6) to five (in Figure 5.9). The cross-plant pipelines are reduced from four to three in

Plant 1, eight to four in Plant 2 and six to three in Plant 3. The total network cost of Plant 1, Plant

2, and Plant 3 are further reduced to 3.01, 2.38, and 2.14 million US$/y respectively. The same

103

number of cross-plant pipelines is observed in timesharing scheme for both POS 1 (Figure 5.7)

and POS 2 (Figure 5.9). The presented timesharing heuristics in this study ensures maximum

cost savings for all participating plants.

Plant 1

Plant 2

Plant 3

F5,11,1=65.78

F1,14,1=73.01

F19,7,1=15.96;

F14,9,2=28.57

F1,9,1=101.36;

F2,8,3=77.77

Fchw Fcw

W

F20,11,1=94.24;

F14,10,2=131.43;

F19,11,3=75.5

1460.02

913.38

1004.17

58.46

890.22

1730.92

815.29

Figure 5.9: Multi-period inter-plant CCWN POS 2 with timesharing scheme (indicated streams

, , and in kg/h)

104

Plant 1

Plant 2

Plant 3

F5,11,1=65.78;

F2,8,3=77.77

F1,14,1=73.01

F19,7,1=15.96;

F14,9,2=28.57;

F19,11,3=75.5

F1,9,1=101.36;

Fchw Fcw

W

F20,11,1=94.24;

F14,10,2=131.43;

1460.02

913.38

1004.17

58.46

890.22

1730.92

815.29

Figure 5.10: Alternative sharing of multi-period cross-plant pipelines for POS 2 (indicated

streams , , and in kg/h)

5.5 Conclusion

A design methodology for multi-period inter-plant CCWN synthesis has been developed. The

proposed design methodology presents a framework for the optimal CCWN considering network

feasibility for multiple periods, consensus of cooperation among participating plants and fresh

chilled and cooling water reduction. In this work, two Pareto optimal solutions are presented for

the establishment of EIP. The presented timesharing scheme is incorporated in the design

methodology to reduce the network complexity and the investment cost of cross-plant pipelines.

A case study has been solved to demonstrate the design methodology. POS 1 identifies the global

minimum cost for the formation of EIP. Though POS 2 has a slightly higher cost than POS 1, it

ensures the same satisfaction level among the participating plants. The proposed framework of

CCWN design will be helpful in planning the implementation of inter-plant cooling utilities

exchange networks.

105

CHAPTER 6 MULTI-OBJECTIVE OPTIMIZATION OF INTER-PLANT CHILLED

AND COOLING WATER NETWORK USING INTEGRATED ANALYTIC

HIERARCHY PROCESS

The synthesis of the optimum IPCCWN is a complex decision making process as it involves

multiple decision-makers and various network design criteria. This chapter demonstrates the

application of the integrated AHP (IAHP) for the formation of IPCCWN. The criterion

weightings are incorporated in mathematical programming to synthesize optimal IPCCWN. The

proposed IAHP model considers each participating plant‘s preference for the criteria.

6.1 Introduction

A strategy in a game usually consists of several possible moves for players. In the context of

game theory, a mixed strategy is a probability (or weightings) distribution over a set of available

moves (or decision criteria) that the players would rank in order of relative importance (von

Neumann and Morgenstern, 1944). The modeling unit for forming an EIP resembles a

cooperative game, aiming to optimize the group rather than individual benefits. Formation of a

mixed strategy game within an EIP can be presented through the combination of the AHP and

mathematical programming. The AHP (Saaty, 1980) is a structured technique for decomposing

complex decision problems into a hierarchy of simple sub-problems, so as to compare the

alternatives easily based on a selected list of decision criteria. The integration of the AHP with

mathematical programming methods can be classified into two broad categories: multi-attribute

decision making and multi-objective decision making. In the former problem, decision makers

select the best alternative from a number of discrete alternatives using mathematical

programming (Malczewski et al., 1997; Akgunduz et al., 2002). Multi-objective decision making

methods address a design problem which involves the choice among a large set of alternatives

defined by a set of constraints (Zhou et al., 2000; Saaty et al., 2003; Wang et al., 2004).

Such an integrated AHP (IAHP) approach has been widely applied in sectors such as financial,

engineering, industry, and social management. It was adopted for land use planning (Malczewski

et al., 1997), logistic distribution (Korpela and Lehmusvaara, 1999), supply chain design (Zhou

et al., 2000; Wang et al., 2004), production capacity allocation (Wang et al., 2004) and airlift

106

capacity planning (Stannard et al., 2006). Among these works, the IAHP works well in an

interactive problem solving mode for the interest groups to take part in the decision making. It

incorporates preferences of the interest groups on multiple objectives, some of which are

conflicting, into the optimization model to maximize the consensus among them. From this, it

has proven to be a more efficient decision-making tool than the stand-alone AHP (Ho, 2007).

There are many different objectives proposed for planning and evaluation of an EIP, particularly

on the analysis of connectivity among the industries (Dai, 2010; Wang et al., 2013; Zeng et al.,

2013). Other objectives in the social management (Jung et al., 2013), economic (Chew et al.,

2008; Rubio-Castro et al., 2010) and environmental (Bagajewicz and Rodera, 2002; Foo, 2008)

aspects have also been addressed in the literature. However, there is a lack of multi-objective

optimization to study the establishment of EIP according to a review by Boix et al. (2015).

Multi-objective optimization (also known as multi-objective programming, multi-criteria

optimization or Pareto optimization) refers to mathematical optimization problem which takes

into the consideration of more than one objective function to be optimized simultaneously.

Solution that cannot be improved in any of the objectives without degrading a least one of the

other objectives is known as Pareto optimal solution. Pareto optimal solutions from weighted

sum multi-objective optimization are a class of solutions for cooperative games. There usually

exist a representative set of Pareto optimal solutions when solving a multi-objective optimization

problems (Ehrgott, 2005).

According to Miettinen (1999) and Diwekar (2003), multi-objective optimization methods can be

divided into two main groups; generating methods and preference-based methods. The former

methods generate one or more Pareto optimal solutions without any inputs from the decision

makers, while the preference-based methods require the inputs from the decision maker at some

stage(s) in solving the problem. Multi-objective optimizations have been proposed in some

previous works, but all of them are limited to single plants. For example, Erol and Thöming

(2005) considered the total annualized cost and environment impacts simultaneously in

the optimization of resource networks. Vazquez-Castillo et al. (2013) introduced a multi-

objective optimization approach for the synthesis of batch water networks considering the issues

of storing hazardous materials and the network economics. The aforementioned works consider

107

only two objectives in the optimization. For cases with multiple objectives to be considered

simultaneously in the optimization of EIPs, a systematic approach is required to take into

account all the participating plants‘ preferences and benefits.

The challenge addressed in the present work is to consider all the relevant objectives and the

preferences of different industrial players simultaneously in the optimization of an EIP, so as to

ensure that a mutually acceptable compromise solution can be found for implementation. This

chapter present the IAHP approach to the optimum IPCCWN by incorporating AHP weightings

into the multi-objective optimization model. The four main criteria considered in the

establishment of IPCCWN are economic performance, environmental impact, connectivity and

network reliability. The mathematical formulations of these criteria are developed and the

weightings of criteria are incorporated in the IPCCWN model to determine the optimal resource

networks.

6.2 Problem statement

The formal problem statement is as follows. Given are a number of industrial plants

involved in the plan to establish an EIP by synthesizing an IPCCWN among them. Given also is

a set of predefined criteria for the evaluation of the symbiotic network. The criteria

considered for establishing an EIP include economic performance, environmental impact,

connectivity and network reliability. The weightings of these criteria are independently

determined by each participating plant based on their preferences. Each plant has its own set of

predefined limiting data for water sinks and water sources . A process sink is the inlet

stream entering a process operation unit, while a process source is the outlet stream leaving a

unit. For an EIP, sets and can be any streams in the form of mass or energy. Fresh resources

are available from external facilities to supplement each participating plant. The main problem is

to determine the optimal IPCCWN design considering all the participating plants‘ preferences in

decision making.

108

6.3 Steps of IAHP approach to the establishment of an EIP

This section describes the steps to include the preferences of all the participating plants for the

criteria in the establishment of an EIP. In the first step, it is to study the main objectives which

have been proposed in the optimization of EIP networks. Step 2 determines the weightings for all

the criteria using the AHP approach. It is then to optimize all these criteria simultaneously in

Step 3 by incorporating the weightings derived in Step 2 to obtain an optimum EIP.

6.3.1 Step 1: Determining the criteria for the establishment of EIP

Step 1 is to determine the main criteria considered in the optimization of an EIP. In the previous

research works, the establishment of EIPs has been studied in different ways. Some are to

optimize the EIP network from the economic aspect and some perform the analysis of network

connectivity. The following sections present the relevant literature review of the proposed

criteria for the EIP.

6.3.1.1 Economic performance

The economic objective can be easily evaluated through mathematical formulation. Many works

have been found to study the interests of the participating plants involved in an EIP by

optimizing their symbiotic network from an economic point of view. Economics remains the

most often used objective in such optimization problems. Chew et al. (2008) analyzed the

optimal solution to direct and indirect inter-plant water integration through minimization. In

Chew et al.‘s work, the includes fresh water, effluent treatment and cross-plant piping costs.

Rubio-Castro et al. (2010) presented a global optimization approach to the water integration of

EIPs with the objective function of minimizing the combination of the fresh water cost, the

treatment cost and the cross-plant piping cost. These authors later extended their work by

reformulating the objective function as the combination of capital and operational costs for the

retrofit of existing water networks, such as reassignment, capacity expansion and efficiency

enhancement of the treatment units. Wang et al. (2013) proposed a stability analysis of the

industrial symbiosis system based on symbiosis profit and cost. The former is defined as:

(6.1)

109

where the ultimate profit represents the profit for the enterprise to gain in the case of industrial

symbiosis, while the original profit represents the profit for the enterprise to gain without

industrial symbiosis. The symbiosis cost is defined as:

(6.2)

Note that the consumption cost in Eq. 2 includes the costs for raw materials, utilities and waste

treatment. Recently, the cost for water reuse has been taken into account by (Leong et al., 2016)

in the integration of inter-plant chilled and cooling water networks.

6.3.1.2 Environmental impact

One of the main motivations for the establishment of EIPs is to reduce environmental impacts.

Developing symbiotic relationships among the plants within an EIP promotes inter-plant

industrial activities such as resources reuse and recycling. There are various ways proposed to

design an EIP with the objective of minimizing the natural resources consumption. Referring to

the literature, the development of industrial symbiosis with resource conservation objectives was

mainly focused on inter-plant heat (Bagajewicz and Rodera, 2002; Matsuda et al., 2009; Klemes

et al., 2013) and water integration (Foo, 2008; Chew et al., 2010a; Chew et al., 2010b; Aviso,

2014). These works used various process integration techniques such as pinch analysis and

mathematical optimization to target the minimum flow rate of fresh resources fed to the inter-

plant network.

In addition to the context of natural resources conservation, there has been a rising interest in the

evaluation of environmental impacts of the industrial symbiosis. Lim and Park (2010) presented

an economic and environmental feasibility study to demonstrate the advantages of industrial

symbiosis. Regarding the environmental aspect, they measured the total carbon footprint as the

indicator for the evaluation of environmental impacts. Sokka et al. (2011) analyzed the

environmental impact reduction by comparing CO2 emissions of existing industrial symbiosis

centered on an integrated pulp and paper manufacturer to those of a stand-alone system. Block et

al. (2011) studied the CO2 neutrality of Herdersbrug Industrial Park, considering only the CO2

released due to electricity generation. Kantor et al. (2012) assessed the reduction in waste and

110

particular emissions, such as CO2, SOx, NOx and solid wastes, for the evaluation of

environmental impact reduction through the establishment of an EIP

6.3.1.3 Connectivity

Connectivity has commonly used to represent the level of integration among the enterprises in

the form of resources sharing. Hence, knowing the number of connections in the total network

would aid the industrial players in decision making and EIP design. Many works have used

binary variables to represent the existence of inter-plant pipelines (Chew et al., 2008; Aviso et

al., 2011; Rubio-Castro et al., 2011; Leong et al., 2016). The binary variable takes the value of

one if the utility/resource linkage exists, and zero if it does not.

The industrial ecosystem could be developed to make it compatible with the way biological

ecosystems functions (Frosch and Gallopoulos, 1989). Erkman (1997) and Allenby and Cooper

(1994) reported their works on industrial ecosystem from the point of view of natural

ecosystems. Hardy and Graedel (2002) proposed a formula (Eq. 6.3) to determine the

connectivity among the enterprises or factories in an EIP using biological ecology tools. The

species and the food links in the natural are analogous to the enterprises and the cross-plant flows

in an EIP respectively.

(6.3)

where = connectivity of the EIP, = number of links between different enterprises, and

= number of enterprises in the EIP.

Dai (2010) defined the eco-connectance among the enterprises in an EIP as shown in Eq.

6.4. Later, Lee et al. (2015) adopted the eco-connectance defined by Dai (2010) to analyze the

economic performance of an EIP.

(6.4)

where = linkage of observable product flows, = linkage of the observable byproduct

and waste flows.

111

6.3.1.4 Network reliability

An EIP consists of independent but interconnected enterprises co-sharing their resources so as to

improve EIP sustainability. However, the latter would be degraded if the EIP network is not

reliable to retain its function under stress. Hence, knowing the network reliability (Aguilar et al.,

2008) is a prerequisite to ensure the EIP sustainability. To this end, the first pivotal step is to

understand vulnerability (Zeng et al., 2013) and resiliency (Zhu and Ruth, 2013; Chopra and

Khanna, 2014) in industrial symbiosis. Vulnerability is the inherent state of the system‘s

susceptibility to harm from the exposure to stresses associated with environmental, social and

infrastructure changes (Adger, 2006), whereas resiliency describes the ability of a system to

adapt and respond to the adverse incidents within acceptable boundaries (Korhonen and Seager,

2008). Stress such as capacity perturbation due to component units‘ inoperability

(Kasivisvanathan et al., 2013; Benjamin et al., 2014a) in one participating plant may propagate

the impact within the EIP network. Such cascading impacts would result in huge economic

losses and major disruption to the entire system (Santos, 2006).

To cope with these, the participating plants should account for resiliency and vulnerability in EIP

network synthesis. The EIP network is considered reliable with optimal resiliency and

vulnerability found among the participating plants. A common strategy to improve resiliency and

reduce vulnerability is to allow some kind of redundancy (Aguilar et al., 2008). The redundancy

refers to the installation of additional component units in parallel as emergency backup during

the system failure. Other than just engineering for redundancy, investing in the optimal system

diversity by replacing the failure mission is an alternative way to meet the capacity requirement

(Korhonen and Seager, 2008). Also, proper management (such as creating contingency plans as

well as long term plans and generating warnings in time to implement the plans) could reduce or

mitigate external threats and thus enhance the overall resiliency (Allenby and Fink, 2005).

In the work of Haimes (2009), vulnerability and resiliency are expressed and quantified through

the assignment of subjective probabilities. When making a judgment about vulnerability and

resiliency, the uncertainty dimension is unavoidable. Not all types of scenarios can be designed

without incorporating the uncertainty dimension (Aven, 2011). This uncertainty is measured by

probability with reference to a degree of the analysts‘ background knowledge. However, the

112

background knowledge on which the probabilities are based could lead to poor predictions.

Hence, the background knowledge is the integral part as it reflects the degree of belief during the

judgment. Benjamin et al. (2014b) also proposed a criticality analysis technique for EIPs. This

work was later extended to account for dynamic considerations (Benjamin et al., 2015b) and for

multiple disruption scenarios (Benjamin et al., 2015a); it is notable that AHP was used in the

latter work to estimate subjective or Bayesian probabilities of mutually exclusive disruptions.

6.3.2 Step 2: Pairwise comparisons of the criteria (AHP approach)

The carried weight of criterion for plant , wc,k, is the priority derived as referred to the input of

importance, or the preference considered by the participating plant . Taking Plant 1 as an

example, if criterion is relatively more important than criterion , then the weighting of

criterion is higher than that of criterion . The weightings of the criteria can be

determined by creating a pairwise comparison matrix . This matrix is a real matrix,

where is the number of the criteria considered. Each entry of matrix represents the

relative importance of criterion to another criterion . The relative importance between two

criteria in the pairwise comparison matrix is quantified on a scale of 1 to 9 as proposed by Saaty

(1980), as shown in Table 6.1. If , then criterion is more important than criterion ; if

, then criterion is less important than criterion . The entry is equal to 1 if

criterion and have the same importance. The pairwise comparisons of the same criteria is

equal to 1 for all criteria . The entries and should satisfy the constraint given in Eq.

6.5.

(6.5)

The eigenvector of each entry is then divided by the sum of its column in the matrix. The left

eigenvector of each criterion are derived using the geometric mean of each row of the

matrix (Eq. 6.6).

∏ (6.6)

where = number of criteria.

The criteria weights of each plant are then obtained by normalizing the respective left

eigenvector in the matrix (Eq. 6.7).

∑ (6.7)

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The sum of the weights of all considered criteria is equal to 1 as shown in Eq. 6.8.

∑ (6.8)

Table 6.1: Scale of relative importance

Intensity of

importance

Definition Explanation

1 Equal importance Two criteria contribute equally to the

objective

3 Weak importance of one over

another

Experience and judgment slightly

favor one criterion over another

5 Essential or strong importance Experience and judgment strongly

favor one criterion over another

7 Demonstrated importance A criterion is strongly favored and

its dominance demonstrated in

practice

9 Absolute importance When compromise is needed

2, 4, 6, 8 Intermediate values between the two

adjacent judgments

Reciprocals of

above nonzero If criterion has one of the above

nonzero numbers assigned to it when

compared with criterion . Then has the reciprocal value when

compared with

6.3.3 Step 3: Embedding criteria weightings in the EIP optimization model - IAHP

This paper proposes the integration of the AHP with mathematical programming for the

establishment of EIPs. Figure 6.1 illustrates the hierarchical representation of the decision-

making problem in the proposed IAHP. Unlike the conventional stand-alone AHP, the proposed

IAHP does not create alternatives. The goal is to synthesize an optimal EIP network considering

all the participating plants‘ preferences. The efficiency ec,k of criterion achieved by plant in

the optimal EIP network is determined by the improvement gained from the base case that

without implementing the EIP. Ranking rc,k is the criterion score achieved by plant in the

optimal EIP network. A simple plot of ranking rc,k versus the respective criterion efficiency ec,k

114

can establish the mathematical relationship between the two variables. This mathematical

relationship is then embedded in the optimization of EIP models. The total score achieved by

plant in the optimal EIP network is given in Eq. 6.9.

∑ (6.9)

Figure 6.1: Decision hierarchy for the establishment of EIP using the proposed IAHP

6.4 Case study

The case study adapted from chapter 4 (Table 4.5) is used to demonstrate the proposed

methodology, considering three plants (Plant 1, Plant 2, and Plant 3) for different entities for

building an EIP through the synthesis of an IPCCWN. The superstructure-based IPCCWN

mathematical models developed in chapter 4, subject to water balance constraints (Eqs. 4.4-4.5);

energy balance constraints (Eq. 4.6); cost constraints (Eqs. 4.7-4.15); are adopted in this work

(see Appendix 4). The overall superstructure includes the possibilities for all the participating

plants‘ sources to be reused within internal and external (cross-plant) sinks.

…

Criteria

:

Goal:

… Participating

plant 𝒌𝟐

Participating

plant

𝒌𝑵𝒑𝒍𝒂𝒏𝒕

Participating

plant (𝒌𝟏

…

Criterion

(𝑪𝟏)

𝒘𝟏 𝟏,

𝒘𝟏 𝟐,…,

𝒘𝟏 𝒌𝑵𝒑𝒍𝒂𝒏𝒕

Criterion

(𝑪𝟐)

𝒘𝟐 𝟏,

𝒘𝟐 𝟐,…,

𝒘𝟐 𝒌𝑵𝒑𝒍𝒂𝒏𝒕

Criterion

(𝑪𝟑)

𝒘𝟑 𝟏,

𝒘𝟑 𝟐,…,

𝒘𝟑 𝒌𝑵𝒑𝒍𝒂𝒏𝒕

Criterion

(𝑪𝑵𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏)

𝒘𝑵𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 𝟏,

𝒘𝑵𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 𝟐,

…,

𝒘𝑵𝒄𝒓𝒊𝒕𝒆𝒓𝒊𝒐𝒏 𝒌𝑵𝒑𝒍𝒂𝒏𝒕

Establishment of EIP

115

6.4.1 The mathematical formulation of the criteria

Figure 6.2 shows the criteria to be considered simultaneously in the optimization an EIP

network. The main criteria proposed for EIP establishment include: economic performance ,

environmental impact , connectivity , and network reliability .The following

sections present the mathematical formulation of the proposed criteria embedded in the

optimization model.

Figure 6.2: Main criteria proposed for the establishment of EIP

6.4.1.1 Criterion – Economic performance

The incurred cost for an IPCCWN consists of the costs for return streams, fresh chilled and

cooling water, reused streams and inter-plant pipelines. The formulation for the of

participating plant with EIP implementation is adapted from chapter 4 (Eq. 4.7-4.15).

The economic performance of participating plant for joining the IPCCWN is the

increase/decrease from the base case without EIP implementation divided by the base case ,

as given in Eq. 6.10.

(6.10)

where = total annualized cost of participating plant without EIP implementation.

The for Plant 1, Plant 2 and Plant 3 are determined to be $1,712,637/y, $835,333/y, and

$439,532/y respectively based on the optimization results obtained from chapter 4. The

constraint for the economic performances for all the participating plants is given in Eq. 6.11.

This constraint ensures that the of each participating plant with EIP implementation would

be at least the same as that in the base case from chapter 4. Table 6.2 shows the rankings on a

Criteria:

Goal:

Economic

performance

Environmenta

l impact

Connectivity

Network

reliability

Establishment of EIP

116

scale of 1 to 9 based on the economic performances for all the participating

plants, calculated using Eq. 6.10. The range of is referred to the of all the

participating plants obtained in the base case and preliminary IPCCWN from chapter 4. The

corresponding linear equation by plotting the rankings against the economic performances

is given in Eq. 6.12.

(6.11)

(6.12)

Table 6.2: Rankings of economic performances for participating plants

Ranking,

Economic performance,

1 0.0000

2 0.0375

3 0.0750

4 0.1125

5 0.1500

6 0.1875

7 0.2250

8 0.2625

9 0.3000

6.4.1.2 Criterion – Environmental impact

The environmental impact is evaluated based on the CO2 footprint due to the production of fresh

chilled and cooling water. The energy consumption for producing fresh chilled and

cooling water ( in participating plant is given by Eq. 6.13 and 6.14 respectively. The

total carbon footprint of participating plant with implementing EIP is calculated using

Eq. 6.15.The carbon footprint of electricity for producing fresh chilled and cooling water is

estimated at 0.662 kg CO2/kWh (Tjan et al., 2010). Note that, this carbon intensity is determined

based on the current Malaysian power generation mix (TNB, 2014) that consists of natural gas,

coal, hydropower and oil, with the contributions of 50, 35, 14 and 1%, respectively.

(6.13)

(6.14)

(6.15)

117

where = fresh chilled water consumption in plant , = fresh cooling water

consumption in plant , = specific heat capacity of water, = difference between final

temperature and initial temperature of water, = coefficient of performance of the chiller,

= coefficient of performance of the cooling tower, yearly operating time.

The environmental impact reduction of participating plant for joining the IPCCWN is

the difference of the total carbon footprint increase/decrease from the base case without EIP

implementation divided by the total carbon footprint of the base case, as shown in Eq. 6.16.

(6.16)

where = total carbon footprint of participating plant with implementing EIP, =

total carbon footprint of participating plant without implementing EIP.

The for Plant 1, Plant 2, and Plant 3 are 7.85 t/y, 2.54 t/y, and 2.02 t/y respectively based

on the optimization results from chapter 4. Table 6.3 shows the ranking on a scale of 1 to 9

based on the environmental impact reduction ) for all the participating plants. The

range of is referred to the carbon footprint of fresh chilled and cooling water consumption

of all the participating plants obtained in the base case and preliminary IPCCWN from chapter 4.

The linear equation by plotting the rankings against the environmental impact reduction

is given in Eq. 6.17.

(6.17)

Table 6.3: Rankings of environmental impact for participating plants

Ranking,

Environmental impact,

1 0.00

2 0.05

3 0.10

4 0.15

5 0.20

6 0.25

7 0.30

8 0.35

9 0.40

118

6.4.1.3 Criterion – Connectivity

The connectivity of an IPCCWN is evaluated based on the number of pipelines formed through

the co-sharing of resources between two participating plants. As an exporter of sources to

plant , the number of pipelines of participating plant is calculated using Eq. 6.18.

As a receiver of the sources from plant , the number of pipelines of participating plant

is calculated using Eq. 6.19. The total number of cross-plant pipelines of participating

plant is then given by Eq. 6.20.

∑ ∑ (6.18)

∑ ∑ (6.19)

∑ ∑ (6.20)

where = binary variable denoting the existence of cross-plant pipelines.

The connectivity of participating plant for joining the IPCCWN is modified based on

Eqs. 6.3 and 6.4. In Eq. 6.21, the connectivity of participating plant is equal to the

total number of cross-plant pipelines in plant divided by the maximum number of

possible cross-plant pipelines in plant .

∑ ∑ , (6.21)

where = number of process sources, and = number of process sink.

Table 6.4 shows the ranking on a scale of 1 to 9 based on the connectivity ) for all

the participating plants, calculated using Eq. 6.21. The range of connectivity is determined from

the preliminary IPCCWN derived from chapter 4. The linear equation by plotting the rankings

against the connectivity ) is given in Eq. 6.22.

