ANALYSIS AND OPTIMISATION OF TOTAL SITE UTILITY SYSTEMS.pdf

ANALYSIS AND OPTIMISATION OF TOTAL SITE UTILITY SYSTEMS

A thesis submitted to the

University of Manchester Institute of Science and Technology

for the degree of

Doctor of Philosophy

by

Zhigang Shang

under the supervision of

Professor Antonis Kokossis

Department of Process Integration

University of Manchester Institute of Science and Technology

Manchester M60 1 QD

August 2000

Declaration

• No portion of the work referred to in this thesis has been submitted in support of an

application for another degree or qualification of this or any other university, or other

institution of learning.

Zhigang Shang

Acknowledgements

I would like to express my sincere gratitude to Professor Antonis Kokossis for his

guidance and encouragement throughout the course of this study. His patience and

understanding have been tremendous. I would like to thank him for spending long hours

on reviewing this thesis.

I would also like to thank Professor Robin Smith, as the head of the department, gave

me the opportunity to do my doctoral degree in the department.

Many thanks to all the staff and students in the department for their support and for

creating a pleasant atmosphere. I consider myself very lucky indeed for having been

able to work in such a friendly and dynamic environment. Big thanks to you for making

my stay in Manchester so wonderful.

I wish to thank member companies of the Process Integration Research Consortium for

funding the research.

I would like to thank my wonderful parents for their love and support throughout my

life. In spite of being thousands of miles away, they have been so close to me with their

prayers and support.

No words can express my gratitude to my beloved wife, Jun. I thank her for her love

and encouragement during this very demanding time.

ii

Abstract

This thesis provides systematic methodologies for the analysis and optimisation of total

site utility systems under operational variations. The methodologies address three major

problems: (i) the optimal design of total site utility systems, (ii) the debottlenecking and

planning optimisation of an existing site, (iii) the optimisation of total site maintenance

scheduling.

A set of new models is developed for boilers, condensing turbines and gas turbines.

These models are used for the analysis and optimisation of site utility systems in view

of operational variations. They enable for an accurate prediction of unit efficiencies and

embody the efficiency trends of realistic units in terms of their variation with capacity,

load and operating conditions.

In the design of site utility systems, it is often the case that strong interactions exist

between the site utility systems and site processes. A novel approach is proposed for the

synthesis and design of site utility systems integrated with site processes. The design

decisions are mainly concerned with the selection of the optimal steam levels, and the

determination of the layout of the utility system. The approach combines the benefits of

pinch analysis, thermodynamic analysis and mathematical optimisation techniques. It

easily identifies the interactions between the utility system and site processes and

greatly reduces the size and complexity of the optimisation problem.

A systematic optimisation methodology is proposed for the debottlenecking and

planning of site utility systems. Given forecasts for the prices and demands of utilities,

the approach determines the best investment scheme for an existing system and the

optimal operational strategies to adopt.

iii

Finally, a multi-period MILP model is presented for the maintenance scheduling

optimisation of total sites. The optimisation method simultaneously considers the

maintenance and operation of the site processes and the utility system. Practical

maintenance constraints of industrial plants are also considered.

iv

Table of Contents

CHAYfER 1. INTRODUCTION .................................................................................. 1

1.1 PROBLEM DESCRIPTION ........................................................................................ 1

1.2 SCOPE OF TIfE TIlESIS ............................................................................................ 2

1.2.1 Design of Total Site Utility Systems ................................................................. 2

1.2.2 Debottlenecking and Planning Optimisation of an Existing Site ..................... 3

1.2.3 Total Site Maintenance Scheduling .................................................................. 3

1.3 OBJECTIVE OF TIfE TIlESIS .................................................................................... 3

1.4 OUTLINE OF TIfE THESIS ........................................................................................ 4

CHAPTER 2. REVIEW OF PREVIOUS WORK ....................................................... 5

2.1 INTRODUCTION ..................................................................................................... 5

2.2 PREVIOUS ApPROACHES TO THE SYNTHESIS AND DESIGN OF SITE UTILITY

SySTEMS ......................................................................................................................... 5

2.3 PREVIOUS APPROACHES TO TIfE DEBOTTLENECKING, PLANNING AND SCHEDULING

OF SITE UTILITY SySTEMS ............................................................................................... 8

2.4 TOTAL SITE ANALySIS .......................................................................................... 9

CHAPTER 3. HARDWARE MODELS ...................................................................... 13

3.1 INTRODUCTION ................................................................................................... 13

3.2 TIlE BOILER HARDWARE MODEL ........................................................................ 14

3.2.1 Model Development ........................................................................................ 14

3.2.2 Summary ......................................................................................................... 19

3.3 TIlE CONDENSING TuRBINE HARDWARE MODEL. ............................................... 20

3.3.1 The Turbine Hardware Model ........................................................................ 20

3.3.2 The Condensing Turbine Hardware Model .................................................... 21

3.3.3 Summary ......................................................................................................... 23

3.4 THE GAS TuRBINE HARDWARE MODEL. ............................................................. 23

v

3.4.1 Model Development ........................................................................................ 24

3.4.2 Summary ......................................................................................................... 29