(6.22)

Table 6.4: Rankings of connectivity for participating plants

Ranking,

Connectivity,

1 0.050

2 0.045

3 0.040

4 0.035

5 0.030

119

6 0.025

7 0.020

8 0.015

9 0.010

6.4.1.4 Criterion – Network reliability

The EIP network reliability for participating plant is evaluated using the R index

defined in Eq. 6.23. This index is a function of the cross-plant flow rate to plant from

other plants . Parameters and reflect the participating plant‘s vulnerability and

resiliency, respectively; represents the susceptibility of plant to the EIP network failure,

whereas is the flow rate tolerance of plant for receiving sources from other plants .

∑ ∑

(6.23)

The values for Plant 1, Plant 2 and Plant 3 are 0.37, 0.42, and 0.87 respectively. These are

subjective probabilities based on the background knowledge of the participating plants‘ analysts,

expressing their uncertainty dimension to the plant vulnerability. Such subjectivity judgment

determines the susceptibility of the participating plants to system failure as referred to the plants‘

redundancy, contingency plan and backup. The values for each link between the plants are

shown in Table 6.5. These tolerances of flow rates indirectly reflect the participating plant‘s

resiliency. A plant is said to have high resiliency when the flow rate tolerance for receiving

sources from other plants is high. Note that, flow rate tolerance seems high differently for every

plant. The flow rate tolerance seems high with the flow rate that is close to the plant cooling

capacity demand. If the EIP network capacity perturbation occurs, a plant with high resiliency

would still be able to meet its own capacity requirement because of its high tolerance of cross-

plant flow rate. The reliability of participating plant for joining the inter-plant CCWN

is determined using Eq. 6.24.

∑ (6.24)

Table 6.6 shows the ranking on a scale of 1 to 9 ( ) based on the network reliability

for all the participating plants. The linear equation by plotting the rankings against the

network reliability is given in Eq. 6.25.

(6.25)

120

Table 6.5: The value (indicated value in kg/h)

Plant 1 Plant 2 Plant 3

Plant 1 - = 167.5 = 83.7

Plant 2 = 239.2 - = 83.7

Plant 3 = 95.7 = 119.6 -

Table 6.6: Rankings of network reliability for participating plants

Ranking,

Network reliability,

1 1.000

2 0.875

3 0.750

4 0.625

5 0.500

6 0.375

7 0.250

8 0.125

9 0.000

6.4.2 Scenario 1 (Different weighting for the criteria)

Scenario 1 considers different weightings for the criteria to establish an EIP among the

participating plants. The weightings of the criteria are determined based on the preferences of the

individual plants‘ stakeholders. Two cases, termed Scenarios 1(a) and 1(b), are analyzed,

considering different objective functions for EIP formation.

(a) Composite maximum overall total scores

Scenario 1(a) targets the global maximum score achieved by the participating plants to form the

EIP. The objective function is to maximize the overall total scores achieved by the participating

plants ( as given in Eq. 6.26.

Max ∑ (6.26)

The pairwise comparison matrixes of the criteria considered for EIP establishment for Plant 1,

Plant 2 and Plant 3 are shown in Tables 6.7-6.9 respectively. Each entry in the pairwise

comparison matrix is determined using the scale of relative importance given in Table 6.1. All

121

entries in the pairwise comparison should satisfy the constraint given in Eq. 6.5, and the final

weightings of the criteria are determined using Eqs. 6.6 and 6.7. Note that the sum of the

weightings of the criteria for each participating plant is equal to 1 as stated in Eq. 6.8. From

Tables 6.7-6.9, the economic performance appears to be the most important criterion for all

the participating plants to be involved in the EIP, followed by the environmental impact .

Table 6.7: Pairwise comparison matrix of the criteria for the establishment of EIP based on Plant

1

Criteria Economic

performance

Environmental

impact

Connectivity

Network

reliability

Weighting

Economic

performance

1 3 4 2 0.482

Environmental

impact

0.33 1 2 2 0.234

Connectivity

0.25 0.5 1 1 0.130

Network

reliability

0.50 0.5 1 1 0.154


2

Criteria Economic

performance

Environmental

impact

Connectivity

Network

reliability

Weighting

Economic

performance

1 3 4 3 0.509

Environmental

impact

0.33 1 2 3 0.247

Connectivity

0.25 0.5 1 1 0.124

Network

reliability

0.33 0.33 1 1 0.120

122


3

Criteria Economic

performance

Environmental

impact

Connectivity

Network

reliability

Weighting

Economic

performance

1 5 7 6 0.635

Environmental

impact

0.2 1 4 3 0.208

Connectivity

0.149 0.25 1 0.50 0.061

Network

reliability

0.167 0.33 2 1 0.096

Figure 6.3 shows the corresponding configuration of the IPCCWN. Four cross-plant pipelines

(bolded line) are used: one from Plant 1 to Plant 2, one from Plant 1 to Plant 3 and two from

Plant 3 to Plant 2. It is found that, Plant 1 and Plant 3 are the source exporters while Plant 2 and

Plant 3 are the source receivers. Plant 2 does not export any sources to other plants, and instead it

receives a total cross-plant flow rate of 232.1 kg/h from Plant 1 and Plant 3. Plant 3 receives

cross-plant flow rate of 73 kg/h from Plant 1.The fresh chilled water consumption is increased

from 610.9 (base case) to 613.6 kg/h in Plant 1, decreased from 179.4 (base case) to 167 kg/h in

Plant 2 and decreased from 157.8 (base case) to 119.8 kg/h in Plant 3. The overall fresh chilled

water consumption for the establishment of IPCCWN is reduced from 947.1 to 900.4 kg/h (a

4.9% reduction). Though the fresh chilled water consumption in Plant 1 increases slightly from

its base case, it could gain the cost saving through the revenue by selling its sources to other

plants. On the other hand, all the participating plants do not import fresh cooling water as shown

in Figure 6.3. The overall fresh cooling water is reduced from 279.7 (base case) to 0 kg/h (a

100% reduction). Table 6.10 shows the scores of each participating plants using the proposed

IAHP. Each plant achieves different total score in the EIP with the global maximum overall total

scores objective function. Plant 3 has the highest total score of 0.814, followed by Plant 1 (0.543)

and Plant 2 (0.356). Among all the participating plants, Plant 3 achieves the highest score of

0.579 in the economic performance criterion with a weighting of 0.635. Since Plant 1 does not

receive any sources from the other plants as shown in Figure 6.3, it can avoid the uncertainties of

123

receiving sources from other plants, such as plant shut down and the inconsistency in source flow

rates. Hence, Plant 1 achieves the full score of 0.154 in the network reliability. Though Plant 1

and Plant 2 do not achieve as high scores in economic performance as Plant 3, they still gain

extra cost savings through the establishment of the EIP.

124

Figure 6.3: IPCCWN for Scenario 1(a)

125

Table 6.10: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 1(a)

Criterion Criteria score


Economic performance 0.237 0.132 0.579

Environmental impact 0.031 0.118 0.137

Connectivity 0.121 0.098 0.029

Network reliability 0.154 0.008 0.068

Total 0.543 0.356 0.814

(b) Max-min total score

Scenario 1(b) subjects to the objective function of maximizing the total score of all the

participating plants (Eq. 6.27) while ensuring the least total score of the participating plants

is maximized (Eq. 6.28). In other words, is solved such that each participating plant achieves

individual total score ) to at least the total score . This max-min strategy is to ensure fair

distribution of benefits for EIP formation.

Max (6.27)

(6.28)

The pairwise comparison matrixes for the criteria are shown in Tables 6.7-6.9 based on the

subjective judgment from Plant 1, Plant 2 and Plant 3 respectively.

Figure 6.4 shows the optimal EIP configuration obtained using the max-min total score strategy.

Compared to the result for Scenario 1(a) (see Figure 6.3), more cross-plant pipelines are

observed in Scenario 1(b) (Figure 6.4). There are six cross-plant pipelines in total: two from

Plant 1 to Plant 2, one from Plant 1 to Plant 3, two from Plant 3 to Plant 1 and one from Plant 3

to Plant 2. As in Scenario 1(a), Plant 2 does not export any sources to other plants. Plant 2

receives the highest cross-plant flow rate of 226.2 kg/h followed by Plant 3 (74.6 kg/h) and Plant

1 (34.5 kg/h). Although the overall fresh chilled and cooling water consumption in this scenario

are reduced by 4.3% and 95.5% respectively compared to the base case, it is slightly higher than

Scenario 1(a). The sources and sinks allocation in this scenario as shown in Figure 6.4 is the

optimum solution that maximize the score of the plant that achieves the lowest in the

establishment of IPCCWN and ensure all plants equally achieve the same score. Table 6.11

shows the criteria scores of all the participating plants for Scenario 1(b). It can be seen that the

126

three participating plants achieve the same total score of 0.444. The economic performance

improves in both Plant 1 and Plant 2 and decreases in Plant 3 as compared to Scenario 1(a).

127

Figure 6.4: IPCCWN for Scenario 1(b)

128

Table 6.11: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 1(b)







Total 0.444 0.444 0.444

6.4.3 Scenario 2 (Same weighting for the criteria)

This scenario considers the same weighting for the criteria. This is to determine if the weighting

of the criteria affects the configuration of the IPCCWN in the EIP. Scenarios 2(a) and 2(b)

present the global maximum and the max-min scores in the IPCCWNs.

(a) Composite maximum overall total scores

Scenario 2(a) uses the same objective function as in Scenario 1(a) (Eq. 6.26). The same

weighting of 0.25 is used for all the criteria in Scenario 2(a). Figure 6.5 shows the IPCCWN

configuration in this scenario. There are three cross-plant pipelines: two from Plant 1 to Plant 2

and one from Plant 1 to Plant 3. From Figure 6.5, Plant 1 is the only source exporter while Plant

2 and Plant 3 act as source receivers. Plant 2 receives cross-plant flow rate of 211.8 kg/h, while

Plant 3 receives 53.6 kg/h. The overall fresh chilled and cooling water consumption are reduced

by 4.5% and 97.2% respectively. Table 6.12 shows the criteria scores achieved by the

participating plants. In this scenario, Plant 3 achieves the highest total score of 0.680, followed

by Plant 1 (0.639) and Plant 2 (0.55). It is observed that, changing the weighting of criteria

would affect the IPCCWN configuration as well as the criteria score. In contrast to Scenario 1(a),

this scenario results in less cross-plant pipelines. Four cross-plant pipelines are used in Scenario

1(a) (see Figure 6.3), while three in Scenario 2(a) as shown in Figure 6.5. Recalling that Scenario

1(a) deems economic performance to be the most important criterion, all the criteria are equally

important in this scenario with the same weighting. The optimization model seeks the solution

that gives the optimal criteria score achieved by the participating plants and thus suggests fewer

cross-plant pipelines in this scenario. This is mainly due to the increased weighting of criteria

such as connectivity and network reliability and the decreased weighting of economic

performance.

129

Figure 6.5: IPCCWN for Scenario 2(a)

130

Table 6.12: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 2(a)







Total 0.639 0.550 0.680

(b)Max-min score

Scenario 2(b) uses the same objective function as in Scenario 1(b) (Eqs. 6.27 and 6.28). The

resulting IPCCWN configuration is shown in Figure 6.6. Three cross-plant pipelines are used:

two from Plant 1 to Plant 2 and one from Plant 3 to Plant 1. From Figure 6.6, Plant 1 acts as both

source exporter and receiver. It exports sources with flow rate of 124.8 kg/h in total to Plant 2

and receive source of 21.2 kg/h from Plant 3. The fresh chilled water consumption is slightly

reduced by 0.1%, while fresh cooling water consumption reduced by 100%. With the same

weighting for all the criteria, fewer cross-plant pipelines are also found in this scenario as

compared to Scenario 1(b). Table 6.13 shows the criteria scores achieved by all the participating

plants in this scenario. In contrast to Scenario 1(b), each participating plant achieved the same

total score of 0.567. Based on the rankings of connectivity (Table 6.4) and network reliability

(Table 6.6), fewer cross-plant pipelines and lower cross-plant flow rates are favoured by the

participating plants. The EIP network is more reliable with lower cross-plant flow rates because

reducing the interdependency in the EIP network could avoid the cascading effect of capacity

perturbation. Therefore, increasing the weightings of criteria for both connectivity and network

reliability in the optimization model of the EIP will reduce the number of cross-plant pipelines

(Figure 6.6).

131

Figure 6.6: Inter-plant CCWN for Scenario 2(b)

132

Table 6.13: The criteria score for Plant 1, Plant 2 and Plant 3 in Scenario 2(b)







Total 0.567 0.567 0.567

6.5 Conclusion

An IAHP approach to multi-objective optimization of EIPs has been developed in this paper. The

proposed approach is beneficial to the decision makers of each plant in that the process of

generating alternative network designs can be eliminated. According to the results for the

IPCCWN case study, each participating plant could gain extra cost savings through collaboration

in an EIP. Also, the implementation of an EIP could reduce the environmental impacts as

compared to the case of stand-alone individual plants. This paper has considered different

scenarios in the optimization of EIP networks. In the first scenario of maximizing the overall

total scores, it is observed that each participating plant achieves different individual total score

showing unequal benefits distribution for the establishment of EIP. Though the max-min strategy

as presented in the second scenario achieves lower overall total score than the first scenario, it

gives the solution that takes into consideration the benefits for all the participating plants equally.

On the other hand, this approach includes all participating plant‘s preference for the criteria in

the EIP network optimization. The preferences of the participating plants for joining the EIP are

reflected by the weightings of criteria and affect the EIP network configuration. Future work will

consider extending the IAHP approach to other integrated energy systems such as bio-refinery

dealing with multiple forms of material and energy.

133

CHAPTER 7 FUTURE RECOMMENDATION

Chilled water system using electrically-driven vapor-compression chillers consume a significant

amount of electric power than absorption chiller. Several research works have shown that

absorption chiller is the best heat recovery units to satisfy cooling demand in large scale

industries where waste heat is available. Kalinowski et al. (2009) analyzed the energy reduction

by using waste heat powered absorption refrigeration system in place of the conventional vapor-

compression refrigeration system for LNG recovery process. Trigeneration, also known as

combined cooling, heat and power (CCHP), is a process that use prime energy resource (e.g. fuel

oil, natural gas etc) and some of the heat produced by a cogeneration plant to generate chilled

water for cooling purpose. Ghaebi et al. (2012) developed R-curve to target the trigeneration

potential by integrating absorption chiller in a total CHP site. On the other hand, absorption

refrigeration system is linked to the combined heat and power (CHP) so as to utilize the waste

heat for heating and/or cooling, thereby realizing the cascade application of prime energy

resource. Popli et al. (2013) suggested the recovery of exhaust gas from gas turbine using waste

heat powered absorption chiller for gas turbine compressor inlet air cooling. Thus, future works

should explore further energy savings through integration of absorption refrigeration system in

chilled water network. Specifically, lithium bromide absorption chiller (Shuangliang, 2013) is

the best heat recovery units in the trigeneration system. It can fully utilize the low potential heat

energy, such as flue gas or waste hot water, to efficiently improve an integrated energy system.

High temperature flue gas can be recovered in trigeneration system using lithium bromide

absorption chiller with turbo generators. For trigeneration installation with internal combustion

engine as drive, flue gas and hot water can be recovered for chilled water regeneration.

134

NOMENCLATURE

Sets

{ } is set of criteria

{ is set of alternative IPCCWN

{ }is a set of process sources

{ | is located in plant } is set of process sources located in plant

{ }is a set of process sinks

{ | is located in plant } is set of process sinks located in plant

{ }is a set of plants

is set of industrial operational time period

| is operational time period of plant is set of operational time period of

plant

Parameters

index of optimism

parameter to fix the lower and upper limits of the water mass flow rate for

determining the existence of pipelines

parameter to fix the lower and upper limits of the inlet water mass flow rate for

determining the existence of cooling tower

parameter to fix the lower and upper limits of the cooling capacity for determining

the existence of chiller

coefficient of cooling tower performance, dimensionless

percent loss of circulating water in cooling tower

parameter to fix the

ratio

efficiency

parameter to fix the lower and upper limits of temperature

water density

annualizing factor

135

initial cost of chiller

cost of chiller related to cooling capacity

cost of cooling tower related to air flow rate

initial cost of cooling tower

cost of cooling tower related to fill volume

unit cost of electricity

unit cost of make-up water

lower limit of the cross-plant stream flow rate

upper limit of the cross-plant stream flow rate

yearly operating time

cycle of concentration, dimensionless

chiller‘s coefficient of performance, dimensionless

specific heat of water

water flow rate requirement of sink

available water flow rate of source i

height of chiller

fill height of cooling tower

distance for all pipelines between two participating plants

distance between the plant and the centralized hub

operational time for period , hr/year

lower limit of total network cost for plant k (desired costs) in the IPCCWN

upper limit of total networtk cost for plant k in the IPCCWN

total network cost of participating plant without EIP implementation

temperature of fresh chilled water

temperature of fresh cooling water

temperature requirement of sink j

temperature of source i

inlet water temperature of cooling tower

outlet water temperature of cooling tower

inlet ambient wet bulb temperature of cooling tower

136

outlet ambient wet bulb temperature of cooling tower

acceleration due to gravity

fixed cost parameter for building one pipeline

fixed cost parameter based on the cross sectional area of pipelines

ranking of criterion for plant

unit cost of fresh chilled water

unit cost of fresh cooling water

unit cost of return stream

unit cost of reused water

stream velocity

mass-fraction humidity of air entering cooling tower

mass-fraction humidity of air leaving cooling tower

Continuous Variables

overall satisfaction level

satisfaction level of plant k

fuzzy relative importance of each pair criteria

entry of matrix representing the relative importance of criteria to another criteria

area of cooling tower mass transfer

lower values of fuzzy synthetic values

medium values of fuzzy synthetic values

upper values of fuzzy synthetic values

investment cost of chiller

investment cost of centralized chiller

investment cost of cooling tower

investment cost of centralized cooling tower

investment cost of the pipeline between the plant and the centralized chiller

investment cost of the pipeline between the plant and the centralized cooling tower

fresh chilled and cooling water cost in plant k

137

efficiency of criterion for plant

cost associated with reused water in plant

flow rate of water from source to sink

air mass flow rate in the cooling tower

mass flow rate of blow-down water in the cooling tower

mass flow rate of blow-down water in the centralized cooling tower

mass flow rate of water in the chiller

mass flow rate of regenerated chilled water from an individual plant's chiller

mass flow rate of water in the centralized chiller

mass flow rate of regenerated chilled water from the centralized chiller

mass flow rate of water in the centralized cooling tower

mass flow rate of regenerated cooling water from the centralized cooling tower

mass flow rate of water in the cooling tower

mass flow rate of regenerated cooling water from an individual plant's cooling

tower

mass flow rate of evaporated water in the cooling tower

make-up water flow rate of the cooling tower

make-up water flow rate of the centralized cooling tower

mass flow rate of a free-cooling stream

mass flow rate of a free-cooling stream from the centralized cooling tower to the

centralized chiller

final score of alternative IPCCWN

mass flow rate of drifted water in the cooling tower

mass flow rate of a source sent to an individual plant's chiller

mass flow rate of a source sent to the centralized chiller

mass flow rate of a source sent to the centralized cooling tower

mass flow rate of a source sent to an individual plant's cooling tower

eigenvector of criterion

integral value of

mass transfer coefficient of the cooling tower

138

lower value of TFN

modal value of TFN

triangular fuzzy number of criteria over criteria

Merkel‘s number of the cooling tower, dimensionless

number of pipelines of participating plant as an exporter of sources to plant

number of pipelines of participating plant as a receiver of sources from plant

operating cost

power consumption

power consumption for producing fresh chilled

power consumption for producing fresh cooling water

annualized inter-plant piping cost of plant k as exporter

annualized inter-plant piping cost of plant k as receiver

fuzzy synthetic values with respect to criteria

index for evaluating network reliability between plant and plant

vulnerability of participating plant

resiliency of participating plant

cost associated with return stream in plant k

total score achieved by plant

criteria score of alternative IPCCWN

total annual cost

total annual power consumption

total carbon footprint of participating plant with implementing EIP

total carbon footprint of participating plant without implementing EIP

overall cost associated with reused streams

total annualized cost of plant k

total number of cross-plant pipelines of participating plant

cooling capacity of the chiller

overall inter-plant piping cost of plant

overall score of the participating plant

temperature of regenerated chilled water supplied by an individual plant's chiller,

139

temperature of regenerated chilled water supplied by the centralized chiller

temperature of regenerated cooling water supplied by the centralized cooling tower

temperature of regenerated cooling water supplied by an individual plant's cooling

tower

inlet water temperature of an individual plant's chiller

inlet water temperature of the centralized chiller

inlet water temperature of the centralized cooling tower

inlet water temperature of an individual plant's cooling tower

upper value of TFN

active volume

flow rate of return stream from source i

final average weight of criterion

Binary variables

binary variable to determine the existence of an individual plant's chiller

binary variable to determine the existence of a centralized chiller

binary variable to determine the existence of an individual plant's cooling tower

binary variable to determine the existence of a centralized cooling tower

binary variable to determine the existence of a pipeline from the centralized chiller

to plant

binary variable to determine the existence of a pipeline from the centralized

cooling tower to plant

binary variables for cross-plant pipelines

binary variable to determine the existence of a pipeline from plant to the

centralized chiller

binary variable to determine the existence of a pipeline from plant to the

centralized cooling tower

140

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APPENDICE

Appendix 1: LINGO ver13 mathematical modelling codes in chapter 3

Appendix 1(a): LINGO ver13 mathematical modelling codes for Base scenario (Example 1)

MIN = TAC;

!============================================================================;

! SPECIFYING THE SOURCE FLOWRATES;

! SOURCE FROM PLANT A;

SOURCEA1=1050; SOURCEA2=1176; SOURCEA3=1428; SOURCEA4=336; SOURCEA5=840;

SOURCEA6=210;

! SOURCE FROM PLANT B;

SOURCEB1=420; SOURCEB2=672; SOURCEB3=1176; SOURCEB4=966;

! SOURCE FROM PLANT C;

SOURCEC1=840; SOURCEC2=420; SOURCEC3=2016;

! SOURCE FLOWRATE BALANCE;

! PLANT A SOURCES FLOW RATE BALANCE;

A1A1 + A1A2 + A1A3 + A1A4 + WWA1CWA + WWA1CHA = SOURCEA1;






! PLANT B SOURCES FLOW RATE BALANCE;

B1B1 + B1B2 + B1B3 + WWB1CWB + WWB1CHB = SOURCEB1;




! PLANT C SOURCES FLOW RATE BALANCE;

C1C1 + C1C2 + WWC1CWC + WWC1CHC = SOURCEC1;



!============================================================================;

! SPECIFYING THE SINK FLOWRATES;

! SINK FROM PLANT A;

SINKA1=1512; SINKA2=1680; SINKA3=504; SINKA4=1344;

! SINK FROM PLANT B;

SINKB1=882; SINKB2=1092; SINKB3=1260;

! SINK FROM PLANT C;

SINKC1=1680; SINKC2=1596;

! SINK FLOWRATE BALANCE;

! SINKS FLOW RATE BALANCE FOR PLANT A;

CWA_A1 + CHA_A1 + A1A1 + A2A1 + A3A1 + A4A1 + A5A1 + A6A1 = SINKA1;




! SINK FLOW RATE BALANCE FOR PLANT B;

CWB_B1 + CHB_B1 + B1B1 + B2B1 + B3B1 + B4B1 = SINKB1;

151



! SINK FLOW RATE BALANCE FOR PLANT C;

CWC_C1 + CHC_C1 + C1C1 + C2C1 +C3C1 = SINKC1;


!============================================================================;

! THERMAL BALANCE;

! TEMPERATURE OF SINK AND SOURCE OF PLANT A;

T_SO_A1 = 11; T_SO_A2 = 20; T_SO_A3 = 35; T_SO_A4 = 58; T_SO_A5 = 65; T_SO_A6

= 70;

T_SI_A1 = 5; T_SI_A2 = 12; T_SI_A3 = 20; T_SI_A4 = 25;

! TEMPERATURE OF SINK AND SOURCE OF PLANT B;

T_SO_B1 = 10; T_SO_B2 = 28; T_SO_B3 = 48; T_SO_B4 = 65;

T_SI_B1 = 5; T_SI_B2 = 17; T_SI_B3 = 24;

! TEMPERATURE OF SINK AND SOURCE OF PLANT C;

T_SO_C1 = 12; T_SO_C2 = 35; T_SO_C3 = 45;

T_SI_C1 = 8; T_SI_C2 = 16;

! THERMAL BALANCE FOR PLANT A;

CWA_A1*T_CW_A + CHA_A1*T_CH_A + A1A1*T_SO_A1 + A2A1*T_SO_A2 + A3A1*T_SO_A3

+ A4A1*T_SO_A4 + A5A1*T_SO_A5 + A6A1*T_SO_A6 = SINKA1*T_SI_A1;







! THERMAL BALANCE FOR PLANT B;

CWB_B1*T_CW_B + CHB_B1*T_CH_B + B1B1*T_SO_B1 + B2B1*T_SO_B2 + B3B1*T_SO_B3 +

B4B1*T_SO_B4 = SINKB1*T_SI_B1;





! THERMAL BALANCE FOR PLANT C;

CWC_C1*T_CW_C + CHC_C1*T_CH_C + C1C1*T_SO_C1 + C2C1*T_SO_C2 +C3C1*T_SO_C3=

SINKC1*T_SI_C1;


SINKC2*T_SI_C2;

!============================================================================;

! FRESH GENERATION;

! FRESH BALANCE IN PLANT A;

WWA1CWA + WWA2CWA + WWA3CWA + WWA4CWA + WWA5CWA + WWA6CWA = CW_A_FLOW_RATE;

CW_A_FLOW_RATE = CWA_A1 + CWA_A2 + CWA_A3 + CWA_A4;

WWA1CHA + WWA2CHA + WWA3CHA + WWA4CHA + WWA5CHA + WWA6CHA = CH_A_FLOW_RATE;

CH_A_FLOW_RATE = CHA_A1 + CHA_A2 + CHA_A3 + CHA_A4;

! FRESH BALANCE IN PLANT B;

WWB1CWB + WWB2CWB + WWB3CWB + WWB4CWB = CW_B_FLOW_RATE;

CW_B_FLOW_RATE = CWB_B1 + CWB_B2 + CWB_B3;

152

WWB1CHB + WWB2CHB + WWB3CHB + WWB4CHB = CH_B_FLOW_RATE;

CH_B_FLOW_RATE = CHB_B1 + CHB_B2 + CHB_B3;

! FRESH BALANCE IN PLANT C;

WWC1CWC + WWC2CWC + WWC3CWC = CW_C_FLOW_RATE;

CW_C_FLOW_RATE = CWC_C1 + CWC_C2;

WWC1CHC + WWC2CHC + WWC3CHC = CH_C_FLOW_RATE;

CH_C_FLOW_RATE = CHC_C1 + CHC_C2;

!============================================================================;

! TEMPERATURE INLET TO COOLING TOWER;

TIN_CWA = (WWA1CWA*T_SO_A1 + WWA2CWA*T_SO_A2 + WWA3CWA*T_SO_A3 +

WWA4CWA*T_SO_A4 + WWA5CWA*T_SO_A5 + WWA6CWA*T_SO_A6)/CW_A_FLOW_RATE;

TIN_CWA >= 35; TIN_CWA <= 75;

TIN_CWB = (WWB1CWB*T_SO_B1 + WWB2CWB*T_SO_B2 + WWB3CWB*T_SO_B3 +

WWB4CWB*T_SO_B4)/CW_B_FLOW_RATE;

TIN_CWB >= 35; TIN_CWB <= 75;

TIN_CWC = (WWC1CWC*T_SO_C1 + WWC2CWC*T_SO_C2 +

WWC3CWC*T_SO_C3)/CW_C_FLOW_RATE;

TIN_CWC >= 35; TIN_CWC <= 75;

! TEMPERATURE INLET TO CHILLER;

TIN_CHA = (WWA1CHA*T_SO_A1 + WWA2CHA*T_SO_A2 + WWA3CHA*T_SO_A3 +

WWA4CHA*T_SO_A4 + WWA5CHA*T_SO_A5 + WWA6CHA*T_SO_A6)/CH_A_FLOW_RATE;

TIN_CHA >= 15; TIN_CHA <= 25;

TIN_CHB = (WWB1CHB*T_SO_B1 + WWB2CHB*T_SO_B2 + WWB3CHB*T_SO_B3 +

WWB4CHB*T_SO_B4)/CH_B_FLOW_RATE;

TIN_CHB >= 15; TIN_CHB <= 25;

TIN_CHC = (WWC1CHC*T_SO_C1 + WWC2CHC*T_SO_C2 +

WWC3CHC*T_SO_C3)/CH_C_FLOW_RATE;

TIN_CHC >= 15; TIN_CHC <= 25;

!============================================================================;

! POWER REQUIREMENT FOR PROCESS COOLING;

! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT A;

POWER_COOLING_TOWER_A = (0.0105*(CW_A_FLOW_RATE*(TIN_CWA-T_CW_A)));

POWER_CHILLER_A = (CH_A_FLOW_RATE*(TIN_CHA-T_CH_A))/4;

POWER_PUMP_CWA = (((CW_A_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;

POWER_PUMP_CHA = (((CH_A_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;

! DIFFERENTIAL HEAD = 10M, PUMP EFFICIENCY = 0.82, C.O.P = 4;

T_CW_A >= 15; T_CW_A <= 25;

T_CH_A >= 5; T_CH_A <= 8;

POWER_A = POWER_COOLING_TOWER_A + POWER_CHILLER_A + POWER_PUMP_CWA +

POWER_PUMP_CHA;

! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT B;

POWER_COOLING_TOWER_B = (0.0105*(CW_B_FLOW_RATE*(TIN_CWB-T_CW_B)));

POWER_CHILLER_B = (CH_B_FLOW_RATE*(TIN_CHB-T_CH_B))/4;

POWER_PUMP_CWB = (((CW_B_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;

POWER_PUMP_CHB = (((CH_B_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;


153

T_CW_B >=15; T_CW_B <=25;

T_CH_B >= 5; T_CH_B <= 8;

POWER_B = POWER_COOLING_TOWER_B + POWER_CHILLER_B + POWER_PUMP_CWB +

POWER_PUMP_CHB;

! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT C;

POWER_COOLING_TOWER_C = (0.0105*(CW_C_FLOW_RATE*(TIN_CWC-T_CW_C)));

POWER_CHILLER_C = (CH_C_FLOW_RATE*(TIN_CHC-T_CH_C))/4;

POWER_PUMP_CWC = (((CW_C_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;

POWER_PUMP_CHC = (((CH_C_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;


T_CW_C >= 15; T_CW_C <= 25;

T_CH_C >= 5; T_CH_C <= 8;

POWER_C = POWER_COOLING_TOWER_C + POWER_CHILLER_C + POWER_PUMP_CWC +

POWER_PUMP_CHC;

! TOTAL OPERATING POWER CONSUMPTION;

TOTAL_POWER_REQUIREMENT = POWER_A + POWER_B + POWER_C;

! COST OF POWER CONSUMPTION;

POWER_COST_A = POWER_A*U_ENERGY*OT_H;

POWER_COST_B = POWER_B*U_ENERGY*OT_H;

POWER_COST_C = POWER_C*U_ENERGY*OT_H;

U_ENERGY = 0.03; !US DOLLAR/KWH;

OT_H = 7920; !330 OPERATING DAY IN HOUR;

!============================================================================;

! MAKE UP WATER OF COOLING TOWER;

! FLOW RATE OF EVAPORATE;

F_EVAP_A = F_AIR_A*(W_OUT - W_IN);

F_EVAP_B = F_AIR_B*(W_OUT - W_IN);

F_EVAP_C = F_AIR_C*(W_OUT - W_IN);

CW_A_FLOW_RATE/4.2/F_AIR_A = 1.2;

CW_B_FLOW_RATE/4.2/F_AIR_B = 1.2;

CW_C_FLOW_RATE/4.2/F_AIR_C = 1.2;

W_OUT = 0.02; W_IN = 0.005;

! FLOW RATE OF DRIFT;

F_DRIFT_A = 0.002*CW_A_FLOW_RATE/4.2;

F_DRIFT_B = 0.002*CW_B_FLOW_RATE/4.2;

F_DRIFT_C = 0.002*CW_C_FLOW_RATE/4.2;

! FLOW RATE OF BLOW DOWN;

F_BD_A = F_EVAP_A/CC-1;

F_BD_B = F_EVAP_B/CC-1;

F_BD_C = F_EVAP_C/CC-1;

CC = 4;

! FLOW RATE OD MAKE UP WATER;

F_MU_A = F_EVAP_A + F_DRIFT_A + F_BD_A;

154

F_MU_B = F_EVAP_B + F_DRIFT_B + F_BD_B;

F_MU_C = F_EVAP_C + F_DRIFT_C + F_BD_C;

! COST OF MAKE UP WATER;

MAKEUP_COST_A = F_MU_A/4.2*U_MAKEUP*OT_S;

MAKEUP_COST_B = F_MU_B/4.2*U_MAKEUP*OT_S;

MAKEUP_COST_C = F_MU_C/4.2*U_MAKEUP*OT_S;

U_MAKEUP = 5.75E-5; !US DOLLAR PER KG WATER;

OT_S = 28512000; !330 DAYS OPERATING IN SEC;

!============================================================================;

! COOLING TOWER;

! LOWER BOUND OF COOLING TOWER;

CW_A_FLOW_RATE >= LBCT*Z_CTA;

CW_B_FLOW_RATE >= LBCT*Z_CTB;

CW_C_FLOW_RATE >= LBCT*Z_CTC;

! UPPER BOUND OF COOLING TOWER;

CW_A_FLOW_RATE <= UBCT*Z_CTA;

CW_B_FLOW_RATE <= UBCT*Z_CTB;

CW_C_FLOW_RATE <= UBCT*Z_CTC;

! BINARY OF COOLING TOWER EXISTENCE;

@BIN(Z_CTA);

@BIN(Z_CTB);

@BIN(Z_CTC);

LBCT = 100;

! COOLING TOWER SIZING;

! OVERALL MASS TRANSFER COEFFICIENT;

KA_A = 2.95*((CW_A_FLOW_RATE/4.2)^0.26)*((F_AIR_A)^0.72);

KA_B = 2.95*((CW_B_FLOW_RATE/4.2)^0.26)*((F_AIR_B)^0.72);

KA_C = 2.95*((CW_C_FLOW_RATE/4.2)^0.26)*((F_AIR_C)^0.72);

! MERKEL’S NO;

MERKELS_A = (CW_A_FLOW_RATE/4.2/F_AIR_A)^N;

MERKELS_B = (CW_B_FLOW_RATE/4.2/F_AIR_B)^N;

MERKELS_C = (CW_C_FLOW_RATE/4.2/F_AIR_C)^N;

N = 0.5;

! VOLUME FILL OF COOLING TOWER;

V_CTA = MERKELS_A*(CW_A_FLOW_RATE/4.2)/KA_A;

V_CTB = MERKELS_B*(CW_B_FLOW_RATE/4.2)/KA_B;

V_CTC = MERKELS_C*(CW_C_FLOW_RATE/4.2)/KA_C;

! INVESTMENT COST OF COOLING TOWER;

COST_CTA = KF*(CCTF*Z_CTA + CCTV*V_CTA + CCTMA*F_AIR_A);

COST_CTB = KF*(CCTF*Z_CTB + CCTV*V_CTB + CCTMA*F_AIR_B);

COST_CTC = KF*(CCTF*Z_CTC + CCTV*V_CTC + CCTMA*F_AIR_C);

KF = 0.2983; ! ANNUALIZED FACTOR;

CCTF = 31185; !INITIAL COST;

CCTV = 1606.15; !US DOLLAR/M3;

CCTMA = 1097.5; !KG/S AIR;

155

!============================================================================;

! CHILLER;

! TONS CAPACITY OF CHILLER;

TONS_A = POWER_CHILLER_A*0.28458;

TONS_B = POWER_CHILLER_B*0.28458;

TONS_C = POWER_CHILLER_C*0.28458;

! LOWER BOUND OF CHILLER CAPACITY;

POWER_CHILLER_A >= LBCH*Z_CHA;

POWER_CHILLER_B >= LBCH*Z_CHB;

POWER_CHILLER_C >= LBCH*Z_CHC;

! UPPER NOUND OF CHILLER CAPACITY;

POWER_CHILLER_A <= UBCH*Z_CHA;

POWER_CHILLER_B <= UBCH*Z_CHB;

POWER_CHILLER_C <= UBCH*Z_CHC;

LBCH = 1000;

! BINARY TERMS OF CHILLER EXISTENCE;

@BIN(Z_CHA);

@BIN(Z_CHB);

@BIN(Z_CHC);

! INVESTMENT COST OF CHILLER;

COST_CHA = KC*(CCH*Z_CHA + TONS_A*U_TONS) ;

COST_CHB = KC*(CCH*Z_CHB + TONS_B*U_TONS);

COST_CHC = KC*(CCH*Z_CHC + TONS_C*U_TONS);

U_TONS = 200; !US DOLLAR/TONS;

KC = 0.256;

CCH = 1246000;

!============================================================================;

! TOTAL ANNUALIZED COST OF EACH PLANT;

TAC_A = POWER_COST_A + MAKEUP_COST_A + COST_CTA + COST_CHA;

TAC_B = POWER_COST_B + MAKEUP_COST_B + COST_CTB + COST_CHB;

TAC_C = POWER_COST_C + MAKEUP_COST_C + COST_CTC + COST_CHC;

TAC = TAC_A + TAC_B + TAC_C;

156

Appendix 1(b): LINGO ver13 mathematical modelling codes for Scenario 1 (Example 1)

MIN = TAC;

!============================================================================;




SOURCEA6=210;






















!============================================================================;



















157



!============================================================================;

! THERMAL BALANCE;



= 70;




T_SI_B1 = 5; T_SI_B2 = 17; T_SI_B3 = 24;


T_SO_C1 = 12; T_SO_C2 = 35; T_SO_C3 = 45;

T_SI_C1 = 8; T_SI_C2 = 16;



















SINKC1*T_SI_C1;


SINKC2*T_SI_C2;

!============================================================================;

! FRESH GENERATION;



CW_A_FLOW_RATE = CWA_A1 + CWA_A2 + CWA_A3 + CWA_A4 + CWA_CHA;

WWA1CHA + WWA2CHA + WWA3CHA + WWA4CHA + WWA5CHA + WWA6CHA + CWA_CHA =

CH_A_FLOW_RATE;

CH_A_FLOW_RATE = CHA_A1 + CHA_A2 + CHA_A3 + CHA_A4;



CW_B_FLOW_RATE = CWB_B1 + CWB_B2 + CWB_B3 + CWB_CHB;

WWB1CHB + WWB2CHB + WWB3CHB + WWB4CHB + CWB_CHB = CH_B_FLOW_RATE;

CH_B_FLOW_RATE = CHB_B1 + CHB_B2 + CHB_B3;

158

!FRESH BALANCE IN PLANT C;


CW_C_FLOW_RATE = CWC_C1 + CWC_C2 + CWC_CHC;

WWC1CHC + WWC2CHC + WWC3CHC + CWC_CHC = CH_C_FLOW_RATE;

CH_C_FLOW_RATE = CHC_C1 + CHC_C2;

!============================================================================;












TIN_CHA = (WWA1CHA*T_SO_A1 + WWA2CHA*T_SO_A2 + WWA3CHA*T_SO_A3 +

WWA4CHA*T_SO_A4 + WWA5CHA*T_SO_A5 + WWA6CHA*T_SO_A6 +

CWA_CHA*T_CW_A)/CH_A_FLOW_RATE;

TIN_CHA >= 15; TIN_CHA <= 25;

TIN_CHB = (WWB1CHB*T_SO_B1 + WWB2CHB*T_SO_B2 + WWB3CHB*T_SO_B3 +

WWB4CHB*T_SO_B4 + CWB_CHB*T_CW_B)/CH_B_FLOW_RATE;

TIN_CHB >= 15; TIN_CHB <= 25;

TIN_CHC = (WWC1CHC*T_SO_C1 + WWC2CHC*T_SO_C2 + WWC3CHC*T_SO_C3 +

CWC_CHC*T_CW_C)/CH_C_FLOW_RATE;

TIN_CHC >= 15; TIN_CHC <= 25;

!============================================================================;


! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT A;


POWER_CHILLER_A = (CH_A_FLOW_RATE*(TIN_CHA-T_CH_A))/4;


POWER_PUMP_CHA = (((CH_A_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;


T_CW_A >= 15; T_CW_A <= 25;

T_CH_A >= 5; T_CH_A <= 8;

POWER_A = POWER_COOLING_TOWER_A + POWER_CHILLER_A + POWER_PUMP_CWA +

POWER_PUMP_CHA;

! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT B;


POWER_CHILLER_B = (CH_B_FLOW_RATE*(TIN_CHB-T_CH_B))/4;


POWER_PUMP_CHB = (((CH_B_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;


159

T_CW_B >=15; T_CW_B <=25;

T_CH_B >= 5; T_CH_B <= 8;

POWER_B = POWER_COOLING_TOWER_B + POWER_CHILLER_B + POWER_PUMP_CWB +

POWER_PUMP_CHB;

! POWER REQUIREMENT FOR PROCESS COOLING IN PLANT C;


POWER_CHILLER_C = (CH_C_FLOW_RATE*(TIN_CHC-T_CH_C))/4;


POWER_PUMP_CHC = (((CH_C_FLOW_RATE)/4.2*9.81*10)/1000)/0.82;


T_CW_C >= 15; T_CW_C <= 25;

T_CH_C >= 5; T_CH_C <= 8;

POWER_C = POWER_COOLING_TOWER_C + POWER_CHILLER_C + POWER_PUMP_CWC +

POWER_PUMP_CHC;









!============================================================================;









W_OUT = 0.02; W_IN = 0.005;









CC = 4;



160









!============================================================================;

! COOLING TOWER;










@BIN(Z_CTA);

@BIN(Z_CTB);

@BIN(Z_CTC);

LBCT = 100;






! MERKEL’S NO;




N = 0.5;













161

!============================================================================;

! CHILLER;


TONS_A = POWER_CHILLER_A*0.28458;

TONS_B = POWER_CHILLER_B*0.28458;

TONS_C = POWER_CHILLER_C*0.28458;


POWER_CHILLER_A >= LBCH*Z_CHA;

POWER_CHILLER_B >= LBCH*Z_CHB;

POWER_CHILLER_C >= LBCH*Z_CHC;

! UPPER NOUND OF CHILLER CAPACITY;

POWER_CHILLER_A <= UBCH*Z_CHA;

POWER_CHILLER_B <= UBCH*Z_CHB;

POWER_CHILLER_C <= UBCH*Z_CHC;

LBCH = 1000;

! BINARY TERMS OF CHILLER EXISTENCE;

@BIN(Z_CHA);

@BIN(Z_CHB);

@BIN(Z_CHC);


COST_CHA = KC*(CCH*Z_CHA + TONS_A*U_TONS) ;

COST_CHB = KC*(CCH*Z_CHB + TONS_B*U_TONS);

COST_CHC = KC*(CCH*Z_CHC + TONS_C*U_TONS);


KC = 0.256;

CCH = 1246000;

!============================================================================;


TAC_A = POWER_COST_A + MAKEUP_COST_A + COST_CTA + COST_CHA;

TAC_B = POWER_COST_B + MAKEUP_COST_B + COST_CTB + COST_CHB;

TAC_C = POWER_COST_C + MAKEUP_COST_C + COST_CTC + COST_CHC;


162

Appendix 1(c): LINGO ver13 mathematical modelling codes for Scenario 2 (Example 1)

MIN = TAC;

!============================================================================;




SOURCEA6=210;







A1A1 + A1A2 + A1A3 + A1A4 + WWA1CWA + WWA1CH = SOURCEA1;







B1B1 + B1B2 + B1B3 + WWB1CWB + WWB1CH = SOURCEB1;





C1C1 + C1C2 + WWC1CWC + WWC1CH = SOURCEC1;



!============================================================================;










CWA_A1 + CH_A1 + A1A1 + A2A1 + A3A1 + A4A1 + A5A1 + A6A1 = SINKA1;





CWB_B1 + CH_B1 + B1B1 + B2B1 + B3B1 + B4B1 = SINKB1;




163

CWC_C1 + CH_C1 + C1C1 + C2C1 +C3C1 = SINKC1;

CWC_C2 + CH_C2 + C1C2 + C2C2 +C3C2 = SINKC2;

!============================================================================;

! THERMAL BALANCE;



= 70;




T_SI_B1 = 5; T_SI_B2 = 17; T_SI_B3 = 24;


T_SO_C1 = 12; T_SO_C2 = 35; T_SO_C3 = 45;

T_SI_C1 = 8; T_SI_C2 = 16;


CWA_A1*T_CW_A + CH_A1*T_CH + A1A1*T_SO_A1 + A2A1*T_SO_A2 + A3A1*T_SO_A3 +

A4A1*T_SO_A4 + A5A1*T_SO_A5 + A6A1*T_SO_A6 = SINKA1*T_SI_A1;








CWB_B1*T_CW_B + CH_B1*T_CH + B1B1*T_SO_B1 + B2B1*T_SO_B2 + B3B1*T_SO_B3 +







CWC_C1*T_CW_C + CH_C1*T_CH + C1C1*T_SO_C1 + C2C1*T_SO_C2 +C3C1*T_SO_C3=

SINKC1*T_SI_C1;

CWC_C2*T_CW_C + CH_C2*T_CH + C1C2*T_SO_C1 + C2C2*T_SO_C2 +C3C2*T_SO_C3=

SINKC2*T_SI_C2;

!============================================================================;

! FRESH GENERATION ;



CW_A_FLOW_RATE = CWA_A1 + CWA_A2 + CWA_A3 + CWA_A4 + CWA_CH;



CW_B_FLOW_RATE = CWB_B1 + CWB_B2 + CWB_B3 + CWB_CH;

! FRESH BALANCE IN PLANT C;


CW_C_FLOW_RATE = CWC_C1 + CWC_C2 + CWC_CH;

! FRESH GENERATION IN CENTRALIZED HUB;

164

WWA1CH + WWA2CH + WWA3CH + WWA4CH + WWA5CH + WWA6CH + CWA_CH + WWB1CH +

WWB2CH + WWB3CH + WWB4CH + CWB_CH + WWC1CH + WWC2CH + WWC3CH + CWC_CH =

CH_FLOW_RATE;

CH_FLOW_RATE = CH_A1 + CH_A2 + CH_A3 + CH_A4 + CH_B1 + CH_B2 + CH_B3 + CH_C1

+ CH_C2;

F_CH_A = WWA1CH + WWA2CH + WWA3CH + WWA4CH + WWA5CH + WWA6CH + CWA_CH;

F_CH_B = WWB1CH + WWB2CH + WWB3CH + WWB4CH + CWB_CH ;

F_CH_C = WWC1CH + WWC2CH + WWC3CH + CWC_CH;

FRESH_CH_A = CH_A1 + CH_A2 + CH_A3 + CH_A4;

FRESH_CH_B = CH_B1 + CH_B2 + CH_B3;

FRESH_CH_C = CH_C1 + CH_C2;

!============================================================================;












TIN_CH = (WWA1CH*T_SO_A1 + WWA2CH*T_SO_A2 + WWA3CH*T_SO_A3 + WWA4CH*T_SO_A4 +

WWA5CH*T_SO_A5 + WWA6CH*T_SO_A6 + CWA_CH*T_CW_A + WWB1CH*T_SO_B1 +

WWB2CH*T_SO_B2 + WWB3CH*T_SO_B3 + WWB4CH*T_SO_B4 + CWB_CH*T_CW_B +

WWC1CH*T_SO_C1 + WWC2CH*T_SO_C2 + WWC3CH*T_SO_C3 +

CWC_CH*T_CW_C)/CH_FLOW_RATE;

TIN_CH >= 15; TIN_CH <= 25;

!============================================================================;



POWER_CEN_CHILLER_A = (FRESH_CH_A*(TIN_CH-T_CH))/4;


POWER_PUMP_CEN_CHA = (((FRESH_CH_A)/4.2*9.81*30)/1000)/0.82;


POWER_CEN_CHILLER_B = (FRESH_CH_B*(TIN_CH-T_CH))/4;


POWER_PUMP_CEN_CHB = (((FRESH_CH_B)/4.2*9.81*30)/1000)/0.82;


POWER_CEN_CHILLER_C = (FRESH_CH_C*(TIN_CH-T_CH))/4;


POWER_PUMP_CEN_CHC = (((FRESH_CH_C)/4.2*9.81*30)/1000)/0.82;

T_CW_A >= 15; T_CW_A <= 25;

T_CW_B >= 15; T_CW_B <= 25;

T_CW_C >= 15; T_CW_C <= 25;

T_CH >= 5; T_CH <= 8;

165

! TOTAL OPERATING POWER CONSUMPTION OF EACH PLANT;

POWER_A = POWER_COOLING_TOWER_A + POWER_CEN_CHILLER_A + POWER_PUMP_CWA +

POWER_PUMP_CEN_CHA;

POWER_B = POWER_COOLING_TOWER_B + POWER_CEN_CHILLER_B + POWER_PUMP_CWB +

POWER_PUMP_CEN_CHB;

POWER_C = POWER_COOLING_TOWER_C + POWER_CEN_CHILLER_C + POWER_PUMP_CWC +

POWER_PUMP_CEN_CHC;







! TOTAL POWER REQUIREMENT;










W_OUT = 0.02; W_IN = 0.005;









CC = 4;











166

!============================================================================;

! COOLING TOWER;










@BIN(Z_CTA);

@BIN(Z_CTB);

@BIN(Z_CTC);

LBCT = 100;






! MERKEL’S NO;




N = 0.5;













!============================================================================;

! CHILLER;


TONS_CEN_CHILLER = (POWER_CEN_CHILLER_A + POWER_CEN_CHILLER_B +

POWER_CEN_CHILLER_C)*0.28458;

CEN_CH_CAPACITY = POWER_CEN_CHILLER_A + POWER_CEN_CHILLER_B +

POWER_CEN_CHILLER_C;


CEN_CH_CAPACITY >= LBCH*Z_CEN_CH;

167

! UPPER BOUND OC CHILLER CAPACITY;

CEN_CH_CAPACITY <= UBCH*Z_CEN_CH;

LBCH = 1000;

! BINARY TERMS OF CENTRALIZED CHILLER;

@BIN(Z_CEN_CH);


COST_CEN_CH = KC*(CCH*Z_CEN_CH + TONS_CEN_CHILLER*U_TONS);


KC = 0.256;

CCH = 1246000;

!============================================================================;

! PIPING;

! LOWER BOUND OF FLOW RATE TO CENTRALIZED UNIT;

F_CH_A >= LBPT*Z_PTA;

F_CH_B >= LBPT*Z_PTB;

F_CH_C >= LBPT*Z_PTC;

! UPPER BOUND OF FLOW RATE TO CENTRALIZED UNIT;

F_CH_A <= UBPT*Z_PTA;

F_CH_B <= UBPT*Z_PTB;

F_CH_C <= UBPT*Z_PTC;

! LOWER BOUND OF FRESH FROM CENTRALIZED CHILLER;

FRESH_CH_A >= LBPF*Z_PFA;

FRESH_CH_B >= LBPF*Z_PFB;

FRESH_CH_C >= LBPF*Z_PFC;

! UPPER BOUND OF FRESH FROM CENTRALIZED CHILLER;

FRESH_CH_A <= UBPF*Z_PFA;

FRESH_CH_B <= UBPF*Z_PFB;

FRESH_CH_C <= UBPF*Z_PFC;

LBPT = 100; LBPF = 100;

UBPT = 5000; UBPF = 5000;

! BINARY FOR PIPING EXISTENCE;

@BIN(Z_PTA);

@BIN(Z_PTB);

@BIN(Z_PTC);

@BIN(Z_PFA);

@BIN(Z_PFB);

@BIN(Z_PFC);

! PIPING COST;

PIPING_COST_A = (171.42*(F_CH_A) + 25000*(Z_PTA))*0.231 + (171.42*(FRESH_CH_A)

+ 25000*(Z_PFA))*0.231 ;

PIPING_COST_B = (171.42*(F_CH_B) + 25000*(Z_PTB))*0.231 + (171.42*(FRESH_CH_B)

+ 25000*(Z_PFB))*0.231 ;

PIPING_COST_C = (171.42*(F_CH_C) + 25000*(Z_PTC))*0.231 + (171.42*(FRESH_CH_C)

+ 25000*(Z_PFC))*0.231 ;

168

!============================================================================;


TAC_A = POWER_COST_A + MAKEUP_COST_A + COST_CTA + COST_CEN_CH/3 +

PIPING_COST_A;

TAC_B = POWER_COST_B + MAKEUP_COST_B + COST_CTB + COST_CEN_CH/3 +

PIPING_COST_B;

TAC_C = POWER_COST_C + MAKEUP_COST_C + COST_CTC + COST_CEN_CH/3 +

PIPING_COST_C;

! TOTAL TAC OF 3 PLANTS;


169

Appendix 1(d): LINGO ver13 mathematical modelling codes for Scenario 3 (Example 1)

MIN = TAC;

!============================================================================;




SOURCEA6=210;







A1A1 + A1A2 + A1A3 + A1A4 + WWA1CW + WWA1CH = SOURCEA1;






!PLANT B SOURCES FLOW RATE BALANCE;

B1B1 + B1B2 + B1B3 + WWB1CW + WWB1CH = SOURCEB1;




!PLANT C SOURCES FLOW RATE BALANCE;

C1C1 + C1C2 + WWC1CW + WWC1CH = SOURCEC1;



!============================================================================;










CW_A1 + CH_A1 + A1A1 + A2A1 + A3A1 + A4A1 + A5A1 + A6A1 = SINKA1;





CW_B1 + CH_B1 + B1B1 + B2B1 + B3B1 + B4B1 = SINKB1;



170


CW_C1 + CH_C1 + C1C1 + C2C1 +C3C1 = SINKC1;

CW_C2 + CH_C2 + C1C2 + C2C2 +C3C2 = SINKC2;

!============================================================================;

! THERMAL BALANCE;



= 70;




T_SI_B1 = 5; T_SI_B2 = 17; T_SI_B3 = 24;


T_SO_C1 = 12; T_SO_C2 = 35; T_SO_C3 = 45;

T_SI_C1 = 8; T_SI_C2 = 16;


CW_A1*T_CW + CH_A1*T_CH + A1A1*T_SO_A1 + A2A1*T_SO_A2 + A3A1*T_SO_A3 +









CW_B1*T_CW + CH_B1*T_CH + B1B1*T_SO_B1 + B2B1*T_SO_B2 + B3B1*T_SO_B3 +







CW_C1*T_CW + CH_C1*T_CH + C1C1*T_SO_C1 + C2C1*T_SO_C2 +C3C1*T_SO_C3=

SINKC1*T_SI_C1;

CW_C2*T_CW + CH_C2*T_CH + C1C2*T_SO_C1 + C2C2*T_SO_C2 +C3C2*T_SO_C3=

SINKC2*T_SI_C2;

!============================================================================;

! FRESH GENERATION ;

WWA1CW + WWA2CW + WWA3CW + WWA4CW + WWA5CW + WWA6CW + WWB1CW + WWB2CW +

WWB3CW + WWB4CW + WWC1CW + WWC2CW + WWC3CW = CW_FLOW_RATE;

CW_FLOW_RATE = CW_A1 + CW_A2 + CW_A3 + CW_A4 + CW_B1 + CW_B2 + CW_B3 + CW_C1

+ CW_C2 + CW_CH;

! FRESH GENERATION IN CENTRALIZED HUB;

WWA1CH + WWA2CH + WWA3CH + WWA4CH + WWA5CH + WWA6CH + WWB1CH + WWB2CH +

WWB3CH + WWB4CH + WWC1CH + WWC2CH + WWC3CH + CW_CH = CH_FLOW_RATE;

CH_FLOW_RATE = CH_A1 + CH_A2 + CH_A3 + CH_A4 + CH_B1 + CH_B2 + CH_B3 + CH_C1

+ CH_C2;

F_CW_A = WWA1CW + WWA2CW + WWA3CW + WWA4CW + WWA5CW + WWA6CW;

171

F_CW_B = WWB1CW + WWB2CW + WWB3CW + WWB4CW;

F_CW_C = WWC1CW + WWC2CW + WWC3CW;

F_CH_A = WWA1CH + WWA2CH + WWA3CH + WWA4CH + WWA5CH + WWA6CH;

F_CH_B = WWB1CH + WWB2CH + WWB3CH + WWB4CH;

F_CH_C = WWC1CH + WWC2CH + WWC3CH;

FRESH_CW_A = CW_A1 + CW_A2 + CW_A3 + CW_A4;

FRESH_CW_B = CW_B1 + CW_B2 + CW_B3;

FRESH_CW_C = CW_C1 + CW_C2;

FRESH_CH_A = CH_A1 + CH_A2 + CH_A3 + CH_A4;

FRESH_CH_B = CH_B1 + CH_B2 + CH_B3;

FRESH_CH_C = CH_C1 + CH_C2;

!============================================================================;


TIN_CW = (WWA1CW*T_SO_A1 + WWA2CW*T_SO_A2 + WWA3CW*T_SO_A3 + WWA4CW*T_SO_A4 +

WWA5CW*T_SO_A5 + WWA6CW*T_SO_A6 + WWB1CW*T_SO_B1 + WWB2CW*T_SO_B2 +

WWB3CW*T_SO_B3 + WWB4CW*T_SO_B4 + WWC1CW*T_SO_C1 + WWC2CW*T_SO_C2 +

WWC3CW*T_SO_C3)/CW_FLOW_RATE;

TIN_CW >= 35; TIN_CW <= 75;


TIN_CH = (WWA1CH*T_SO_A1 + WWA2CH*T_SO_A2 + WWA3CH*T_SO_A3 + WWA4CH*T_SO_A4 +

WWA5CH*T_SO_A5 + WWA6CH*T_SO_A6 + WWB1CH*T_SO_B1 + WWB2CH*T_SO_B2 +

WWB3CH*T_SO_B3 + WWB4CH*T_SO_B4 + WWC1CH*T_SO_C1 + WWC2CH*T_SO_C2 +

WWC3CH*T_SO_C3 + CW_CH*T_CW)/CH_FLOW_RATE;

TIN_CH >= 15; TIN_CH <= 25;

!============================================================================;


POWER_CEN_CT_A = (0.0105*((FRESH_CW_A + CW_CH/3)*(TIN_CW-T_CW)));

POWER_PUMP_CW_A = (((FRESH_CW_A)/4.2*9.81*30)/1000)/0.82;

POWER_CEN_CH_A = (FRESH_CH_A*(TIN_CH-T_CH))/4;

POWER_PUMP_CH_A = (((FRESH_CH_A)/4.2*9.81*30)/1000)/0.82;

!DIFFERENTIAL HEAD = 10M, PUMP EFFICIENCY = 0.82, COP = 4;

POWER_CEN_CT_B = (0.0105*((FRESH_CW_B + CW_CH/3)*(TIN_CW-T_CW)));

POWER_PUMP_CW_B = (((FRESH_CW_B)/4.2*9.81*30)/1000)/0.82;

POWER_CEN_CH_B = (FRESH_CH_B*(TIN_CH-T_CH))/4;

POWER_PUMP_CH_B = (((FRESH_CH_B)/4.2*9.81*30)/1000)/0.82;


POWER_CEN_CT_C = (0.0105*((FRESH_CW_C + CW_CH/3)*(TIN_CW-T_CW)));

POWER_PUMP_CW_C = (((FRESH_CW_C)/4.2*9.81*30)/1000)/0.82;

POWER_CEN_CH_C = (FRESH_CH_C*(TIN_CH-T_CH))/4;

POWER_PUMP_CH_C = (((FRESH_CH_C)/4.2*9.81*30)/1000)/0.82;


T_CW >= 15; T_CW <= 25;

T_CH >= 5; T_CH <= 8;

POWER_A = POWER_CEN_CT_A + POWER_PUMP_CW_A + POWER_CEN_CH_A + POWER_PUMP_CH_A;

POWER_B = POWER_CEN_CT_B + POWER_PUMP_CW_B + POWER_CEN_CH_B + POWER_PUMP_CH_B;

POWER_C = POWER_CEN_CT_C + POWER_PUMP_CW_C + POWER_CEN_CH_C + POWER_PUMP_CH_C;

172









!============================================================================;



F_EVAP = F_AIR*(W_OUT - W_IN);

CW_FLOW_RATE/4.2/F_AIR_A = 1.2;

W_OUT = 0.02; W_IN = 0.005;


F_DRIFT = 0.002*CW_FLOW_RATE/4.2;


F_BD = F_EVAP/CC-1;

CC = 4;


F_MU = F_EVAP + F_DRIFT + F_BD;


MAKEUP_COST = F_MU/4.2*U_MAKEUP*OT_S;



!============================================================================;

! COOLING TOWER;


CW_FLOW_RATE >= LBCT*Z_CT;


CW_FLOW_RATE <= UBCT*Z_CT;


@BIN(Z_CT);

LBCT = 100;



KA = 2.95*((CW_FLOW_RATE/4.2)^0.26)*((F_AIR)^0.72);

! MERKEL’S NO;

MERKELS = (CW_FLOW_RATE/4.2/F_AIR)^N;

N = 0.5;


V_CT = MERKELS*(CW_FLOW_RATE/4.2)/KA;

173


COST_CT = KF*(CCTF*Z_CT + CCTV*V_CT + CCTMA*F_AIR);





!============================================================================;

! CHILLER;


TONS_CEN_CHILLER = (POWER_CEN_CH_A + POWER_CEN_CH_B +

POWER_CEN_CH_C )*0.28458;

CEN_CH_CAPACITY = POWER_CEN_CH_A + POWER_CEN_CH_B + POWER_CEN_CH_C ;


CEN_CH_CAPACITY >= LBCH*Z_CEN_CH;

! UPPER BOUND OC CHILLER CAPACITY;

CEN_CH_CAPACITY <= UBCH*Z_CEN_CH;

LBCH = 1000;

! BINARY TERMS OF CENTRALIZED CHILLER;

@BIN(Z_CEN_CH);


COST_CEN_CH = KC*(CCH*Z_CEN_CH + TONS_CEN_CHILLER*U_TONS);


KC = 0.256;

CCH = 1246000;

!============================================================================;

! PIPING;

! LOWER BOUND OF FLOW RATE TO CENTRALIZED COOLING TOWER;

F_CW_A >= LBPT*Z_PCTA;

F_CW_B >= LBPT*Z_PCTB;

F_CW_C >= LBPT*Z_PCTC;

! UPPER BOUND OF FLOW RATE TO CENTRALIZED COOLING TOWER;

F_CW_A <= UBPT*Z_PCTA;

F_CW_B <= UBPT*Z_PCTB;

F_CW_C <= UBPT*Z_PCTC;

! LOWER BOUND OF FLOW RATE TO CENTRALIZED CHILLER;

F_CH_A >= LBPH*Z_PCHA;

F_CH_B >= LBPH*Z_PCHB;

F_CH_C >= LBPH*Z_PCHC;

! UPPER BOUND OF FLOW RATE TO CENTRALIZED UNIT;

F_CH_A <= UBPH*Z_PCHA;

F_CH_B <= UBPH*Z_PCHB;

F_CH_C <= UBPH*Z_PCHC;

! LOWER BOUND OF FRESH FROM CENTRALIZED COOLING TOWER;

FRESH_CW_A >= LBPFT*Z_PFCTA;

FRESH_CW_B >= LBPFT*Z_PFCTB;

174

FRESH_CW_C >= LBPFT*Z_PFCTC;

! UPPER BOUND OF FRESH FROM CENTRALIZED OOLING TOWER;

FRESH_CW_A <= UBPFT*Z_PFCTA;

FRESH_CW_B <= UBPFT*Z_PFCTB;

FRESH_CW_C <= UBPFT*Z_PFCTC;

! LOWER BOUND OF FRESH FROM CENTRALIZED CHILLER;

FRESH_CH_A >= LBPFH*Z_PFCHA;

FRESH_CH_B >= LBPFH*Z_PFCHB;

FRESH_CH_C >= LBPFH*Z_PFCHC;

! UPPER BOUND OF FRESH FROM CENTRALIZED CHILLER;

FRESH_CH_A <= UBPFH*Z_PFCHA;

FRESH_CH_B <= UBPFH*Z_PFCHB;

FRESH_CH_C <= UBPFH*Z_PFCHC;

LBPT = 100; LBPH = 100; LBPFT = 100; LBPFH = 100;

! BINARY FOR PIPING EXISTENCE;

@BIN(Z_PCTA); @BIN(Z_PCHA);

@BIN(Z_PCTB); @BIN(Z_PCHB);

@BIN(Z_PCTC); @BIN(Z_PCHC);

@BIN(Z_PFCTA);@BIN(Z_PFCHA);

@BIN(Z_PFCTB);@BIN(Z_PFCHB);

@BIN(Z_PFCTC);@BIN(Z_PFCHC);

! PIPING COST;

PIPING_COST_A = (171.42*(F_CW_A) + 25000*(Z_PCTA))*0.231 + (171.42*(F_CH_A) +

25000*(Z_PCHA))*0.231 + (171.42*(FRESH_CW_A) + 25000*(Z_PFCTA))*0.231 +

(171.42*(FRESH_CH_A) + 25000*(Z_PFCHA))*0.231 ;

PIPING_COST_B = (171.42*(F_CW_B) + 25000*(Z_PCTB))*0.231 + (171.42*(F_CH_B) +

25000*(Z_PCHB))*0.231 + (171.42*(FRESH_CW_B) + 25000*(Z_PFCTB))*0.231 +

(171.42*(FRESH_CH_B) + 25000*(Z_PFCHB))*0.231;

PIPING_COST_C = (171.42*(F_CW_C) + 25000*(Z_PCTC))*0.231 + (171.42*(F_CH_C) +

25000*(Z_PCHC))*0.231 + (171.42*(FRESH_CW_C) + 25000*(Z_PFCTC))*0.231 +

(171.42*(FRESH_CH_C) + 25000*(Z_PFCHC))*0.231;

!============================================================================;


TAC_A = POWER_COST_A + MAKEUP_COST/3 + COST_CT/3 + COST_CEN_CH/3 +

PIPING_COST_A;

TAC_B = POWER_COST_B + MAKEUP_COST/3 + COST_CT/3 + COST_CEN_CH/3 +

PIPING_COST_B;

TAC_C = POWER_COST_C + MAKEUP_COST/3 + COST_CT/3 + COST_CEN_CH/3 +

PIPING_COST_C;

! TOTAL TAC OF 3 PLANTS;


175


LINGO ver13 mathematical modelling codes for generating alternative IPCCWN

MAX = LAMBDA;

FCCW=CHILLED_WATER+COOLING_WATER;

TOTAL_COSTS = COSTS_A+COSTS_B+COSTS_C;

FRESH_COSTS=CHILLED_WATER_COSTS+COOLING_WATER_COSTS;

! CHILLED WATER COST OF RM 10 PER KG AND 330 OPERATING DAYS PER YEAR;

CHILLED_WATER_COSTS = F_CHILLED_COSTS_A + F_CHILLED_COSTS_B +

F_CHILLED_COSTS_C;

! COOLING WATER COST OF RM 5 PER KG AND 330 OPERATING DAYS PER YEAR;

COOLING_WATER_COSTS = F_COOLING_COSTS_A + F_COOLING_COSTS_B +

F_COOLING_COSTS_C;

! SETTING THE LOWER BOUND AS ZERO;

LB = 0;

! PIPING DISTANCE OF 100 METERS;

D = 100;

DT = 0.5;

!============================================================================;



SOURCEA1=939.75; SOURCEA2=130.58; SOURCEA3=130.92; SOURCEA4=318.51;


SOURCEA9=26.75; SOURCEA10=107.84;


SOURCEB1=209; SOURCEB2=418; SOURCEB3=250.8; SOURCEB4=125.40; SOURCEB5=83.60;

SOURCEB6=459.80; SOURCEB7=1881; SOURCEB8=2173.6;


SOURCEC1=551.76; SOURCEC2=968.57; SOURCEC3=304.9;


A1A1 + A1A2 + A1A3 + A1A4 + A1A5 + A1B1 + A1B2 + A1B3 + A1B4 + A1B5 + A1B6 +

A1B7 + A1C1 + A1C2 + A1C3 + WWA1 = SOURCEA1;

















176

A10A1 + A10A2 + A10A3 + A10A4 + A10A5 + A10B1 + A10B2 + A10B3 + A10B4 + A10B5

+ A10B6 + A10B7 + A10C1 + A10C2 + A10C3 + WWA10 = SOURCEA10;

B1A1 + B1A2 + B1A3 + B1A4 + B1A5 + B1B1 + B1B2 + B1B3 + B1B4 + B1B5 + B1B6 +

B1B7 + B1C1 + B1C2 + B1C3 + WWB1 = SOURCEB1;















C1A1 + C1A2 + C1A3 + C1A4 + C1A5 + C1B1 + C1B2 + C1B3 + C1B4 + C1B5 + C1B6 +

C1B7 + C1C1 + C1C2 + C1C3 + WWC1 = SOURCEC1;





!============================================================================;



SINKA1=2528.31; SINKA2=41.72; SINKA3=175.48; SINKA4=234.92; SINKA5=134.59;


SINKB1=627; SINKB2=125.40; SINKB3=250.80; SINKB4=543.4; SINKB5=836;

SINKB6=1964.6; SINKB7=1254;


SINKC1=500.8; SINKC2=645.53; SINKC3=678.90;


CH1 + CW1 + A1A1 + A2A1 + A3A1 + A4A1 + A5A1 + A6A1 + A7A1 + A8A1 + A9A1 +

A10A1 + B1A1 + B2A1 + B3A1 + B4A1 + B5A1 + B6A1 + B7A1 + B8A1 + C1A1 + C2A1

+C3A1 = SINKA1;



+C3A2 = SINKA2;



+C3A3 = SINKA3;



+C3A4 = SINKA4;



+C3A5 = SINKA5;

CH6 + CW6 + A1B1 + A2B1 + A3B1 + A4B1 + A5B1 + A6B1 + A7B1 + A8B1 + A9B1 +

A10B1 + B1B1 + B2B1 + B3B1 + B4B1 + B5B1 + B6B1 + B7B1 + B8B1 + C1B1 + C2B1

+C3B1 = SINKB1;



+C3B2 = SINKB2;

177



+C3B3 = SINKB3;



+C3B4 = SINKB4;



+C3B5 = SINKB5;



+C3B6 = SINKB6;



+C3B7 = SINKB7;

CH13 + CW13 + A1C1 + A2C1 + A3C1 + A4C1 + A5C1 + A6C1 + A7C1 + A8C1 + A9C1 +

A10C1 + B1C1 + B2C1 + B3C1 + B4C1 + B5C1 + B6C1 + B7C1 + B8C1 + C1C1 + C2C1

+C3C1 = SINKC1;



+C3C2 = SINKC2;



+C3C3 = SINKC3;

! COMPONENT BALANCE;

CH1*6.67 + CW1*19.80 + A1A1*10 + A2A1*10.5 + A3A1*11.11 + A4A1*16.67 +

A5A1*17.7 + A6A1*19 + A7A1*20 + A8A1*20.88 + A9A1*22.6 + A10A1*24.01 +

B1A1*(11.67+DT) + B2A1*(17.67+DT) + B3A1*(20+DT) + B4A1*(21+DT) + B5A1*(23+DT)

+ B6A1*(24+DT) + B7A1*(40+DT) + B8A1*(75+DT) + C1A1*(8.67+DT) + C2A1*(19+DT)

+C3A1*(26.67+DT)= SINKA1*6.67;

CH2*6.67 + CW2*19.80 + A1A2*10 + A2A2*10.5 + A3A2*11.11 + A4A2*16.67 +

A5A2*17.7 + A6A2*19 + A7A2*20 + A8A2*20.88 + A9A2*22.6 + A10A2*24.01 +



+C3A2*(26.67+DT)= SINKA2*8;

CH3*6.67 + CW3*19.80 + A1A3*10 + A2A3*10.5 + A3A3*11.11 + A4A3*16.67 +

A5A3*17.7 + A6A3*19 + A7A3*20 + A8A3*20.88 + A9A3*22.6 + A10A3*24.01 +



+C3A3*(26.67+DT)= SINKA3*10;

CH4*6.67 + CW4*19.80 + A1A4*10 + A2A4*10.5 + A3A4*11.11 + A4A4*16.67 +

A5A4*17.7 + A6A4*19 + A7A4*20 + A8A4*20.88 + A9A4*22.6 + A10A4*24.01 +



+C3A4*(26.67+DT)= SINKA4*15;

CH5*6.67 + CW5*19.80 + A1A5*10 + A2A5*10.5 + A3A5*11.11 + A4A5*16.67 +

A5A5*17.7 + A6A5*19 + A7A5*20 + A8A5*20.88 + A9A5*22.6 + A10A5*24.01 +



+C3A5*(26.67+DT)= SINKA5*17;

CH6*6.67 + CW6*19.80 + A1B1*(10+DT) + A2B1*(10.5+DT) + A3B1*(11.11+DT) +

A4B1*(16.67+DT) + A5B1*(17.7+DT) + A6B1*(19+DT) + A7B1*(20+DT) +

A8B1*(20.88+DT) + A9B1*(22.6+DT) + A10B1*(24.01+DT) + B1B1*11.67 + B2B1*17.67

+ B3B1*20 + B4B1*21 + B5B1*23 + B6B1*24 + B7B1*40 + B8B1*75 + C1B1*(8.67+DT)

+ C2B1*(19+DT) +C3B1*(26.67+DT)= SINKB1*6.67;

178





+ C2B2*(19+DT) +C3B2*(26.67+DT)= SINKB2*8;





+ C2B3*(19+DT) +C3B3*(26.67+DT)= SINKB3*15;





+ C2B4*(19+DT) +C3B4*(26.67+DT)= SINKB4*17;





+ C2B5*(19+DT) +C3B5*(26.67+DT)= SINKB5*20;





+ C2B6*(19+DT) +C3B6*(26.67+DT)= SINKB6*30;





+ C2B7*(19+DT) +C3B7*(26.67+DT)= SINKB7*55;

CH13*6.67 + CW13*19.80 + A1C1*(10+DT) + A2C1*(10.5+DT) + A3C1*(11.11+DT) +

A4C1*(16.67+DT) + A5C1*(17.7+DT) + A6C1*(19+DT) + A7C1*(20+DT) +

A8C1*(20.88+DT) + A9C1*(22.6+DT) + A10C1*(24.01+DT) + B1C1*(11.67+DT) +

B2C1*(17.67+DT) + B3C1*(20+DT) + B4C1*(21+DT) + B5C1*(23+DT) + B6C1*(24+DT) +

B7C1*(40+DT) + B8C1*(75+DT) + C1C1*8.67 + C2C1*19 +C3C1*26.67= SINKC1*6.67;











!============================================================================;

! TOTAL FRESH SOURCE;

CHILLED_WATER = CH1 + CH2 + CH3 + CH4 + CH5 + CH6 + CH7 + CH8 + CH9 + CH10 +

CH11 + CH12 + CH13 + CH14 + CH15;

COOLING_WATER = CW1 + CW2 + CW3 + CW4 + CW5 + CW6 + CW7 + CW8 + CW9 + CW10 +

CW11 + CW12 + CW13 + CW14 + CW15;

! PIPING FLOWRATE LOWER BOUNDS (ONLY INTER-PLANT PIPING FLOWRATES ARE

CONSIDERED, INTRA-PLANT IS NEGLECTED);

179

A1B1>=LB*B_A1B1; A1B2>=LB*B_A1B2; A1B3>=LB*B_A1B3; A1B4>=LB*B_A1B4;

A1B5>=LB*B_A1B5; A1B6>=LB*B_A1B6; A1B7>=LB*B_A1B7; A1C1>=LB*B_A1C1;

A1C2>=LB*B_A1C2; A1C3>=LB*B_A1C3;



























A10C2>=LB*B_A10C2; A10C3>=LB*B_A10C3;

B1A1>=LB*B_B1A1; B1A2>=LB*B_B1A2; B1A3>=LB*B_B1A3; B1A4>=LB*B_B1A4;

B1A5>=LB*B_B1A5; B1C1>=LB*B_B1C1; B1C2>=LB*B_B1C2; B1C3>=LB*B_B1C3;















C1A1>=LB*B_C1A1; C1A2>=LB*B_C1A2; C1A3>=LB*B_C1A3; C1A4>=LB*B_C1A4;

C1A5>=LB*B_C1A5; C1B1>=LB*B_C1B1; C1B2>=LB*B_C1B2; C1B3>=LB*B_C1B3;

C1B4>=LB*B_C1B4; C1B5>=LB*B_C1B5; C1B6>=LB*B_C1B6; C1B7>=LB*B_C1B7;







180

! PIPING FLOWRATE UPPER BOUNDS (ONLY INTER-PLANT PIPING FLOWRATES ARE


A1B1<=SOURCEA1*B_A1B1; A1B2<=SOURCEA1*B_A1B2; A1B3<=SOURCEA1*B_A1B3;


A1B7<=SOURCEA1*B_A1B7; A1C1<=SOURCEA1*B_A1C1; A1C2<=SOURCEA1*B_A1C2;

A1C3<=SOURCEA1*B_A1C3;





































B1A1<=SOURCEB1*B_B1A1; B1A2<=SOURCEB1*B_B1A2; B1A3<=SOURCEB1*B_B1A3;

B1A4<=SOURCEB1*B_B1A4; B1A5<=SOURCEB1*B_B1A5; B1C1<=SOURCEB1*B_B1C1;

B1C2<=SOURCEB1*B_B1C2; B1C3<=SOURCEB1*B_B1C3;










181













C1A1<=SOURCEC1*B_C1A1; C1A2<=SOURCEC1*B_C1A2; C1A3<=SOURCEC1*B_C1A3;

C1A4<=SOURCEC1*B_C1A4; C1A5<=SOURCEC1*B_C1A5; C1B1<=SOURCEC1*B_C1B1;

C1B2<=SOURCEC1*B_C1B2; C1B3<=SOURCEC1*B_C1B3; C1B4<=SOURCEC1*B_C1B4;










! CONVERTING INTO BINARY VARIABLES;

@BIN(B_A1B1);@BIN(B_A1B2);@BIN(B_A1B3);@BIN(B_A1B4);@BIN(B_A1B5);@BIN(B_A1B6)

;@BIN(B_A1B7);@BIN(B_A1C1);@BIN(B_A1C2); @BIN(B_A1C3);

















@BIN(B_A10B1);@BIN(B_A10B2);@BIN(B_A10B3);@BIN(B_A10B4);@BIN(B_A10B5);@BIN(B_

A10B6);@BIN(B_A10B7);@BIN(B_A10C1);@BIN(B_A10C2); @BIN(B_A10C3);

@BIN(B_B1A1);@BIN(B_B1A2);@BIN(B_B1A3);@BIN(B_B1A4);@BIN(B_B1A5);@BIN(B_B1C1)

;@BIN(B_B1C2);@BIN(B_B1C3);







182









@BIN(B_C1A1);@BIN(B_C1A2);@BIN(B_C1A3);@BIN(B_C1A4);@BIN(B_C1A5);@BIN(B_C1B1)

;@BIN(B_C1B2);@BIN(B_C1B3);@BIN(B_C1B4);@BIN(B_C1B5);@BIN(B_C1B6);@BIN(B_C1B7

);



);



);

! PIPING COSTS FOR INTER-PLANT, PIPING COSTS FOR INTRA-PLANT IS NEGLECTED

(GIVE);

PC1 = (2*(A1B1 + A1B2 + A1B3 + A1B4 + A1B5 + A1B6 + A1B7 + A1C1 + A1C2 + A1C3)

+ 250*(B_A1B1 + B_A1B2 + B_A1B3 + B_A1B4 + B_A1B5 + B_A1B6 + B_A1B7 + B_A1C1

+ B_A1C2 + B_A1C3))*D*0.231;



+ B_A2C2 + B_A2C3))*D*0.231;



+ B_A3C2 + B_A3C3))*D*0.231;



+ B_A4C2 + B_A4C3))*D*0.231;



+ B_A5C2 + B_A5C3))*D*0.231;



+ B_A6C2 + B_A6C3))*D*0.231;



+ B_A7C2 + B_A7C3))*D*0.231;



+ B_A8C2 + B_A8C3))*D*0.231;



+ B_A9C2 + B_A9C3))*D*0.231;

PC10 = (2*(A10B1 + A10B2 + A10B3 + A10B4 + A10B5 + A10B6 + A10B7 + A10C1 +

A10C2 + A10C3) + 250*(B_A10B1 + B_A10B2 + B_A10B3 + B_A10B4 + B_A10B5 +

B_A10B6 + B_A10B7 + B_A10C1 + B_A10C2 + B_A10C3))*D*0.231;

PC11 = (2*(B1A1 + B1A2 + B1A3 + B1A4 + B1A5 + B1C1 + B1C2 +B1C3) +

250*(B_B1A1 + B_B1A2 + B_B1A3 + B_B1A4 + B_B1A5 + B_B1C1 + B_B1C2 +

B_B1C3))*D*0.231;

183



B_B2C3))*D*0.231;



B_B3C3))*D*0.231;



B_B4C3))*D*0.231;



B_B5C3))*D*0.231;



B_B6C3))*D*0.231;



B_B7C3))*D*0.231;



B_B8C3))*D*0.231;

PC19 = (2*(C1A1 + C1A2 + C1A3 + C1A4 + C1A5 + C1B1 + C1B2 + C1B3 + C1B4 +

C1B5 + C1B6 + C1B7) + 250*(B_C1A1 + B_C1A2 + B_C1A3 + B_C1A4 + B_C1A5 +

B_C1B1 + B_C1B2 + B_C1B3 + B_C1B4 + B_C1B5 + B_C1B6 + B_C1B7))*D*0.231;







! PIPING COSTS FOR INTER-PLANT, (RECEIVED);

PCR1 = (2*(B1A1 + B2A1 + B3A1 + B4A1 + B5A1 + B6A1 + B7A1 + B8A1 + C1A1 +

C2A1 + C3A1) + 250*(B_B1A1 + B_B2A1 + B_B3A1 + B_B4A1 + B_B5A1 + B_B6A1 +

B_B7A1 + B_B8A1 + B_C1A1 + B_C2A1 + B_C3A1))*D*0.231;













PCR6 = (2*(A1B1 + A2B1 + A3B1 + A4B1 + A5B1 + A6B1 + A7B1 + A8B1 + A9B1 +

A10B1 + C1B1 + C2B1 + C3B1) + 250*(B_A1B1 + B_A2B1 + B_A3B1 + B_A4B1 +

B_A5B1 + B_A6B1 + B_A7B1 + B_A8B1 + B_A9B1 + B_A10B1 + B_C1B1 + B_C2B1 +

B_C3B1))*D*0.231;




B_C3B2))*D*0.231;

184




B_C3B3))*D*0.231;




B_C3B4))*D*0.231;


A10B5 + C1B5 + C2B5 + C3B5) + 250*(B_A1B5 + B_A2B5 + B_A3B5 + B_A4B5 + B_A5B5

+ B_A6B5 + B_A7B5 + B_A8B5 + B_A9B5 + B_A10B5 + B_C1B5 + B_C2B5 +

B_C3B5))*D*0.231;




B_C3B6))*D*0.231;




B_C3B7))*D*0.231;

PCR13 = (2*(A1C1 + A2C1 + A3C1 + A4C1 + A5C1 + A6C1 + A7C1 + A8C1 + A9C1 +

A10C1 + B1C1 + B2C1 + B3C1 + B4C1 + B5C1 + B6C1 + B7C1 + B8C1) + 250*(B_A1C1

+ B_A2C1 + B_A3C1 + B_A4C1 + B_A5C1 + B_A6C1 + B_A7C1 + B_A8C1 + B_A9C1 +

B_A10C1 + B_B1C1 + B_B2C1 + B_B3C1 + B_B4C1 + B_B5C1 + B_B6C1 + B_B7C1 +

B_B8C1))*D*0.231;





B_B8C2))*D*0.231;





B_B8C3))*D*0.231;

PIPING_COSTS_A = (PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 + PC9 +

PC10)/2 + (PCR1 + PCR2 + PCR3 + PCR4 + PCR5)/2;

PIPING_COSTS_B = (PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 + PC18)/2 +

(PCR6 + PCR7 + PCR8 + PCR9 + PCR10 + PCR11 + PCR12)/2;

PIPING_COSTS_C = (PC19 + PC20 + PC21)/2 + (PCR13 + PCR14 + PCR15)/2;

! PLANT A, B, C GIVE;

A1B1 + A1B2 + A1B3 + A1B4 + A1B5 + A1B6 + A1B7 + A1C1 + A1C2 + A1C3 = GIVE_A1;









A10B1 + A10B2 + A10B3 + A10B4 + A10B5 + A10B6 + A10B7 + A10C1 + A10C2 + A10C3

= GIVE_A10;

B1A1 + B1A2 + B1A3 + B1A4 + B1A5 + B1C1 + B1C2 + B1C3 = GIVE_B1;


185








C1B7 = GIVE_C1;


C2B7 = GIVE_C2;


C3B7 = GIVE_C3;

! PLANT A, B, C EARN;

EARN_A=(GIVE_A1+GIVE_A2+GIVE_A3+GIVE_A4+GIVE_A5+GIVE_A6+GIVE_A7+GIVE_A8+GIVE_

A9+GIVE_A10)*0.06/4.18*330*24;

EARN_B=(GIVE_B1+GIVE_B2+GIVE_B3+GIVE_B4+GIVE_B5+GIVE_B6+GIVE_B7+GIVE_B8)*0.06

/4.18*330*24;

EARN_C=(GIVE_C1+GIVE_C2+GIVE_C3)*0.06/4.18*330*24;

! PLANT A, B ,C RECEIVED;

B1A1 + B2A1 + B3A1 + B4A1 + B5A1 + B6A1 + B7A1 + B8A1 + C1A1 + C2A1 +C3A1 =

REUSE_A1;


REUSE_A2;


REUSE_A3;


REUSE_A4;


REUSE_A5;

A1B1 + A2B1 + A3B1 + A4B1 + A5B1 + A6B1 + A7B1 + A8B1 + A9B1 + A10B1 + C1B1 +

C2B1 +C3B1 = REUSE_B1;













A1C1 + A2C1 + A3C1 + A4C1 + A5C1 + A6C1 + A7C1 + A8C1 + A9C1 + A10C1 + B1C1 +

B2C1 + B3C1 + B4C1 + B5C1 + B6C1 + B7C1 + B8C1 = REUSE_C1;





! PLANT A, B, C REUSE COSTS;

REUSE_COSTS_A=(REUSE_A1+REUSE_A2+REUSE_A3+REUSE_A4+REUSE_A5)*0.06/4.18*330*24;

REUSE_COSTS_B=(REUSE_B1+REUSE_B2+REUSE_B3+REUSE_B4+REUSE_B5+REUSE_B6+REUSE_B7

)*0.06/4.18*330*24;

REUSE_COSTS_C=(REUSE_C1+REUSE_C2+REUSE_C3)*0.06/4.18*330*24;

186

! FRESH CHILLED WATER FOR PLANT A,B,C;

F_CHILLED_WATER_A=CH1+CH2+CH3+CH4+CH5;

F_CHILLED_WATER_B=CH6+CH7+CH8+CH9+CH10+CH11+CH12;

F_CHILLED_WATER_C=CH13+CH14+CH15;

! FRESH VOOLING WATER FOR PLANT A,B,C;

F_COOLING_WATER_A=CW1+CW2+CW3+CW4+CW5;

F_COOLING_WATER_B=CW6+CW7+CW8+CW9+CW10+CW11+CW12;

F_COOLING_WATER_C=CW13+CW14+CW15;

LAMBDA>=0; LAMBDA<=1;

! FRESH CHILLED WATER PLANT A,B,C;

F_CHILLED_COSTS_A=(F_CHILLED_WATER_A*0.254/4.18*330*24);

F_CHILLED_COSTS_B=(F_CHILLED_WATER_B*0.254/4.18*330*24);

F_CHILLED_COSTS_C=(F_CHILLED_WATER_C*0.254/4.18*330*24);

! FRESHCOOLING WATER PLANT A,B,C;

F_COOLING_COSTS_A=(F_COOLING_WATER_A*0.15/4.18*330*24);

F_COOLING_COSTS_B=(F_COOLING_WATER_B*0.15/4.18*330*24);

F_COOLING_COSTS_C=(F_COOLING_WATER_C*0.15/4.18*330*24);

! WASTE COSTS;

WASTE_COSTS_A=(WWA1+WWA2+WWA3+WWA4+WWA5+WWA6+WWA7+WWA8+WWA9+WWA10)*(0.1/4.18*

330*24);

WASTE_COSTS_B=(WWB1+WWB2+WWB3+WWB4+WWB5+WWB6+WWB7+WWB8)*(0.1/4.18*330*24);

WASTE_COSTS_C=(WWC1+WWC2+WWC3)*(0.1/4.18*330*24);

! COST OF PLANT A,B,C;

COSTS_A=(F_CHILLED_COSTS_A)+(F_COOLING_COSTS_A)+(PIPING_COSTS_A)+WASTE_COSTS_

A+REUSE_COSTS_A-EARN_A;

COSTS_B=(F_CHILLED_COSTS_B)+(F_COOLING_COSTS_B)+(PIPING_COSTS_B)+WASTE_COSTS_

B+REUSE_COSTS_B-EARN_B;

COSTS_C=(F_CHILLED_COSTS_C)+(F_COOLING_COSTS_C)+(PIPING_COSTS_C)+WASTE_COSTS_

C+REUSE_COSTS_C-EARN_C;

! LOWER AND UPPER BOUND OF EACH PLANT COSTS;

COSTS_A < 1712637; COSTS_A >= FUZZY_A;

COSTS_B < 835333.2; COSTS_B >= FUZZY_B;

COSTS_C < 439532; COSTS_C >= FUZZY_C;

! FUZZY;

FUZZY_A=1563262;

FUZZY_B=685958;

FUZZY_C=290157;

! CALCULATING FOR LAMBDA OF EACH PLANT;

LAMBDA_A = 1-((COSTS_A-FUZZY_A)/(1712637-FUZZY_A));

LAMBDA_B = 1-((COSTS_B-FUZZY_B)/(835333.2-FUZZY_B));

LAMBDA_C = 1-((COSTS_C-FUZZY_C)/(439532-FUZZY_C));

! LAMBDA CANNOT EXCEED LAMBDA OF EACH PLANT;

LAMBDA <= LAMBDA_A;

LAMBDA <= LAMBDA_B;

LAMBDA <= LAMBDA_C;

187


LINGO ver13 mathematical modelling codes for Pareto optimal multi-period IPCCWNs

MAX = LAMBDA;

FCCW = CHILLED_WATER_P1 + COOLING_WATER_P1 + CHILLED_WATER_P2 +

COOLING_WATER_P2 + CHILLED_WATER_P3 + COOLING_WATER_P3;

TOTAL_COSTS = COSTS_A_P1 + COSTS_B_P1 + COSTS_C_P1 + COSTS_A_P2 + COSTS_B_P2

+ COSTS_C_P2 + COSTS_A_P3 + COSTS_B_P3 + COSTS_C_P3;


LB = 0;


D = 100;

DT = 0.5;

!============================================================================;

! PERIOD 1;



SOURCEA1_P1=939.75; SOURCEA2_P1=130.58; SOURCEA3_P1=130.92;

SOURCEA4_P1=318.51; SOURCEA5_P1=1078.82; SOURCEA6_P1=90.7; SOURCEA7_P1=144.22;

SOURCEA8_P1=146.93; SOURCEA9_P1=26.75; SOURCEA10_P1=107.84;


SOURCEB1_P1=209; SOURCEB2_P1=418; SOURCEB3_P1=250.8; SOURCEB4_P1=125.40;

SOURCEB5_P1=83.60; SOURCEB6_P1=459.80; SOURCEB7_P1=1881; SOURCEB8_P1=2173.6;


SOURCEC1_P1=551.76; SOURCEC2_P1=968.58; SOURCEC3_P1=304.9;


A1A1_P1 + A1A2_P1 + A1A3_P1 + A1A4_P1 + A1A5_P1 + A1B1_P1 + A1B2_P1 + A1B3_P1

+ A1B4_P1 + A1B5_P1 + A1B6_P1 + A1B7_P1 + A1C1_P1 + A1C2_P1 + A1C3_P1 +

WWA1_P1 = SOURCEA1_P1;



















188







A10A1_P1 + A10A2_P1 + A10A3_P1 + A10A4_P1 + A10A5_P1 + A10B1_P1 + A10B2_P1 +

A10B3_P1 + A10B4_P1 + A10B5_P1 + A10B6_P1 + A10B7_P1 + A10C1_P1 + A10C2_P1 +

A10C3_P1 + WWA10_P1 = SOURCEA10_P1;

B1A1_P1 + B1A2_P1 + B1A3_P1 + B1A4_P1 + B1A5_P1 + B1B1_P1 + B1B2_P1 + B1B3_P1

+ B1B4_P1 + B1B5_P1 + B1B6_P1 + B1B7_P1 + B1C1_P1 + B1C2_P1 + B1C3_P1 +

WWB1_P1 = SOURCEB1_P1;






















C1A1_P1 + C1A2_P1 + C1A3_P1 + C1A4_P1 + C1A5_P1 + C1B1_P1 + C1B2_P1 + C1B3_P1

+ C1B4_P1 + C1B5_P1 + C1B6_P1 + C1B7_P1 + C1C1_P1 + C1C2_P1 + C1C3_P1 +

WWC1_P1 = SOURCEC1_P1;







!============================================================================;



SINKA1_P1=2528.31; SINKA2_P1=41.72; SINKA3_P1=175.48; SINKA4_P1=234.92;

SINKA5_P1=134.59;


SINKB1_P1=627; SINKB2_P1=125.40; SINKB3_P1=250.80; SINKB4_P1=543.4;

SINKB5_P1=836; SINKB6_P1=1964.6; SINKB7_P1=1254;


SINKC1_P1=500.81; SINKC2_P1=645.53; SINKC3_P1=678.90;


CH1_P1 + CW1_P1 + A1A1_P1 + A2A1_P1 + A3A1_P1 + A4A1_P1 + A5A1_P1 + A6A1_P1 +

A7A1_P1 + A8A1_P1 + A9A1_P1 + A10A1_P1 + B1A1_P1 + B2A1_P1 + B3A1_P1 +

189

B4A1_P1 + B5A1_P1 + B6A1_P1 + B7A1_P1 + B8A1_P1 + C1A1_P1 + C2A1_P1 + C3A1_P1

= SINKA1_P1;




= SINKA2_P1;




= SINKA3_P1;




= SINKA4_P1;




= SINKA5_P1;

CH6_P1 + CW6_P1 + A1B1_P1 + A2B1_P1 + A3B1_P1 + A4B1_P1 + A5B1_P1 + A6B1_P1 +

A7B1_P1 + A8B1_P1 + A9B1_P1 + A10B1_P1 + B1B1_P1 + B2B1_P1 + B3B1_P1 +

B4B1_P1 + B5B1_P1 + B6B1_P1 + B7B1_P1 + B8B1_P1 + C1B1_P1 + C2B1_P1 + C3B1_P1

= SINKB1_P1;




= SINKB2_P1;




= SINKB3_P1;




= SINKB4_P1;

CH10_P1 + CW10_P1 + A1B5_P1 + A2B5_P1 + A3B5_P1 + A4B5_P1 + A5B5_P1 + A6B5_P1

+ A7B5_P1 + A8B5_P1 + A9B5_P1 + A10B5_P1 + B1B5_P1 + B2B5_P1 + B3B5_P1 +


= SINKB5_P1;




= SINKB6_P1;




= SINKB7_P1;

CH13_P1 + CW13_P1 + A1C1_P1 + A2C1_P1 + A3C1_P1 + A4C1_P1 + A5C1_P1 + A6C1_P1

+ A7C1_P1 + A8C1_P1 + A9C1_P1 + A10C1_P1 + B1C1_P1 + B2C1_P1 + B3C1_P1 +

B4C1_P1 + B5C1_P1 + B6C1_P1 + B7C1_P1 + B8C1_P1 + C1C1_P1 + C2C1_P1 + C3C1_P1

= SINKC1_P1;




= SINKC2_P1;



190


= SINKC3_P1;


CH1_P1*6.67 + CW1_P1*19.80 + A1A1_P1*10 + A2A1_P1*10.5 + A3A1_P1*11.11 +

A4A1_P1*16.67 + A5A1_P1*17.7 + A6A1_P1*19 + A7A1_P1*20 + A8A1_P1*20.88 +

A9A1_P1*22.6 + A10A1_P1*24.01 + B1A1_P1*(11.67+DT) + B2A1_P1*(17.67+DT) +

B3A1_P1*(20+DT) + B4A1_P1*(21+DT) + B5A1_P1*(23+DT) + B6A1_P1*(24+DT) +

B7A1_P1*(40+DT) + B8A1_P1*(75+DT) + C1A1_P1*(8.67+DT) + C2A1_P1*(19+DT) +

C3A1_P1*(26.67+DT)= SINKA1_P1*6.67;






C3A2_P1*(26.67+DT)= SINKA2_P1*8;






C3A3_P1*(26.67+DT)= SINKA3_P1*10;






C3A4_P1*(26.67+DT)= SINKA4_P1*15;






C3A5_P1*(26.67+DT)= SINKA5_P1*17;

CH6_P1*6.67 + CW6_P1*19.80 + A1B1_P1*(10+DT) + A2B1_P1*(10.5+DT) +

A3B1_P1*(11.11+DT) + A4B1_P1*(16.67+DT) + A5B1_P1*(17.7+DT) + A6B1_P1*(19+DT)

+ A7B1_P1*(20+DT) + A8B1_P1*(20.88+DT) + A9B1_P1*(22.6+DT) +

A10B1_P1*(24.01+DT) + B1B1_P1*11.67 + B2B1_P1*17.67 + B3B1_P1*20 + B4B1_P1*21

+ B5B1_P1*23 + B6B1_P1*24 + B7B1_P1*40 + B8B1_P1*75 + C1B1_P1*(8.67+DT) +

C2B1_P1*(19+DT) + C3B1_P1*(26.67+DT)= SINKB1_P1*6.67;






C2B2_P1*(19+DT) + C3B2_P1*(26.67+DT)= SINKB2_P1*8;











191





















CH13_P1*6.67 + CW13_P1*19.80 + A1C1_P1*(10+DT) + A2C1_P1*(10.5+DT) +

A3C1_P1*(11.11+DT) + A4C1_P1*(16.67+DT) + A5C1_P1*(17.7+DT) + A6C1_P1*(19+DT)

+ A7C1_P1*(20+DT) + A8C1_P1*(20.88+DT) + A9C1_P1*(22.6+DT) +

A10C1_P1*(24.01+DT) + B1C1_P1*(11.67+DT) + B2C1_P1*(17.67+DT) +

B3C1_P1*(20+DT) + B4C1_P1*(21+DT) + B5C1_P1*(23+DT) + B6C1_P1*(24+DT) +

B7C1_P1*(40+DT) + B8C1_P1*(75+DT) + C1C1_P1*8.67 + C2C1_P1*19 +

C3C1_P1*26.67= SINKC1_P1*6.67;







C3C2_P1*26.67= SINKC2_P1*9.67;







C3C3_P1*26.67= SINKC3_P1*16.67;

!============================================================================;


CHILLED_WATER_P1 = CH1_P1 + CH2_P1 + CH3_P1 + CH4_P1 + CH5_P1 + CH6_P1 +

CH7_P1 + CH8_P1 + CH9_P1 + CH10_P1 + CH11_P1 + CH12_P1 + CH13_P1 + CH14_P1 +

CH15_P1;

COOLING_WATER_P1 = CW1_P1 + CW2_P1 + CW3_P1 + CW4_P1 + CW5_P1 + CW6_P1 +

CW7_P1 + CW8_P1 + CW9_P1 + CW10_P1 + CW11_P1 + CW12_P1 + CW13_P1 + CW14_P1 +

CW15_P1;



A1B1_P1>=LB*B_A1B1_P1; A1B2_P1>=LB*B_A1B2_P1; A1B3_P1>=LB*B_A1B3_P1;


A1B7_P1>=LB*B_A1B7_P1; A1C1_P1>=LB*B_A1C1_P1; A1C2_P1>=LB*B_A1C2_P1;

A1C3_P1>=LB*B_A1C3_P1;

192




































A10C3_P1>=LB*B_A10C3_P1;

B1A1_P1>=LB*B_B1A1_P1; B1A2_P1>=LB*B_B1A2_P1; B1A3_P1>=LB*B_B1A3_P1;

B1A4_P1>=LB*B_B1A4_P1; B1A5_P1>=LB*B_B1A5_P1; B1C1_P1>=LB*B_B1C1_P1;

B1C2_P1>=LB*B_B1C2_P1; B1C3_P1>=LB*B_B1C3_P1;
















193







C1A1_P1>=LB*B_C1A1_P1; C1A2_P1>=LB*B_C1A2_P1; C1A3_P1>=LB*B_C1A3_P1;

C1A4_P1>=LB*B_C1A4_P1; C1A5_P1>=LB*B_C1A5_P1; C1B1_P1>=LB*B_C1B1_P1;

C1B2_P1>=LB*B_C1B2_P1; C1B3_P1>=LB*B_C1B3_P1; C1B4_P1>=LB*B_C1B4_P1;












A1B1_P1<=SOURCEA1_P1*B_A1B1_P1; A1B2_P1<=SOURCEA1_P1*B_A1B2_P1;



A1B7_P1<=SOURCEA1_P1*B_A1B7_P1; A1C1_P1<=SOURCEA1_P1*B_A1C1_P1;

A1C2_P1<=SOURCEA1_P1*B_A1C2_P1; A1C3_P1<=SOURCEA1_P1*B_A1C3_P1;































194
















B1A1_P1<=SOURCEB1_P1*B_B1A1_P1; B1A2_P1<=SOURCEB1_P1*B_B1A2_P1;


B1A5_P1<=SOURCEB1_P1*B_B1A5_P1; B1C1_P1<=SOURCEB1_P1*B_B1C1_P1;

B1C2_P1<=SOURCEB1_P1*B_B1C2_P1; B1C3_P1<=SOURCEB1_P1*B_B1C3_P1;





























C1A1_P1<=SOURCEC1_P1*B_C1A1_P1; C1A2_P1<=SOURCEC1_P1*B_C1A2_P1;


C1A5_P1<=SOURCEC1_P1*B_C1A5_P1; C1B1_P1<=SOURCEC1_P1*B_C1B1_P1;

C1B2_P1<=SOURCEC1_P1*B_C1B2_P1; C1B3_P1<=SOURCEC1_P1*B_C1B3_P1;



195














@BIN(B_A1B1_P1);@BIN(B_A1B2_P1);@BIN(B_A1B3_P1);@BIN(B_A1B4_P1);@BIN(B_A1B5_P

1);@BIN(B_A1B6_P1);@BIN(B_A1B7_P1);@BIN(B_A1C1_P1);@BIN(B_A1C2_P1);

@BIN(B_A1C3_P1);



@BIN(B_A2C3_P1);



@BIN(B_A3C3_P1);



@BIN(B_A4C3_P1);



@BIN(B_A5C3_P1);



@BIN(B_A6C3_P1);



@BIN(B_A7C3_P1);



@BIN(B_A8C3_P1);



@BIN(B_A9C3_P1);

@BIN(B_A10B1_P1);@BIN(B_A10B2_P1);@BIN(B_A10B3_P1);@BIN(B_A10B4_P1);@BIN(B_A1

0B5_P1);@BIN(B_A10B6_P1);@BIN(B_A10B7_P1);@BIN(B_A10C1_P1);@BIN(B_A10C2_P1);

@BIN(B_A10C3_P1);

@BIN(B_B1A1_P1);@BIN(B_B1A2_P1);@BIN(B_B1A3_P1);@BIN(B_B1A4_P1);@BIN(B_B1A5_P

1);@BIN(B_B1C1_P1);@BIN(B_B1C2_P1);@BIN(B_B1C3_P1);











196





@BIN(B_C1A1_P1);@BIN(B_C1A2_P1);@BIN(B_C1A3_P1);@BIN(B_C1A4_P1);@BIN(B_C1A5_P

1);@BIN(B_C1B1_P1);@BIN(B_C1B2_P1);@BIN(B_C1B3_P1);@BIN(B_C1B4_P1);@BIN(B_C1B

5_P1);@BIN(B_C1B6_P1);@BIN(B_C1B7_P1);








(GIVE);

PC1_P1 = (2*(A1B1_P1 + A1B2_P1 + A1B3_P1 + A1B4_P1 + A1B5_P1 + A1B6_P1 +

A1B7_P1 + A1C1_P1 + A1C2_P1 + A1C3_P1 ) + 250*(B_A1B1_P1 + B_A1B2_P1 +

B_A1B3_P1 + B_A1B4_P1 + B_A1B5_P1 + B_A1B6_P1 + B_A1B7_P1 + B_A1C1_P1 +

B_A1C2_P1 + B_A1C3_P1))*D*0.231;




B_A2C2_P1 + B_A2C3_P1))*D*0.231;




B_A3C2_P1 + B_A3C3_P1))*D*0.231;




B_A4C2_P1 + B_A4C3_P1))*D*0.231;




B_A5C2_P1 + B_A5C3_P1))*D*0.231;




B_A6C2_P1 + B_A6C3_P1))*D*0.231;




B_A7C2_P1 + B_A7C3_P1))*D*0.231;




B_A8C2_P1 + B_A8C3_P1))*D*0.231;




B_A9C2_P1 + B_A9C3_P1))*D*0.231;

PC10_P1 = (2*(A10B1_P1 + A10B2_P1 + A10B3_P1 + A10B4_P1 + A10B5_P1 + A10B6_P1

+ A10B7_P1 + A10C1_P1 + A10C2_P1 + A10C3_P1 ) + 250*(B_A10B1_P1 + B_A10B2_P1

+ B_A10B3_P1 + B_A10B4_P1 + B_A10B5_P1 + B_A10B6_P1 + B_A10B7_P1 + B_A10C1_P1

+ B_A10C2_P1 + B_A10C3_P1))*D*0.231;

197

PC11_P1 = (2*(B1A1_P1 + B1A2_P1 + B1A3_P1 + B1A4_P1 + B1A5_P1 + B1C1_P1 +

B1C2_P1 + B1C3_P1) + 250*(B_B1A1_P1 + B_B1A2_P1 + B_B1A3_P1 + B_B1A4_P1 +

B_B1A5_P1 + B_B1C1_P1 + B_B1C2_P1 + B_B1C3_P1))*D*0.231;






















PC19_P1 = (2*(C1A1_P1 + C1A2_P1 + C1A3_P1 + C1A4_P1 + C1A5_P1 + C1B1_P1 +

C1B2_P1 + C1B3_P1 + C1B4_P1 + C1B5_P1 + C1B6_P1 + C1B7_P1 ) + 250*(B_C1A1_P1

+ B_C1A2_P1 + B_C1A3_P1 + B_C1A4_P1 + B_C1A5_P1 + B_C1B1_P1 + B_C1B2_P1 +

B_C1B3_P1 + B_C1B4_P1 + B_C1B5_P1 + B_C1B6_P1 + B_C1B7_P1))*D*0.231;










PCR1_P1 = (2*(B1A1_P1 + B2A1_P1 + B3A1_P1 + B4A1_P1 + B5A1_P1 + B6A1_P1 +

B7A1_P1 + B8A1_P1 + C1A1_P1 + C2A1_P1 + C3A1_P1) + 250*(B_B1A1_P1 + B_B2A1_P1

+ B_B3A1_P1 + B_B4A1_P1 + B_B5A1_P1 + B_B6A1_P1 + B_B7A1_P1 + B_B8A1_P1 +

B_C1A1_P1 + B_C2A1_P1 + B_C3A1_P1))*D*0.231;




B_C1A2_P1 + B_C2A2_P1 + B_C3A2_P1))*D*0.231;




B_C1A3_P1 + B_C2A3_P1 + B_C3A3_P1))*D*0.231;




B_C1A4_P1 + B_C2A4_P1 + B_C3A4_P1))*D*0.231;

198




B_C1A5_P1 + B_C2A5_P1 + B_C3A5_P1))*D*0.231;

PCR6_P1 = (2*(A1B1_P1 + A2B1_P1 + A3B1_P1 + A4B1_P1 + A5B1_P1 + A6B1_P1 +

A7B1_P1 + A8B1_P1 + A9B1_P1 + A10B1_P1 + C1B1_P1 + C2B1_P1 + C3B1_P1) +

250*(B_A1B1_P1 + B_A2B1_P1 + B_A3B1_P1 + B_A4B1_P1 + B_A5B1_P1 + B_A6B1_P1 +

B_A7B1_P1 + B_A8B1_P1 + B_A9B1_P1 + B_A10B1_P1 + B_C1B1_P1 + B_C2B1_P1 +

B_C3B1_P1))*D*0.231;





B_C3B2_P1))*D*0.231;





B_C3B3_P1))*D*0.231;





B_C3B4_P1))*D*0.231;





B_C3B5_P1))*D*0.231;





B_C3B6_P1))*D*0.231;





B_C3B7_P1))*D*0.231;

PCR13_P1 = (2*(A1C1_P1 + A2C1_P1 + A3C1_P1 + A4C1_P1 + A5C1_P1 + A6C1_P1 +

A7C1_P1 + A8C1_P1 + A9C1_P1 + A10C1_P1 + B1C1_P1 + B2C1_P1 + B3C1_P1 +

B4C1_P1 + B5C1_P1 + B6C1_P1 + B7C1_P1 + B8C1_P1) + 250*(B_A1C1_P1 + B_A2C1_P1

+ B_A3C1_P1 + B_A4C1_P1 + B_A5C1_P1 + B_A6C1_P1 + B_A7C1_P1 + B_A8C1_P1 +

B_A9C1_P1 + B_A10C1_P1 + B_B1C1_P1 + B_B2C1_P1 + B_B3C1_P1 + B_B4C1_P1 +

B_B5C1_P1 + B_B6C1_P1 + B_B7C1_P1 + B_B8C1_P1))*D*0.231;











199



PIPING_COSTS_A_P1 = (PC1_P1 + PC2_P1 + PC3_P1 + PC4_P1 + PC5_P1 + PC6_P1 +

PC7_P1 + PC8_P1 + PC9_P1 + PC10_P1)/2 + (PCR1_P1 + PCR2_P1 + PCR3_P1 +

PCR4_P1 + PCR5_P1)/2;

PIPING_COSTS_B_P1 = (PC11_P1 + PC12_P1 + PC13_P1 + PC14_P1 + PC15_P1 +

PC16_P1 + PC17_P1 + PC18_P1)/2 + (PCR6_P1 + PCR7_P1 + PCR8_P1 + PCR9_P1 +

PCR10_P1 + PCR11_P1 + PCR12_P1)/2;

PIPING_COSTS_C_P1 = (PC19_P1 + PC20_P1 + PC21_P1)/2 + (PCR13_P1 + PCR14_P1 +

PCR15_P1)/2;


A1B1_P1 + A1B2_P1 + A1B3_P1 + A1B4_P1 + A1B5_P1 + A1B6_P1 + A1B7_P1 + A1C1_P1

+ A1C2_P1 + A1C3_P1 = GIVE_A1_P1;


+ A2C2_P1 + A2C3_P1 = GIVE_A2_P1;


+ A3C2_P1 + A3C3_P1 = GIVE_A3_P1;


+ A4C2_P1 + A4C3_P1 = GIVE_A4_P1;


+ A5C2_P1 + A5C3_P1 = GIVE_A5_P1;


+ A6C2_P1 + A6C3_P1 = GIVE_A6_P1;


+ A7C2_P1 + A7C3_P1 = GIVE_A7_P1;


+ A8C2_P1 + A8C3_P1 = GIVE_A8_P1;


+ A9C2_P1 + A9C3_P1 = GIVE_A9_P1;

A10B1_P1 + A10B2_P1 + A10B3_P1 + A10B4_P1 + A10B5_P1 + A10B6_P1 + A10B7_P1 +

A10C1_P1 + A10C2_P1 + A10C3_P1 = GIVE_A10_P1;

B1A1_P1 + B1A2_P1 + B1A3_P1 + B1A4_P1 + B1A5_P1 + B1C1_P1 + B1C2_P1 + B1C3_P1

= GIVE_B1_P1;


= GIVE_B2_P1;


= GIVE_B3_P1;


= GIVE_B4_P1;


= GIVE_B5_P1;


= GIVE_B6_P1;


= GIVE_B7_P1;


= GIVE_B8_P1;


+ C1B4_P1 + C1B5_P1 + C1B6_P1 + C1B7_P1 = GIVE_C1_P1;






200

EARN_A_P1=(GIVE_A1_P1 + GIVE_A2_P1 + GIVE_A3_P1 + GIVE_A4_P1 + GIVE_A5_P1 +

GIVE_A6_P1 + GIVE_A7_P1 + GIVE_A8_P1 + GIVE_A9_P1 +

GIVE_A10_P1)*0.08/4.18*110*24;

EARN_B_P1=(GIVE_B1_P1 + GIVE_B2_P1 + GIVE_B3_P1 + GIVE_B4_P1 + GIVE_B5_P1 +

GIVE_B6_P1 + GIVE_B7_P1 + GIVE_B8_P1)*0.08/4.18*110*24;

EARN_C_P1=(GIVE_C1_P1 + GIVE_C2_P1 + GIVE_C3_P1)*0.08/4.18*110*24;


B1A1_P1 + B2A1_P1 + B3A1_P1 + B4A1_P1 + B5A1_P1 + B6A1_P1 + B7A1_P1 + B8A1_P1

+ C1A1_P1 + C2A1_P1 + C3A1_P1 = REUSE_A1_P1;









A1B1_P1 + A2B1_P1 + A3B1_P1 + A4B1_P1 + A5B1_P1 + A6B1_P1 + A7B1_P1 + A8B1_P1

+ A9B1_P1 + A10B1_P1 + C1B1_P1 + C2B1_P1 + C3B1_P1 = REUSE_B1_P1;













A1C1_P1 + A2C1_P1 + A3C1_P1 + A4C1_P1 + A5C1_P1 + A6C1_P1 + A7C1_P1 + A8C1_P1

+ A9C1_P1 + A10C1_P1 + B1C1_P1 + B2C1_P1 + B3C1_P1 + B4C1_P1 + B5C1_P1 +

B6C1_P1 + B7C1_P1 + B8C1_P1 = REUSE_C1_P1;








REUSE_COSTS_A_P1 =(REUSE_A1_P1 + REUSE_A2_P1 + REUSE_A3_P1 + REUSE_A4_P1 +

REUSE_A5_P1)*0.08/4.18*110*24;

REUSE_COSTS_B_P1 =(REUSE_B1_P1 + REUSE_B2_P1 + REUSE_B3_P1 + REUSE_B4_P1 +

REUSE_B5_P1 + REUSE_B6_P1 + REUSE_B7_P1)*0.08/4.18*110*24;

REUSE_COSTS_C_P1 =(REUSE_C1_P1 + REUSE_C2_P1 + REUSE_C3_P1)*0.08/4.18*110*24;


F_CHILLED_WATER_A_P1 = CH1_P1 + CH2_P1 + CH3_P1 + CH4_P1 + CH5_P1;

F_CHILLED_WATER_B_P1 = CH6_P1 + CH7_P1 + CH8_P1 + CH9_P1 + CH10_P1 + CH11_P1

+ CH12_P1;

F_CHILLED_WATER_C_P1 = CH13_P1 + CH14_P1 + CH15_P1;


F_COOLING_WATER_A_P1 = CW1_P1 + CW2_P1 + CW3_P1 + CW4_P1 + CW5_P1;

201

F_COOLING_WATER_B_P1 = CW6_P1 + CW7_P1 + CW8_P1 + CW9_P1 + CW10_P1 + CW11_P1

+ CW12_P1;

F_COOLING_WATER_C_P1 = CW13_P1 + CW14_P1 + CW15_P1;


F_CHILLED_COSTS_A_P1 =(F_CHILLED_WATER_A_P1*0.654/4.18*110*24);

F_CHILLED_COSTS_B_P1 =(F_CHILLED_WATER_B_P1*0.654/4.18*110*24);

F_CHILLED_COSTS_C_P1 =(F_CHILLED_WATER_C_P1*0.654/4.18*110*24);


F_COOLING_COSTS_A_P1 =(F_COOLING_WATER_A_P1*0.25/4.18*110*24);

F_COOLING_COSTS_B_P1 =(F_COOLING_WATER_B_P1*0.25/4.18*110*24);

F_COOLING_COSTS_C_P1 =(F_COOLING_WATER_C_P1*0.25/4.18*110*24);

! WASTE COSTS;

WASTE_COSTS_A_P1 =(WWA1_P1 + WWA2_P1 + WWA3_P1 + WWA4_P1 + WWA5_P1 + WWA6_P1

+ WWA7_P1 + WWA8_P1 + WWA9_P1 + WWA10_P1)*(0.1/4.18*110*24);

WASTE_COSTS_B_P1 =(WWB1_P1 + WWB2_P1 + WWB3_P1 + WWB4_P1 + WWB5_P1 + WWB6_P1

+ WWB7_P1 + WWB8_P1)*(0.1/4.18*110*24);

WASTE_COSTS_C_P1 =(WWC1_P1 + WWC2_P1 + WWC3_P1)*(0.1/4.18*110*24);


COSTS_A_P1

=(F_CHILLED_COSTS_A_P1)+(F_COOLING_COSTS_A_P1)+(PIPING_COSTS_A_P1)+(WASTE_COS

TS_A_P1)+(REUSE_COSTS_A_P1)-EARN_A_P1;

COSTS_B_P1

=(F_CHILLED_COSTS_B_P1)+(F_COOLING_COSTS_B_P1)+(PIPING_COSTS_B_P1)+(WASTE_COS

TS_B_P1)+(REUSE_COSTS_B_P1)-EARN_B_P1;

COSTS_C_P1

=(F_CHILLED_COSTS_C_P1)+(F_COOLING_COSTS_C_P1)+(PIPING_COSTS_C_P1)+(WASTE_COS

TS_C_P1)+(REUSE_COSTS_C_P1)-EARN_C_P1;

!============================================================================;

! PERIOD 2;



SOURCEA1_P2=836; SOURCEA2_P2=1045; SOURCEA3_P2=668.8; SOURCEA4_P2=752.4;

SOURCEA5_P2=376.2; SOURCEA6_P2=627; SOURCEA7_P2=209;


SOURCEB1_P2=209; SOURCEB2_P2=2424.4; SOURCEB3_P2=710.6; SOURCEB4_P2=459.8;

SOURCEB5_P2=292.6;


SOURCEC1_P2=794.2; SOURCEC2_P2=1881; SOURCEC3_P2=501.6; SOURCEC4_P2=376.2;



+ A1B4_P2 + A1B5_P2 + A1C1_P2 + A1C2_P2 + A1C3_P2 + A1C4_P2 + WWA1_P2 =

SOURCEA1_P2;



SOURCEA2_P2;



SOURCEA3_P2;



SOURCEA4_P2;

202



SOURCEA5_P2;



SOURCEA6_P2;



SOURCEA7_P2;


+ B1B4_P2 + B1B5_P2 + B1C1_P2 + B1C2_P2 + B1C3_P2 + B1C4_P2 + WWB1_P2 =

SOURCEB1_P2;



SOURCEB2_P2;



SOURCEB3_P2;



SOURCEB4_P2;



SOURCEB5_P2;


+ C1B4_P2 + C1B5_P2 + C1C1_P2 + C1C2_P2 + C1C3_P2 + C1C4_P2 + WWC1_P2 =

SOURCEC1_P2;



SOURCEC2_P2;



SOURCEC3_P2;



SOURCEC4_P2;

!============================================================================;



SINKA1_P2=1045; SINKA2_P2=627; SINKA3_P2=1254; SINKA4_P2=836; SINKA5_P2=752.4;


SINKB1_P2=627; SINKB2_P2=836; SINKB3_P2=1170.4; SINKB4_P2=710.6;

SINKB5_P2=752.4;


SINKC1_P2=1086.8; SINKC2_P2=1588.4; SINKC3_P2=501.6; SINKC4_P2=376.2;



A7A1_P2 + B1A1_P2 + B2A1_P2 + B3A1_P2 + B4A1_P2 + B5A1_P2 + C1A1_P2 + C2A1_P2

+ C3A1_P2 + C4A1_P2 = SINKA1_P2;



+ C3A2_P2 + C4A2_P2 = SINKA2_P2;

203



+ C3A3_P2 + C4A3_P2 = SINKA3_P2;



+ C3A4_P2 + C4A4_P2 = SINKA4_P2;



+ C3A5_P2 + C4A5_P2 = SINKA5_P2;


A7B1_P2 + B1B1_P2 + B2B1_P2 + B3B1_P2 + B4B1_P2 + B5B1_P2 + C1B1_P2 + C2B1_P2

+ C3B1_P2 + C4B1_P2 = SINKB1_P2;



+ C3B2_P2 + C4B2_P2 = SINKB2_P2;



+ C3B3_P2 + C4B3_P2 = SINKB3_P2;



+ C3B4_P2 + C4B4_P2 = SINKB4_P2;


+ A7B5_P2 + B1B5_P2 + B2B5_P2 + B3B5_P2 + B4B5_P2 + B5B5_P2 + C1B5_P2 +

C2B5_P2 + C3B5_P2 + C4B5_P2 = SINKB5_P2;


+ A7C1_P2 + B1C1_P2 + B2C1_P2 + B3C1_P2 + B4C1_P2 + B5C1_P2 + C1C1_P2 +

C2C1_P2 + C3C1_P2 + C4C1_P2 = SINKC1_P2;











CH1_P2*6 + CW1_P2*20 + A1A1_P2*10 + A2A1_P2*13.5 + A3A1_P2*15 + A4A1_P2*17 +

A5A1_P2*19.5 + A6A1_P2*24.5 + A7A1_P2*36 + B1A1_P2*(10+DT) + B2A1_P2*(14.5+DT)

+ B3A1_P2*(20+DT) + B4A1_P2*(30+DT) + B5A1_P2*(32+DT) + C1A1_P2*(11.5+DT) +

C2A1_P2*(12.5+DT) + C3A1_P2*(23.6+DT) + C4A1_P2*(29.8+DT) = SINKA1_P2*6;















204



CH6_P2*6 + CW6_P2*20 + A1B1_P2*(10+DT) + A2B1_P2*(13.5+DT) + A3B1_P2*(15+DT)

+ A4B1_P2*(17+DT) + A5B1_P2*(19.5+DT) + A6B1_P2*(24.5+DT) + A7B1_P2*(36+DT) +

B1B1_P2*10 + B2B1_P2*14.5 + B3B1_P2*20 + B4B1_P2*30 + B5B1_P2*32 +

C1B1_P2*(11.5+DT) + C2B1_P2*(12.5+DT) + C3B1_P2*(23.6+DT) + C4B1_P2*(29.8+DT)

= SINKB1_P2*6;





= SINKB2_P2*7;





= SINKB3_P2*10;





= SINKB4_P2*17;





= SINKB5_P2*20;

CH11_P2*6 + CW11_P2*20 + A1C1_P2*(10+DT) + A2C1_P2*(13.5+DT) + A3C1_P2*(15+DT)

+ A4C1_P2*(17+DT) + A5C1_P2*(19.5+DT) + A6C1_P2*(24.5+DT) + A7C1_P2*(36+DT) +

B1C1_P2*(10+DT) + B2C1_P2*(14.5+DT) + B3C1_P2*(20+DT) + B4C1_P2*(30+DT) +

B5C1_P2*(32+DT) + C1C1_P2*11.5 + C2C1_P2*12.5 + C3C1_P2*23.6 + C4C1_P2*29.8 =

SINKC1_P2*6;





SINKC2_P2*9;





SINKC3_P2*17;





SINKC4_P2*20;

!============================================================================;



CH7_P2 + CH8_P2 + CH9_P2 + CH10_P2 + CH11_P2 + CH12_P2 + CH13_P2 + CH14_P2;


CW7_P2 + CW8_P2 + CW9_P2 + CW10_P2 + CW11_P2 + CW12_P2 + CW13_P2 + CW14_P2;

205




A1B4_P2>=LB*B_A1B4_P2; A1B5_P2>=LB*B_A1B5_P2; A1C1_P2>=LB*B_A1C1_P2;

A1C2_P2>=LB*B_A1C2_P2; A1C3_P2>=LB*B_A1C3_P2; A1C4_P2>=LB*B_A1C4_P2;





















B1C2_P2>=LB*B_B1C2_P2; B1C3_P2>=LB*B_B1C3_P2; B1C4_P2>=LB*B_B1C4_P2;
















C1B5_P2>=LB*B_C1B5_P2;













206







A1C4_P2<=SOURCEA1_P2*B_A1C4_P2;



































B1C4_P2<=SOURCEB1_P2*B_B1C4_P2;














207






























2);@BIN(B_A1C1_P2);@BIN(B_A1C2_P2); @BIN(B_A1C3_P2); @BIN(B_A1C4_P2);














2);@BIN(B_B1C1_P2);@BIN(B_B1C2_P2);@BIN(B_B1C3_P2); @BIN(B_B1C4_P2);









208


;@BIN(B_C1B2);@BIN(B_C1B3);@BIN(B_C1B4);@BIN(B_C1B5);








(GIVE);

PC1_P2 = (2*(A1B1_P2 + A1B2_P2 + A1B3_P2 + A1B4_P2 + A1B5_P2 + A1C1_P2 +

A1C2_P2 + A1C3_P2 + A1C4_P2) + 250*(B_A1B1_P2 + B_A1B2_P2 + B_A1B3_P2 +

B_A1B4_P2 + B_A1B5_P2 + B_A1C1_P2 + B_A1C2_P2 + B_A1C3_P2 +

B_A1C4_P2))*D*0.231;




B_A2C4_P2))*D*0.231;




B_A3C4_P2))*D*0.231;




B_A4C4_P2))*D*0.231;




B_A5C4_P2))*D*0.231;




B_A6C4_P2))*D*0.231;




B_A7C4_P2))*D*0.231;


B1C2_P2 + B1C3_P2 + B1C4_P2) + 250*(B_B1A1_P2 + B_B1A2_P2 + B_B1A3_P2 +

B_B1A4_P2 + B_B1A5_P2 + B_B1C1_P2 + B_B1C2_P2 + B_B1C3_P2 +

B_B1C4_P2))*D*0.231;




B_B2C4_P2))*D*0.231;




B_B3C4_P2))*D*0.231;




B_B4C4_P2))*D*0.231;

209




B_B5C4_P2))*D*0.231;


C1B2_P2 + C1B3_P2 + C1B4_P2 + C1B5_P2 ) + 250*(B_C1A1_P2 + B_C1A2_P2 +

B_C1A3_P2 + B_C1A4_P2 + B_C1A5_P2 + B_C1B1_P2 + B_C1B2_P2 + B_C1B3_P2 +

B_C1B4_P2 + B_C1B5_P2 ))*D*0.231;




B_C2B4_P2 + B_C2B5_P2 ))*D*0.231;




B_C3B4_P2 + B_C3B5_P2 ))*D*0.231;




B_C4B4_P2 + B_C4B5_P2 ))*D*0.231;


PCR1_P2 = (2*(B1A1_P2 + B2A1_P2 + B3A1_P2 + B4A1_P2 + B5A1_P2 + C1A1_P2 +

C2A1_P2 + C3A1_P2 + C4A1_P2) + 250*(B_B1A1_P2 + B_B2A1_P2 + B_B3A1_P2 +

B_B4A1_P2 + B_B5A1_P2 + B_C1A1_P2 + B_C2A1_P2 + B_C3A1_P2 + C4A1_P2))*D*0.231;














A7B1_P2 + C1B1_P2 + C2B1_P2 + C3B1_P2 + C4B1_P2) + 250*(B_A1B1_P2 +

B_A2B1_P2 + B_A3B1_P2 + B_A4B1_P2 + B_A5B1_P2 + B_A6B1_P2 + B_A7B1_P2 +

B_C1B1_P2 + B_C2B1_P2 + B_C3B1_P2 + C4B1_P2))*D*0.231;













PCR10_P2= (2*(A1B5_P2 + A2B5_P2 + A3B5_P2 + A4B5_P2 + A5B5_P2 + A6B5_P2 +


210




A7C1_P2 + B1C1_P2 + B2C1_P2 + B3C1_P2 + B4C1_P2 + B5C1_P2 ) + 250*(B_A1C1_P2


B_B1C1_P2 + B_B2C1_P2 + B_B3C1_P2 + B_B4C1_P2 + B_B5C1_P2 ))*D*0.231;














PC7_P2)/2 + (PCR1_P2 + PCR2_P2 + PCR3_P2 + PCR4_P2 + PCR5_P2)/2;

PIPING_COSTS_B_P2 = (PC8_P2 + PC9_P2 + PC10_P2 + PC11_P2 + PC12_P2)/2 +

(PCR6_P2 + PCR7_P2 + PCR8_P2 + PCR9_P2 + PCR10_P2)/2;

PIPING_COSTS_C_P2 = (PC13_P2 + PC14_P2 + PC15_P2 + PC16_P2)/2 + (PCR11_P2 +

PCR12_P2 + PCR13_P2 + PCR14_P2)/2;


A1B1_P2 + A1B2_P2 + A1B3_P2 + A1B4_P2 + A1B5_P2 + A1C1_P2 + A1C2_P2 + A1C3_P2

+ A1C4_P2 = GIVE_A1_P2;


+ A2C4_P2 = GIVE_A2_P2;


+ A3C4_P2 = GIVE_A3_P2;


+ A4C4_P2 = GIVE_A4_P2;


+ A5C4_P2 = GIVE_A5_P2;


+ A6C4_P2 = GIVE_A6_P2;


+ A6C4_P2 = GIVE_A7_P2;


+ B1C4_P2 = GIVE_B1_P2;


+ B2C4_P2 = GIVE_B2_P2;


+ B3C4_P2 = GIVE_B3_P2;


+ B4C4_P2 = GIVE_B4_P2;


+ B5C4_P2 = GIVE_B5_P2;


+ C1B4_P2 + C1B5_P2 = GIVE_C1_P2;

211


+ C2B4_P2 + C2B5_P2 = GIVE_C2_P2;


+ C3B4_P2 + C3B5_P2 = GIVE_C3_P2;


+ C4B4_P2 + C4B5_P2 = GIVE_C4_P2;


EARN_A_P2 = (GIVE_A1_P2 + GIVE_A2_P2 + GIVE_A3_P2 + GIVE_A4_P2 + GIVE_A5_P2 +

GIVE_A6_P2 + GIVE_A7_P2)*0.05/4.18*110*24;

EARN_B_P2 = (GIVE_B1_P2 + GIVE_B2_P2 + GIVE_B3_P2 + GIVE_B4_P2 +

GIVE_B5_P2)*0.05/4.18*110*24;

EARN_C_P2 = (GIVE_C1_P2 + GIVE_C2_P2 + GIVE_C3_P2 +

GIVE_C4_P2)*0.05/4.18*110*24;



+ C4A1_P2 = REUSE_A1_P2;









A1B1_P2 + A2B1_P2 + A3B1_P2 + A4B1_P2 + A5B1_P2 + A6B1_P2 + A7B1_P2 + C1B1_P2

+ C2B1_P2 + C3B1_P2 + C4B1_P2 = REUSE_B1_P2;









A1C1_P2 + A2C1_P2 + A3C1_P2 + A4C1_P2 + A5C1_P2 + A6C1_P2 + A7C1_P2 + B1C1_P2

+ B2C1_P2 + B3C1_P2 + B4C1_P2 + B5C1_P2 = REUSE_C1_P2;








REUSE_COSTS_A_P2=(REUSE_A1_P2 + REUSE_A2_P2 + REUSE_A3_P2 + REUSE_A4_P2 +

REUSE_A5_P2)*0.05/4.18*110*24;

REUSE_COSTS_B_P2=(REUSE_B1_P2 + REUSE_B2_P2 + REUSE_B3_P2 + REUSE_B4_P2 +

REUSE_B5_P2)*0.05/4.18*110*24;

REUSE_COSTS_C_P2=(REUSE_C1_P2 + REUSE_C2_P2 + REUSE_C3_P2 +

REUSE_C4_P2)*0.05/4.18*110*24;



212

F_CHILLED_WATER_B_P2 = CH6_P2 + CH7_P2 + CH8_P2 + CH9_P2 + CH10_P2;

F_CHILLED_WATER_C_P2 = CH11_P2 + CH12_P2 + CH13_P2 + CH14_P2;

! FRESH COOLING WATER FOR PLANT A,B,C;


F_COOLING_WATER_B_P2 = CW6_P2 + CW7_P2 + CW8_P2 + CW9_P2 + CW10_P2;

F_COOLING_WATER_C_P2 = CW11_P2 + CW12_P2 + CW13_P2 + CW14_P2;






F_COOLING_COSTS_A_P2 = (F_COOLING_WATER_A_P2*0.23/4.18*110*24);

F_COOLING_COSTS_B_P2 = (F_COOLING_WATER_B_P2*0.23/4.18*110*24);

F_COOLING_COSTS_C_P2 = (F_COOLING_WATER_C_P2*0.23/4.18*110*24);

! WASTE COSTS;


+ WWA7_P2)*(0.1/4.18*110*24);

WASTE_COSTS_B_P2 =(WWB1_P2 + WWB2_P2 + WWB3_P2 + WWB4_P2 +

WWB5_P2)*(0.1/4.18*110*24);

WASTE_COSTS_C_P2 =(WWC1_P2 + WWC2_P2 + WWC3_P2 + WWC4_P2)*(0.1/4.18*110*24);


COSTS_A_P2=(F_CHILLED_COSTS_A_P2)+(F_COOLING_COSTS_A_P2)+(PIPING_COSTS_A_P2)+

(WASTE_COSTS_A_P2)+(REUSE_COSTS_A_P2)-EARN_A_P2;

COSTS_B_P2=(F_CHILLED_COSTS_B_P2)+(F_COOLING_COSTS_B_P2)+(PIPING_COSTS_B_P2)+

(WASTE_COSTS_B_P2)+(REUSE_COSTS_B_P2)-EARN_B_P2;

COSTS_C_P2=(F_CHILLED_COSTS_C_P2)+(F_COOLING_COSTS_C_P2)+(PIPING_COSTS_C_P2)+

(WASTE_COSTS_C_P2)+(REUSE_COSTS_C_P2)-EARN_C_P2;

!============================================================================;

! PERIOD 3;



SOURCEA1_P3=1964.6; SOURCEA2_P3=1212.2; SOURCEA3_P3=543.4; SOURCEA4_P3=501.6;

SOURCEA5_P3=209; SOURCEA6_P3=292.6; SOURCEA7_P3=376.2; SOURCEA8_P3=961.4;

SOURCEA9_P3=627; SOURCEA10_P3=836;


SOURCEB1_P3=376.2; SOURCEB2_P3=752.4; SOURCEB3_P3=1170.4; SOURCEB4_P3=627;

SOURCEB5_P3=710.6; SOURCEB6_P3=1212.2; SOURCEB7_P3=1463;


SOURCEC1_P3=334.4; SOURCEC2_P3=1755.6; SOURCEC3_P3=1212.2; SOURCEC4_P3=292.6;

SOURCEC5_P3=1128.6; SOURCEC6_P3=501.6;



+ A1B4_P3 + A1B5_P3 + A1B6_P3 + A1C1_P3 + A1C2_P3 + A1C3_P3 + A1C4_P3 +








213



















A10A1_P3 + A10A2_P3 + A10A3_P3 + A10A4_P3 + A10A5_P3 + A10B1_P3 + A10B2_P3 +

A10B3_P3 + A10B4_P3 + A10B5_P3 + A10B6_P3 + A10C1_P3 + A10C2_P3 + A10C3_P3 +

A10C4_P3 + WWA10_P3 = SOURCEA10_P3;


+ B1B4_P3 + B1B5_P3 + B1B6_P3 + B1C1_P3 + B1C2_P3 + B1C3_P3 + B1C4_P3 +





















+ C1B4_P3 + C1B5_P3 + C1B6_P3 + C1C1_P3 + C1C2_P3 + C1C3_P3 + C1C4_P3 +











214







!============================================================================;



SINKA1_P3=2717; SINKA2_P3=459.8; SINKA3_P3=1045; SINKA4_P3=1337.6;

SINKA5_P3=1964.6;


SINKB1_P3=836; SINKB2_P3=292.6; SINKB3_P3=1170.4; SINKB4_P3=627;

SINKB5_P3=710.6; SINKB6_P3=2675.2;


SINKC1_P3=2090; SINKC2_P3=752.4; SINKC3_P3=459.8; SINKC4_P3=1922.8;




B4A1_P3 + B5A1_P3 + B6A1_P3 + B7A1_P3 + C1A1_P3 + C2A1_P3 + C3A1_P3 + C4A1_P3

+ C5A1_P3 + C6A1_P3 = SINKA1_P3;




+ C5A2_P3 + C6A2_P3 = SINKA2_P3;




+ C5A3_P3 + C6A3_P3 = SINKA3_P3;




+ C5A4_P3 + C6A4_P3 = SINKA4_P3;




+ C5A5_P3 + C6A5_P3 = SINKA5_P3;



B4B1_P3 + B5B1_P3 + B6B1_P3 + B7B1_P3 + C1B1_P3 + C2B1_P3 + C3B1_P3 + C4B1_P3

+ C5B1_P3 + C6B1_P3 = SINKB1_P3;




+ C5B2_P3 + C6B2_P3 = SINKB2_P3;




+ C5B3_P3 + C6B3_P3 = SINKB3_P3;




+ C5B4_P3 + C6B4_P3 = SINKB4_P3;

215




+ C5B5_P3 + C6B5_P3 = SINKB5_P3;




+ C5B6_P3 + C6B6_P3 = SINKB6_P3;



B4C1_P3 + B5C1_P3 + B6C1_P3 + B7C1_P3 + C1C1_P3 + C2C1_P3 + C3C1_P3 + C4C1_P3

+ C5C1_P3 + C6C1_P3 = SINKC1_P3;




+ C5C2_P3 + C6C2_P3 = SINKC2_P3;




+ C5C3_P3 + C6C3_P3 = SINKC3_P3;




+ C5C4_P3 + C6C4_P3 = SINKC4_P3;


CH1_P3*6 + CW1_P3*20 + A1A1_P3*10 + A2A1_P3*12 + A3A1_P3*14 + A4A1_P3*17 +

A5A1_P3*23 + A6A1_P3*25 + A7A1_P3*28 + A8A1_P3*30 + A9A1_P3*39 + A10A1_P3*55

+ B1A1_P3*(12+DT) + B2A1_P3*(15+DT) + B3A1_P3*(18+DT) + B4A1_P3*(20+DT) +

B5A1_P3*(25+DT) + B6A1_P3*(32+DT) + B7A1_P3*(40+DT) + C1A1_P3*(14+DT) +

C2A1_P3*(16+DT) + C3A1_P3*(21+DT) + C4A1_P3*(30+DT) + C5A1_P3*(36+DT) +

C6A1_P3*(40+DT) = SINKA1_P3*7;






C6A2_P3*(40+DT) = SINKA2_P3*8;






C6A3_P3*(40+DT) = SINKA3_P3*10;






C6A4_P3*(40+DT) = SINKA4_P3*17;






C6A5_P3*(40+DT) = SINKA5_P3*21;

216

CH6_P3*6 + CW6_P3*20 + A1B1_P3*(10+DT) + A2B1_P3*(12+DT) + A3B1_P3*(14+DT)

+ A4B1_P3*(17+DT) + A5B1_P3*(23+DT) + A6B1_P3*(25+DT) + A7B1_P3*(28+DT) +

A8B1_P3*(30+DT) + A9B1_P3*(39+DT) + A10B1_P3*(55+DT) + B1B1_P3*12 +

B2B1_P3*15 + B3B1_P3*18 + B4B1_P3*20 + B5B1_P3*25 + B6B1_P3*32 + B7B1_P3*40 +

C1B1_P3*(14+DT) + C2B1_P3*(16+DT) + C3B1_P3*(21+DT) + C4B1_P3*(30+DT) +

C5B1_P3*(36+DT) + C6B1_P3*(40+DT) = SINKB1_P3*6;































CH12_P3*6 + CW12_P3*20 + A1C1_P3*(10+DT) + A2C1_P3*(12+DT) + A3C1_P3*(14+DT)

+ A4C1_P3*(17+DT) + A5C1_P3*(23+DT) + A6C1_P3*(25+DT) + A7C1_P3*(28+DT) +

A8C1_P3*(30+DT) + A9C1_P3*(39+DT) + A10C1_P3*(55+DT) + B1C1_P3*(12+DT) +


B6C1_P3*(32+DT) + B7C1_P3*(40+DT) + C1C1_P3*14 + C2C1_P3*16 + C3C1_P3*21 +

C4C1_P3*30 + C5C1_P3*36 + C6C1_P3*40 = SINKC1_P3*8;













217







!===========================================================================;



CH7_P3 + CH8_P3 + CH9_P3 + CH10_P3 + CH11_P3 + CH12_P3 + CH13_P3 + CH14_P3 +

CH15_P3;


CW7_P3 + CW8_P3 + CW9_P3 + CW10_P3 + CW11_P3 + CW12_P3 + CW13_P3 + CW14_P3 +

CW15_P3;


CONSIDERED, INTRA-PLANT IS NEGLECTED) (GIVE);







































218


A10C4_P3>=LB*B_A10C4_P3;

























C1B5_P3>=LB*B_C1B5_P3; C1B6_P3>=LB*B_C1B6_P3;






















CONSIDERED, INTRA-PLANT IS NEGLECTED) (RECEIVE);






219
























































220































C1B6_P3<=SOURCEC1_P3*B_C1B6_P3;

























221









3);@BIN(B_A1B6_P3);@BIN(B_A1C1_P3);@BIN(B_A1C2_P3); @BIN(B_A1C3_P3);

@BIN(B_A1C4_P3);



@BIN(B_A2C4_P3);



@BIN(B_A3C4_P3);



@BIN(B_A4C4_P3);



@BIN(B_A5C4_P3);



@BIN(B_A6C4_P3);



@BIN(B_A7C4_P3);



@BIN(B_A8C4_P3);



@BIN(B_A9C4_P3);

@BIN(B_A10B1_P3);@BIN(B_A10B2_P3);@BIN(B_A10B3_P3);@BIN(B_A10B4_P3);@BIN(B_A1

0B5_P3);@BIN(B_A10B6_P3);@BIN(B_A10C1_P3);@BIN(B_A10C2_P3); @BIN(B_A10C3_P3);

@BIN(B_A10C4_P3);


3);@BIN(B_B1C1_P3);@BIN(B_B1C2_P3);@BIN(B_B1C3_P3);@BIN(B_B1C4_P3);















5_P3);@BIN(B_C1B6_P3);

222



5_P3);@BIN(B_C2B6_P3);



5_P3);@BIN(B_C3B6_P3);



5_P3);@BIN(B_C4B6_P3);



5_P3);@BIN(B_C5B6_P3);



5_P3);@BIN(B_C6B6_P3);


(GIVE);


A1C1_P3 + A1C2_P3 + A1C3_P3 + A1C4_P3) + 250*(B_A1B1_P3 + B_A1B2_P3 +

B_A1B3_P3 + B_A1B4_P3 + B_A1B5_P3 + B_A1B6_P3 + B_A1C1_P3 + B_A1C2_P3 +

B_A1C3_P3 + B_A1C4_P3))*D*0.231;




B_A2C3_P3 + B_A2C4_P3))*D*0.231;




B_A3C3_P3 + B_A3C4_P3))*D*0.231;




B_A4C3_P3 + B_A4C4_P3))*D*0.231;




B_A5C3_P3 + B_A5C4_P3))*D*0.231;




B_A6C3_P3 + B_A6C4_P3))*D*0.231;




B_A7C3_P3 + B_A7C4_P3))*D*0.231;




B_A8C3_P3 + B_A8C4_P3))*D*0.231;




B_A9C3_P3 + B_A9C4_P3))*D*0.231;

PC10_P3 = (2*(A10B1_P3 + A10B2_P3 + A10B3_P3 + A10B4_P3 + A10B5_P3 + A10B6_P3

+ A10C1_P3 + A10C2_P3 + A10C3_P3 + A10C4_P3) + 250*(B_A10B1_P3 + B_A10B2_P3 +

223


B_A10C3_P3 + B_A10C4_P3))*D*0.231;




B_B1C4_P3))*D*0.231;




B_B2C4_P3))*D*0.231;




B_B3C4_P3))*D*0.231;




B_B4C4_P3))*D*0.231;




B_B5C4_P3))*D*0.231;




B_B6C4_P3))*D*0.231;




B_B7C4_P3))*D*0.231;


C1B2_P3 + C1B3_P3 + C1B4_P3 + C1B5_P3 + C1B6_P3 ) + 250*(B_C1A1_P3 +

B_C1A2_P3 + B_C1A3_P3 + B_C1A4_P3 + B_C1A5_P3 + B_C1B1_P3 + B_C1B2_P3 +

B_C1B3_P3 + B_C1B4_P3 + B_C1B5_P3 + B_C1B6_P3 ))*D*0.231;





















224



B7A1_P3 + C1A1_P3 + C2A1_P3 + C3A1_P3 + C4A1_P3 + C5A1_P3 + C6A1_P3) +

250*(B_B1A1_P3 + B_B2A1_P3 + B_B3A1_P3 + B_B4A1_P3 + B_B5A1_P3 + B_B6A1_P3 +

B_B7A1_P3 + B_C1A1_P3 + B_C2A1_P3 + B_C3A1_P3 + B_C4A1_P3 + B_C5A1_P3 +

B_C6A1_P3))*D*0.231;





B_C6A2_P3))*D*0.231;





B_C6A3_P3))*D*0.231;





B_C6A4_P3))*D*0.231;





B_C6A5_P3))*D*0.231;


A7B1_P3 + A8B1_P3 + A9B1_P3 + A10B1_P3 + C1B1_P3 + C2B1_P3 + C3B1_P3 +

C4B1_P3 + C5B1_P3 + C6B1_P3) + 250*(B_A1B1_P3 + B_A2B1_P3 + B_A3B1_P3 +


B_A10B1_P3 + B_C1B1_P3 + B_C2B1_P3 + B_C3B1_P3 + B_C4B1_P3 + B_C5B1_P3 +

B_C6B1_P3))*D*0.231;






B_C6B2_P3))*D*0.231;






B_C6B3_P3))*D*0.231;






B_C6B4_P3))*D*0.231;






B_C6B5_P3))*D*0.231;

225






B_C6B6_P3))*D*0.231;



B4C1_P3 + B5C1_P3 + B6C1_P3 + B7C1_P3) + 250*(B_A1C1_P3 + B_A2C1_P3 +

B_A3C1_P3 + B_A4C1_P3 + B_A5C1_P3 + B_A6C1_P3 + B_A7C1_P3 + B_A8C1_P3 +


B_B5C1_P3 + B_B6C1_P3 + B_B7C1_P3))*D*0.231;






B_B5C2_P3 + B_B6C2_P3 + B_B7C2_P3))*D*0.231;






B_B5C3_P3 + B_B6C3_P3 + B_B7C3_P3))*D*0.231;






B_B5C4_P3 + B_B6C4_P3 + B_B7C4_P3))*D*0.231;


PC7_P3 + PC8_P3 + PC9_P3 + PC10_P3)/2 + (PCR1_P3 + PCR2_P3 + PCR3_P3 +

PCR4_P3 + PCR5_P3)/2;

PIPING_COSTS_B_P3 = (PC11_P3 + PC12_P3 + PC13_P3 + PC14_P3 + PC15_P3 +

PC16_P3 + PC17_P3)/2 + (PCR6_P3 + PCR7_P3 + PCR8_P3 + PCR9_P3 + PCR10_P3 +

PCR11_P3)/2;

PIPING_COSTS_C_P3 = (PC18_P3 + PC19_P3 + PC20_P3 + PC21_P3 + PC22_P3 +

PC23_P3)/2 + (PCR12_P3 + PCR13_P3 + PCR14_P3 + PCR15_P3)/2;


A1B1_P3 + A1B2_P3 + A1B3_P3 + A1B4_P3 + A1B5_P3 + A1B6_P3 + A1C1_P3 + A1C2_P3

+ A1C3_P3 + A1C4_P3 = GIVE_A1_P3;


+ A2C3_P3 + A2C4_P3 = GIVE_A2_P3;


+ A3C3_P3 + A3C4_P3 = GIVE_A3_P3;


+ A4C3_P3 + A4C4_P3 = GIVE_A4_P3;


+ A5C3_P3 + A5C4_P3 = GIVE_A5_P3;


+ A6C3_P3 + A6C4_P3 = GIVE_A6_P3;


+ A7C3_P3 + A7C4_P3 = GIVE_A7_P3;

226


+ A8C3_P3 + A8C4_P3 = GIVE_A8_P3;


+ A9C3_P3 + A9C4_P3 = GIVE_A9_P3;

A10B1_P3 + A10B2_P3 + A10B3_P3 + A10B4_P3 + A10B5_P3 + A10B6_P3 + A10C1_P3 +

A10C2_P3 + A10C3_P3 + A10C4_P3 = GIVE_A10_P3;


+ B1C4_P3 = GIVE_B1_P3;


+ B2C4_P3 = GIVE_B2_P3;


+ B3C4_P3 = GIVE_B3_P3;


+ B4C4_P3 = GIVE_B4_P3;


+ B5C4_P3 = GIVE_B5_P3;


+ B6C4_P3 = GIVE_B6_P3;


+ B7C4_P3 = GIVE_B7_P3;


+ C1B4_P3 + C1B5_P3 + C1B6_P3 = GIVE_C1_P3;












EARN_A_P3=(GIVE_A1_P3 + GIVE_A2_P3 + GIVE_A3_P3 + GIVE_A4_P3 + GIVE_A5_P3 +

GIVE_A6_P3 + GIVE_A7_P3 + GIVE_A8_P3 + GIVE_A9_P3 +

GIVE_A10_P3)*0.08/4.18*110*24;

EARN_B_P3=(GIVE_B1_P3 + GIVE_B2_P3 + GIVE_B3_P3 + GIVE_B4_P3 + GIVE_B5_P3 +

GIVE_B6_P3 + GIVE_B7_P3)*0.08/4.18*110*24;

EARN_C_P3=(GIVE_C1_P3 + GIVE_C2_P3 + GIVE_C3_P3 + GIVE_C4_P3 + GIVE_C5_P3 +

GIVE_C6_P3)*0.08/4.18*110*24;


B1A1_P3 + B2A1_P3 + B3A1_P3 + B4A1_P3 + B5A1_P3 + B6A1_P3 + B7A1_P3 + C1A1_P3

+ C2A1_P3 + C3A1_P3 + C4A1_P3 + C5A1_P3 + C6A1_P3 = REUSE_A1_P3;









227


+ A9B1_P3 + A10B1_P3 + C1B1_P3 + C2B1_P3 + C3B1_P3 + C4B1_P3 + C5B1_P3 +

C6B1_P3 = REUSE_B1_P3;


















B6C1_P3 + B7C1_P3 = REUSE_C1_P3;











REUSE_COSTS_A_P3 = (REUSE_A1_P3 + REUSE_A2_P3 + REUSE_A3_P3 + REUSE_A4_P3 +

REUSE_A5_P3)*0.08/4.18*110*24;

REUSE_COSTS_B_P3 = (REUSE_B1_P3 + REUSE_B2_P3 + REUSE_B3_P3 + REUSE_B4_P3 +

REUSE_B5_P3 + REUSE_B6_P3)*0.08/4.18*110*24;

REUSE_COSTS_C_P3 = (REUSE_C1_P3 + REUSE_C2_P3 + REUSE_C3_P3 +

REUSE_C4_P3)*0.08/4.18*110*24;



F_CHILLED_WATER_B_P3 = CH6_P3 + CH7_P3 + CH8_P3 + CH9_P3 + CH10_P3 + CH11_P3;

F_CHILLED_WATER_C_P3 = CH12_P3 + CH13_P3 + CH14_P3 + CH15_P3;



F_COOLING_WATER_B_P3 = CW6_P3 + CW7_P3 + CW8_P3 + CW9_P3 + CW10_P3 + CW11_P3;

F_COOLING_WATER_C_P3 = CW12_P3 + CW13_P3 + CW14_P3 + CW15_P3;






F_COOLING_COSTS_A_P3 =(F_COOLING_WATER_A_P3*0.23/4.18*110*24);

228

F_COOLING_COSTS_B_P3 =(F_COOLING_WATER_B_P3*0.23/4.18*110*24);

F_COOLING_COSTS_C_P3 =(F_COOLING_WATER_C_P3*0.23/4.18*110*24);

! WASTE COSTS;


+ WWA7_P3 + WWA8_P3 + WWA9_P3 + WWA10_P3)*(0.1/4.18*110*24);

WASTE_COSTS_B_P3 =(WWB1_P3 + WWB2_P3 + WWB3_P3 + WWB4_P3 + WWB5_P3 + WWB6_P3

+ WWB7_P3)*(0.1/4.18*110*24);

WASTE_COSTS_C_P3 =(WWC1_P3 + WWC2_P3 + WWC3_P3 + WWC4_P3 + WWC5_P3 +

WWC6_P3)*(0.1/4.18*110*24);


COSTS_A_P3

=(F_CHILLED_COSTS_A_P3)+(F_COOLING_COSTS_A_P3)+(PIPING_COSTS_A_P3)+(WASTE_COS

TS_A_P3)+(REUSE_COSTS_A_P3)-EARN_A_P3;

COSTS_B_P3

=(F_CHILLED_COSTS_B_P3)+(F_COOLING_COSTS_B_P3)+(PIPING_COSTS_B_P3)+(WASTE_COS

TS_B_P3)+(REUSE_COSTS_B_P3)-EARN_B_P3;

COSTS_C_P3

=(F_CHILLED_COSTS_C_P3)+(F_COOLING_COSTS_C_P3)+(PIPING_COSTS_C_P3)+(WASTE_COS

TS_C_P3)+(REUSE_COSTS_C_P3)-EARN_C_P3;

!============================================================================;

! OVERALL TAC FOR ALL PERIODS;

COSTS_A = COSTS_A_P1 + COSTS_A_P2 + COSTS_A_P3;

COSTS_B = COSTS_B_P1 + COSTS_B_P2 + COSTS_B_P3;

COSTS_C = COSTS_C_P1 + COSTS_C_P2 + COSTS_C_P3;

! LOWER AND UPPER BOUND OF EACH PLANT COSTS;

COSTS_A < 3195205; COSTS_A >= FUZZY_A;

COSTS_B < 2733237; COSTS_B >= FUZZY_B;

COSTS_C < 2397910; COSTS_C >= FUZZY_C;

! FUZZY;

FUZZY_A = 2611127; !8.7%REDUCTION;

FUZZY_B = 1682907; !8.7%REDUCTION;

FUZZY_C = 1626007; !8.7%REDUCTION;


LAMBDA_A = 1-((COSTS_A-FUZZY_A)/(3195205-FUZZY_A));

LAMBDA_B = 1-((COSTS_B-FUZZY_B)/(2733237-FUZZY_B));

LAMBDA_C = 1-((COSTS_C-FUZZY_C)/(2397910-FUZZY_C));

LAMBDA<=LAMBDA_A;

LAMBDA<=LAMBDA_B;

lAMBDA<=LAMBDA_C;

LAMBDA>=0; LAMBDA<=1;

229


LINGO ver13 mathematical modelling codes for Scenario 1 (Max-min total scores)

MAX=LAMBDA;

FCCW=CHILLED_WATER+COOLING_WATER;

TOTAL_COSTS = COSTS_A+COSTS_B+COSTS_C;

FRESH_COSTS=CHILLED_WATER_COSTS+COOLING_WATER_COSTS;

! CHILLED WATER COST OF RM 10 PER KG AND 330 OPERATING DAYS PER YEAR;

CHILLED_WATER_COSTS = F_CHILLED_COSTS_A + F_CHILLED_COSTS_B +

F_CHILLED_COSTS_C;

! COOLING WATER COST OF RM 5 PER KG AND 330 OPERATING DAYS PER YEAR;

COOLING_WATER_COSTS = F_COOLING_COSTS_A + F_COOLING_COSTS_B +

F_COOLING_COSTS_C;


LB = 50;


D = 100;

DT = 0.5;

!============================================================================;





SOURCEA9=26.75; SOURCEA10=107.84;


SOURCEB1=209; SOURCEB2=418; SOURCEB3=250.8; SOURCEB4=125.40; SOURCEB5=83.60;

SOURCEB6=459.80; SOURCEB7=1881; SOURCEB8=2173.6;


SOURCEC1=551.76; SOURCEC2=968.57; SOURCEC3=304.9;

NO_SOURCE_A = 10;

NO_SOURCE_B = 8;

NO_SOURCE_C = 3;

F_SOURCE_A = SOURCEA1 + SOURCEA2 + SOURCEA3 + SOURCEA4 + SOURCEA5 + SOURCEA6

+ SOURCEA7 + SOURCEA8 + SOURCEA9 + SOURCEA10;

F_SOURCE_B = SOURCEB1 + SOURCEB2 + SOURCEB3 + SOURCEB4 + SOURCEB5 + SOURCEB6

+ SOURCEB7 + SOURCEB8;

F_SOURCE_C = SOURCEC1 + SOURCEC2 + SOURCEC3;










230











A10A1 + A10A2 + A10A3 + A10A4 + A10A5 + A10B1 + A10B2 + A10B3 + A10B4 + A10B5

+ A10B6 + A10B7 + A10C1 + A10C2 + A10C3 + WWA10 = SOURCEA10;























!============================================================================;



SINKA1=2528.31; SINKA2=41.72; SINKA3=175.48; SINKA4=234.92; SINKA5=134.59;


SINKB1=627; SINKB2=125.40; SINKB3=250.80; SINKB4=543.4; SINKB5=836;

SINKB6=1964.6; SINKB7=1254;


SINKC1=500.8; SINKC2=645.53; SINKC3=678.90;

NO_SINK_A = 5;

NO_SINK_B = 7;

NO_SINK_C = 3;

F_SINK_A = SINKA1 + SINKA2 + SINKA3 + SINKA4 + SINKA5;

F_SINK_B = SINKB1 + SINKB2 + SINKB3 + SINKB4 + SINKB5 + SINKB6 + SINKB7;

F_SINK_C = SINKC1 + SINKC2 + SINKC3;




+C3A1 = SINKA1;

231



+C3A2 = SINKA2;



+C3A3 = SINKA3;



+C3A4 = SINKA4;



+C3A5 = SINKA5;



+C3B1 = SINKB1;



+C3B2 = SINKB2;



+C3B3 = SINKB3;



+C3B4 = SINKB4;



+C3B5 = SINKB5;



+C3B6 = SINKB6;



+C3B7 = SINKB7;



+C3C1 = SINKC1;



+C3C2 = SINKC2;



+C3C3 = SINKC3;


CH1*6.67 + CW1*19.80 + A1A1*10 + A2A1*10.5 + A3A1*11.11 + A4A1*16.67 +

A5A1*17.7 + A6A1*19 + A7A1*20 + A8A1*20.88 + A9A1*22.6 + A10A1*24.01 +



+C3A1*(26.67+DT)= SINKA1*6.67;

CH2*6.67 + CW2*19.80 + A1A2*10 + A2A2*10.5 + A3A2*11.11 + A4A2*16.67 +

A5A2*17.7 + A6A2*19 + A7A2*20 + A8A2*20.88 + A9A2*22.6 + A10A2*24.01 +



+C3A2*(26.67+DT)= SINKA2*8;

CH3*6.67 + CW3*19.80 + A1A3*10 + A2A3*10.5 + A3A3*11.11 + A4A3*16.67 +

A5A3*17.7 + A6A3*19 + A7A3*20 + A8A3*20.88 + A9A3*22.6 + A10A3*24.01 +


232


+C3A3*(26.67+DT)= SINKA3*10;

CH4*6.67 + CW4*19.80 + A1A4*10 + A2A4*10.5 + A3A4*11.11 + A4A4*16.67 +

A5A4*17.7 + A6A4*19 + A7A4*20 + A8A4*20.88 + A9A4*22.6 + A10A4*24.01 +



+C3A4*(26.67+DT)= SINKA4*15;

CH5*6.67 + CW5*19.80 + A1A5*10 + A2A5*10.5 + A3A5*11.11 + A4A5*16.67 +

A5A5*17.7 + A6A5*19 + A7A5*20 + A8A5*20.88 + A9A5*22.6 + A10A5*24.01 +



+C3A5*(26.67+DT)= SINKA5*17;





+ C2B1*(19+DT) +C3B1*(26.67+DT)= SINKB1*6.67;





+ C2B2*(19+DT) +C3B2*(26.67+DT)= SINKB2*8;





+ C2B3*(19+DT) +C3B3*(26.67+DT)= SINKB3*15;





+ C2B4*(19+DT) +C3B4*(26.67+DT)= SINKB4*17;





+ C2B5*(19+DT) +C3B5*(26.67+DT)= SINKB5*20;





+ C2B6*(19+DT) +C3B6*(26.67+DT)= SINKB6*30;





+ C2B7*(19+DT) +C3B7*(26.67+DT)= SINKB7*55;











233






!============================================================================;


CHILLED_WATER = CH1 + CH2 + CH3 + CH4 + CH5 + CH6 + CH7 + CH8 + CH9 + CH10 +

CH11 + CH12 + CH13 + CH14 + CH15;

COOLING_WATER = CW1 + CW2 + CW3 + CW4 + CW5 + CW6 + CW7 + CW8 + CW9 + CW10 +

CW11 + CW12 + CW13 + CW14 + CW15;
































A10C2>=LB*B_A10C2; A10C3>=LB*B_A10C3;











234
























































235






















































236





@BIN(B_A10B1);@BIN(B_A10B2);@BIN(B_A10B3);@BIN(B_A10B4);@BIN(B_A10B5);@BIN(B_

A10B6);@BIN(B_A10B7);@BIN(B_A10C1);@BIN(B_A10C2); @BIN(B_A10C3);



















);



);



);


(GIVE);

PC1 = (2*(A1B1 + A1B2 + A1B3 + A1B4 + A1B5 + A1B6 + A1B7 + A1C1 + A1C2 + A1C3

250*(B_A1B1 + B_A1B2 + B_A1B3 + B_A1B4 + B_A1B5 + B_A1B6 + B_A1B7 + B_A1C1 +

B_A1C2 + B_A1C3))*D*0.231;



+ B_A2C2 + B_A2C3))*D*0.231;



+ B_A3C2 + B_A3C3))*D*0.231;



+ B_A4C2 + B_A4C3))*D*0.231;



B_A5C2 + B_A5C3))*D*0.231;



+ B_A6C2 + B_A6C3))*D*0.231;



B_A7C2 + B_A7C3))*D*0.231;

237



B_A8C2 + B_A8C3))*D*0.231;



B_A9C2 + B_A9C3))*D*0.231;

PC10 = (2*(A10B1 + A10B2 + A10B3 + A10B4 + A10B5 + A10B6 + A10B7 + A10C1 +

A10C2 + A10C3 250*(B_A10B1 + B_A10B2 + B_A10B3 + B_A10B4 + B_A10B5 +

B_A10B6 + B_A10B7 + B_A10C1 + B_A10C2 + B_A10C3))*D*0.231;



B_B1C3))*D*0.231;



B_B2C3))*D*0.231;



B_B3C3))*D*0.231;



B_B4C3))*D*0.231;



B_B5C3))*D*0.231;



B_B6C3))*D*0.231;



B_B7C3))*D*0.231;



B_B8C3))*D*0.231;




















238










B_C3B1))*D*0.231;




B_C3B2))*D*0.231;




B_C3B3))*D*0.231;




B_C3B4))*D*0.231;




B_C3B5))*D*0.231;




B_C3B6))*D*0.231;




B_C3B7))*D*0.231;





B_B8C1))*D*0.231;





B_B8C2))*D*0.231;





B_B8C3))*D*0.231;

PIPING_COSTS_A = (PC1 + PC2 + PC3 + PC4 + PC5 + PC6 + PC7 + PC8 + PC9 +

PC10)/2 + (PCR1 + PCR2 + PCR3 + PCR4 + PCR5)/2;

PIPING_COSTS_B = (PC11 + PC12 + PC13 + PC14 + PC15 + PC16 + PC17 + PC18)/2 +

(PCR6 + PCR7 + PCR8 + PCR9 + PCR10 + PCR11 + PCR12)/2;

PIPING_COSTS_C = (PC19 + PC20 + PC21)/2 + (PCR13 + PCR14 + PCR15)/2;

239











A10B1 + A10B2 + A10B3 + A10B4 + A10B5 + A10B6 + A10B7 + A10C1 + A10C2 + A10C3

= GIVE_A10;










C1B7 = GIVE_C1;


C2B7 = GIVE_C2;


C3B7 = GIVE_C3;


EARN_A=(GIVE_A1+GIVE_A2+GIVE_A3+GIVE_A4+GIVE_A5+GIVE_A6+GIVE_A7+GIVE_A8+GIVE_

A9+GIVE_A10)*0.06/4.18*330*24;

EARN_B=(GIVE_B1+GIVE_B2+GIVE_B3+GIVE_B4+GIVE_B5+GIVE_B6+GIVE_B7+GIVE_B8)*0.06

/4.18*330*24;

EARN_C=(GIVE_C1+GIVE_C2+GIVE_C3)*0.06/4.18*330*24;



REUSE_A1;


REUSE_A2;


REUSE_A3;


REUSE_A4;


REUSE_A5;











240












REUSE_COSTS_A=(REUSE_A1+REUSE_A2+REUSE_A3+REUSE_A4+REUSE_A5)*0.06/4.18*330*24;

REUSE_COSTS_B=(REUSE_B1+REUSE_B2+REUSE_B3+REUSE_B4+REUSE_B5+REUSE_B6+REUSE_B7

)*0.06/4.18*330*24;

REUSE_COSTS_C=(REUSE_C1+REUSE_C2+REUSE_C3)*0.06/4.18*330*24;


F_CHILLED_WATER_A=CH1+CH2+CH3+CH4+CH5;

F_CHILLED_WATER_B=CH6+CH7+CH8+CH9+CH10+CH11+CH12;

F_CHILLED_WATER_C=CH13+CH14+CH15;

! FRESH COOLING WATER FOR PLANT A,B,C;

F_COOLING_WATER_A=CW1+CW2+CW3+CW4+CW5;

F_COOLING_WATER_B=CW6+CW7+CW8+CW9+CW10+CW11+CW12;

F_COOLING_WATER_C=CW13+CW14+CW15;


F_CHILLED_COSTS_A=(F_CHILLED_WATER_A*0.254/4.18*330*24);

F_CHILLED_COSTS_B=(F_CHILLED_WATER_B*0.254/4.18*330*24);

F_CHILLED_COSTS_C=(F_CHILLED_WATER_C*0.254/4.18*330*24);


F_COOLING_COSTS_A=(F_COOLING_WATER_A*0.15/4.18*330*24);

F_COOLING_COSTS_B=(F_COOLING_WATER_B*0.15/4.18*330*24);

F_COOLING_COSTS_C=(F_COOLING_WATER_C*0.15/4.18*330*24);

! WASTE COSTS;

WASTE_COSTS_A=(WWA1+WWA2+WWA3+WWA4+WWA5+WWA6+WWA7+WWA8+WWA9+WWA10)*(0.1/4.18*

330*24);

WASTE_COSTS_B=(WWB1+WWB2+WWB3+WWB4+WWB5+WWB6+WWB7+WWB8)*(0.1/4.18*330*24);

WASTE_COSTS_C=(WWC1+WWC2+WWC3)*(0.1/4.18*330*24);


COSTS_A=(F_CHILLED_COSTS_A)+(F_COOLING_COSTS_A)+(PIPING_COSTS_A)+WASTE_COSTS_

A+REUSE_COSTS_A-EARN_A;

COSTS_B=(F_CHILLED_COSTS_B)+(F_COOLING_COSTS_B)+(PIPING_COSTS_B)+WASTE_COSTS_

B+REUSE_COSTS_B-EARN_B;

COSTS_C=(F_CHILLED_COSTS_C)+(F_COOLING_COSTS_C)+(PIPING_COSTS_C)+WASTE_COSTS_

C+REUSE_COSTS_C-EARN_C;

! TAC OF BASE CASE;

TAC_BC_A = 1712637; TAC_BC_B = 835333; TAC_BC_C = 439532;

! COST SAVING EFFICIENCY;

E_C1_A = (TAC_BC_A - COSTS_A)/TAC_BC_A;

E_C1_B = (TAC_BC_B - COSTS_B)/TAC_BC_B;

241

E_C1_C = (TAC_BC_C - COSTS_C)/TAC_BC_C;

E_C1_A > 0.05;

E_C1_B > 0.05;

E_C1_C > 0.05;

! AVERAGE AHP SCORE FOR COST SAVINGS (C1);

AVG_AHP_A_C1 = ((40*(E_C1_A)+1)/9)*0.4;

AVG_AHP_B_C1 = ((133.33*(E_C1_B)+1)/9)*0.35;

AVG_AHP_C_C1 = ((40*(E_C1_C)+1)/9)*0.28;

! POWER CONSUMPTION OF CHILLED AND COOLING WATER;

PC_CHILLED_WATER_A =

((F_CHILLED_WATER_A/3600)*8.33)/4+(F_CHILLED_WATER_A/4.18/3600*10*9.8)/(1000*

0.82);

PC_CHILLED_WATER_B =

((F_CHILLED_WATER_B/3600)*8.33)/4+(F_CHILLED_WATER_B/4.18/3600*10*9.8)/(1000*

0.82);

PC_CHILLED_WATER_C =

((F_CHILLED_WATER_C/3600)*8.33)/4+(F_CHILLED_WATER_C/4.18/3600*10*9.8)/(1000*

0.82);

PC_COOLING_WATER_A =

(0.0105*F_COOLING_WATER_A*10.2/3600)+(F_COOLING_WATER_A/4.18/3600*10*9.8)/(10

00*0.82);

PC_COOLING_WATER_B =

(0.0105*F_COOLING_WATER_B*10.2/3600)+(F_COOLING_WATER_B/4.18/3600*10*9.8)/(10

00*0.82);

PC_COOLING_WATER_C =

(0.0105*F_COOLING_WATER_C*10.2/3600)+(F_COOLING_WATER_C/4.18/3600*10*9.8)/(10

00*0.82);

! CO2 EMISSION;

CO2_A = (PC_CHILLED_WATER_A + PC_COOLING_WATER_A)*7920*0.662;

CO2_B = (PC_CHILLED_WATER_B + PC_COOLING_WATER_B)*7920*0.662;

CO2_C = (PC_CHILLED_WATER_C + PC_COOLING_WATER_C)*7920*0.662;

TOTAL_CO2 = CO2_A + CO2_B + CO2_C;

! CO2 EMISSION OF BASE CASE;

CO2_A_BC = 7850.57;

CO2_B_BC = 2535.11;

CO2_C_BC = 2014.78;

TOTAL_CO2_BC = CO2_A_BC + CO2_B_BC + CO2_C_BC;

! CO2 EFFICIENCY;

E_C2_A = (CO2_A_BC-CO2_A)/CO2_A_BC;

E_C2_B = (CO2_B_BC-CO2_B)/CO2_B_BC;

E_C2_C = (CO2_C_BC-CO2_C)/CO2_C_BC;

! AVERAGE AHP SCORE FOR SUSTAINABILITY (C2);

AVG_AHP_A_C2 = ((1000*(E_C2_A)+1)/9)*0.1;

AVG_AHP_B_C2 = ((40*(E_C2_B)+1)/9)*0.18;

AVG_AHP_C_C2 = ((20*(E_C2_C)+1)/9)*0.25;

! NO. OF EXISTING LINKS;

242

! PLANT A;

EX_A_1 = (B_A1B1 + B_A1B2 + B_A1B3 + B_A1B4 + B_A1B5 + B_A1B6 + B_A1B7 +

B_A1C1 + B_A1C2 + B_A1C3);


B_A2C1 + B_A2C2 + B_A2C3);


B_A3C1 + B_A3C2 + B_A3C3);


B_A4C1 + B_A4C2 + B_A4C3);


B_A5C1 + B_A5C2 + B_A5C3);


B_A6C1 + B_A6C2 + B_A6C3);


B_A7C1 + B_A7C2 + B_A7C3);


B_A8C1 + B_A8C2 + B_A8C3);


B_A9C1 + B_A9C2 + B_A9C3);

EX_A_10 = (B_A10B1 + B_A10B2 + B_A10B3 + B_A10B4 + B_A10B5 + B_A10B6 +

B_A10B7 + B_A10C1 + B_A10C2 + B_A10C3);

IM_A_1 = (B_B1A1 + B_B2A1 + B_B3A1 + B_B4A1 + B_B5A1 + B_B6A1 + B_B7A1 +

B_B8A1 + B_C1A1 + B_C2A1 + B_C3A1);


B_B8A2 + B_C1A2 + B_C2A2 + B_C3A2);


B_B8A3 + B_C1A3 + B_C2A3 + B_C3A3);


B_B8A4 + B_C1A4 + B_C2A4 + B_C3A4);


B_B8A5 + B_C1A5 + B_C2A5 + B_C3A5);

TOTAL_LINK_A = EX_A_1 + EX_A_2 + EX_A_3 + EX_A_4 + EX_A_5 + EX_A_6 + EX_A_7 +

EX_A_8 + EX_A_9 + EX_A_10 + IM_A_1 + IM_A_2 + IM_A_3 + IM_A_4 + IM_A_5;

ACTUAL_LINK_A = (NO_SOURCE_A*(NO_SINK_B+NO_SINK_C)) +

(NO_SINK_A*(NO_SOURCE_B+NO_SOURCE_C));

EX_B_1 = (B_B1A1 + B_B1A2 + B_B1A3 + B_B1A4 + B_B1A5 + B_B1C1 + B_B1C2 +

B_B1C3);


B_B2C3);


B_B3C3);


B_B4C3);


B_B5C3);


B_B6C3);


B_B7C3);


B_B8C3);

IM_B_1 = (B_A1B1 + B_A2B1 + B_A3B1 + B_A4B1 + B_A5B1 + B_A6B1 + B_A7B1 +

B_A8B1 + B_A9B1 + B_A10B1 + B_C1B1 + B_C2B1 + B_C3B1);

243













TOTAL_LINK_B = EX_B_1 + EX_B_2 + EX_B_3 + EX_B_4 + EX_B_5 + EX_B_6 + EX_B_7 +

EX_B_8 + IM_B_1 + IM_B_2 + IM_B_3 + IM_B_4 + IM_B_5 + IM_B_6 + IM_B_7;

ACTUAL_LINK_B = (NO_SOURCE_B*(NO_SINK_A+NO_SINK_C)) +

(NO_SINK_B*(NO_SOURCE_A+NO_SOURCE_C));

EX_C_1 = (B_C1A1 + B_C1A2 + B_C1A3 + B_C1A4 + B_C1A5 + B_C1B1 + B_C1B2 +

B_C1B3 + B_C1B4 + B_C1B5 + B_C1B6 + B_C1B7);





IM_C_1 = (B_A1C1 + B_A2C1 + B_A3C1 + B_A4C1 + B_A5C1 + B_A6C1 + B_A7C1 +

B_A8C1 + B_A9C1 + B_A10C1 + B_B1C1 + B_B2C1 + B_B3C1 + B_B4C1 + B_B5C1 +

B_B6C1 + B_B7C1 + B_B8C1);



B_B6C2 + B_B7C2 + B_B8C2);



B_B6C3 + B_B7C3 + B_B8C3);

TOTAL_LINK_C = EX_C_1 + EX_C_2 + EX_C_3 + IM_C_1 + IM_C_2 + IM_C_3;

ACTUAL_LINK_C = (NO_SOURCE_C*(NO_SINK_A+NO_SINK_B)) +

(NO_SINK_C*(NO_SOURCE_A+NO_SOURCE_B));

CONNECTIVITY_A = TOTAL_LINK_A/ACTUAL_LINK_A;

CONNECTIVITY_B = TOTAL_LINK_B/ACTUAL_LINK_B;

CONNECTIVITY_C = TOTAL_LINK_C/ACTUAL_LINK_C;

AVG_AHP_A_C3 = (((-133.33)*(CONNECTIVITY_A)+11)/9)*0.27;

AVG_AHP_B_C3 = (((-200)*(CONNECTIVITY_B)+9)/9)*0.19;

AVG_AHP_C_C3 = (((-200)*(CONNECTIVITY_C)+11)/9)*0.21;

! RISK C4;

RT_A = 0.37; RT_B = 0.42; RT_C = 0.87;

! B TO A;

B_A_1 = (B1A1 + B2A1 + B3A1 + B4A1 + B5A1 + B6A1 + B7A1 + B8A1);





244

B_TO_A = (B_A_1 + B_A_2 + B_A_3 + B_A_4 + B_A_5)/1000*RT_B;

! C TO A;

C_A_1 = (C1A1 + C2A1 + C3A1);

C_A_2 = (C1A2 + C2A2 + C3A2);

C_A_3 = (C1A3 + C2A3 + C3A3);

C_A_4 = (C1A4 + C2A4 + C3A4);

C_A_5 = (C1A5 + C2A5 + C3A5);

C_TO_A = (C_A_1 + C_A_2 + C_A_3 + C_A_4 + C_A_5)/400*RT_C;

! A TO B;

A_B_1 = (A1B1 + A2B1 + A3B1 + A4B1 + A5B1 + A6B1 + A7B1 + A8B1 + A9B1 +

A10B1);


A10B2);


A10B3);


A10B4);


A10B5);


A10B6);


A10B7);

A_TO_B = (A_B_1 + A_B_2 + A_B_3 + A_B_4 + A_B_5 + A_B_6 + A_B_7)/700*RT_A;

! C TO B;

C_B_1 = (C1B1 + C2B1 + C3B1);

C_B_2 = (C1B2 + C2B2 + C3B2);

C_B_3 = (C1B3 + C2B3 + C3B3);

C_B_4 = (C1B4 + C2B4 + C3B4);

C_B_5 = (C1B5 + C2B5 + C3B5);

C_B_6 = (C1B6 + C2B6 + C3B6);

C_B_7 = (C1B7 + C2B7 + C3B7);

C_TO_B = (C_B_1 + C_B_2 + C_B_3 + C_B_4 + C_B_5 + C_B_6 + C_B_7)/500*RT_C;

! A TO C;

A_C_1 = (A1C1 + A2C1 + A3C1 + A4C1 + A5C1 + A6C1 + A7C1 + A8C1 + A9C1 +

A10C1);


A10C2);


A10C3);

A_TO_C = (A_C_1 + A_C_2 + A_C_3)/350*RT_A;

! B TO C;

B_C_1 = (B1C1 + B2C1 + B3C1 + B4C1 + B5C1 + B6C1 + B7C1 + B8C1);



B_TO_C = (B_C_1 + B_C_2 + B_C_3)/350*RT_B;

245

! AVERAGE AHP SCORE FOR RISKS;

AVG_AHP_A_C4 = (((-8)*(B_TO_A + C_TO_A) + 9)/9)*0.23;

AVG_AHP_B_C4 = (((-20)*(A_TO_B + C_TO_B) + 11)/9)*0.28;

AVG_AHP_C_C4 = (((-10)*(A_TO_C + B_TO_C) + 11)/9)*0.26;

! TOTAL AVERAGE AHP SCORE;

TOTAL_AHP_A = AVG_AHP_A_C1 + AVG_AHP_A_C2 + AVG_AHP_A_C3 + AVG_AHP_A_C4 ;

TOTAL_AHP_B = AVG_AHP_B_C1 + AVG_AHP_B_C2 + AVG_AHP_B_C3 + AVG_AHP_B_C4 ;

TOTAL_AHP_C = AVG_AHP_C_C1 + AVG_AHP_C_C2 + AVG_AHP_C_C3 + AVG_AHP_C_C4 ;


! FUZZY;

FUZZY_A=1;

FUZZY_B=1;

FUZZY_C=1;


LAMBDA_A = (TOTAL_AHP_A)/(FUZZY_A);

LAMBDA_B = (TOTAL_AHP_B)/(FUZZY_B);

LAMBDA_C = (TOTAL_AHP_C)/(FUZZY_C);


LAMBDA <= LAMBDA_A;

LAMBDA <= LAMBDA_B;

LAMBDA <= LAMBDA_C;

process synthesis and optimization of an … · process synthesis and optimization of an integrated...

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