3.5 CONCLUSIONS ..................................................................................................... 29

CHAPTER 4. STEAM LEVEL OPTIMISA TION .................................................... 31

4.1 INTRODUCTION ................................................................................................... 31

4.2 THE STRATEGY ................................................................................................... 33

4.3 THE TRANSHIPMENT NETWORK OF A TOTAL SITE ............................................... 33

4.4 OPTIMISATION MODEL ........................................................................................ 38

4.4.1 Model Formulation ......................................................................................... 41

4.4.2 Remarks on the Optimisation Model ............................................................. .47

4.5 CASE STUDIES ..................................................................................................... 48

4.5.1 Case 1: Steam Level Optimisation under a Single Scenario .......................... 48

4.5.2 Case 2: Steam Level Optimisation under Four Scenarios .............................. 53

4.5.3 Summary ......................................................................................................... 56

4.6 CONCLUSIONS ..................................................................................................... 58

CHAPTER 5. LAYOUT SCREENING AND OPTIMISATION ............................. 59

5.1 INTRODUCTION .................................................................................................... 59

5.2 THE STRATEGY ................................................................................................... 61

5.3 TOTAL SITE ANALySIS ........................................................................................ 63

5.4 THERMODYNAMIC ANALySIS .............................................................................. 64

5.4.1 Thermodynamic Efficiencies and Utility Structures ..................... .................. 65

5.4.2 The Thermodynamic Efficiency Curve ............................................................ 72

5.5 THE GENERATION OF THE SUPERSTRUCTURE ...................................................... 73

5.5.1 Superset of Back-pressure Steam Turbines .................................................... 74

5.5.2 Superset of Gas Turbines ................................................................................ 76

5.5.3 Superset of Boilers ............................................................... ........................... 78

5.5.4 Superset of VHP Condensing Steam Turbines ................................................ 79

5.5.5 Superset of Surplus Steam Condensing Turbines ........................................... 80

5.5.6 Reheat Cycles .................................................................................................. 81

5.6 OPTIMISATION MODEL ........................................................................................ 81

vi

5.6.1 Model Formulation ......................................................................................... B4

5.6.2 Remarks and Discussion ................................................................................. 90

5.7 SYNTIIESIS OF COMPLEX STEAM TuRBINES ........................................................ 90

5.8 CASE STUDIES ..................................................................................................... 91

5.B.1 Case Study 1 ................................................................................................... 92

5.B.2 Case Study 2 ................................................................................................... 99

5.B.3 Discussion .................................................................................................. ... 101

5.9 CONCLUSIONS ................................................................................................... 102

CHAPTER 6. DEBOTTLENECKING AND PLANNING OPTIMISATION OF

AN EXISTING SITE .................................................................................................. 103

6.1 INTRODUCTION ................................................................................................. 103

6.2 OPTIMISATION SlRATEGY ................................................................................. 105

6.3 STAGE I: OPTIMISATION OF THE EXISTING SYSTEM .......................................... 106

6.4 STAGE II: TOTAL SITE ANALYSIS ...................................................................... 106

6.5 STAGE III: THERMODYNAMIC ANALYSIS .......................................................... 108

6.5.1 The Thermodynamic Efficiency Curve/or Debottlenecking ......................... 10B

6.5.2 Identification o/the Promising Debottlenecking Options ............................ 109

6.5.3 The Debottlenecking Superstructure ............................................................ 112

6.6 STAGE IV: OPTIMISATION ................................................................................. 113

6.6.1 Mathematical Formulation ........................................................................... 116

6.6.2 Solution Methods .......................................................................................... 121

6.7 CASE STUDIES ................................................................................................... 122

6.7.1 Case Study 1 ................................................................................................. 122

6.7.2 An Industrial Case Study .............................................................................. 131

6.8 CONCLUSIONS ................................................................................................... 139

CHAPTER 7. TOTAL SITE MAINTENANCE SCHEDULING ..•..•............•........ 140

7.1 INTRODUCTION ................................................................................................. 140

7.2 MATHEMATICAL MODEL .................................................................................. 141

7.2.1 Objective Function ........................................................................................ 144

7.2.2 Peiformance Models ..................................................................................... 144

vii

7.2.3 Steam Mass Balances ............................................. ...................................... 147

7.2.4 Power Balance ................ .............................................................................. 147

7.2.5 Maintenance Constraints ............................ .................. "."."." .. "."."""""." 148

7.3 MAINTENANCE CASE STUDY ............................................................................ 151

7.4 CONCLUSIONS ................................................................................................... 154

CHAPTER 8. CONCLUSIONS AND FUTURE WORK ........................................ lS8

8.1 INTRODUCTION ................................................................ """ .. """" .. "."."."." .158

8.2 CONCLUSIONS ................................................................................................... 158

8.2.1 Design o/Total Site Utility Systems ............................................................. 158

8.2.2 Debottlenecking and Planning Optimisation o/the Existing Site ................ 160

8.2.3 Total Site Maintenance Scheduling .............................................................. 161

8.3 FuTURE WORK .................................................................................................. 161

REFE REN CES ............................................................................................................ 163

APPENDIX A. CORRELATIONS OF THE THM ..••..•••....•.......•........................... 168

APPENDIX B. REGRESSION OF CONDENSING TURBINE EFFICIENCY

DATA ............................................................................................................................ 170

APPENDIX C. REGRESSION OF GAS TURBINE EFFICIENCY DATA ......... 173

viii

List of Figures

Figure 1-1: Schematic of a total site under operational variations 2

Figure 2-1: Total Site Profiles (TSP) 10

Figure 2-2: The construction of the Site Composite Curves 10

Figure 2-3: The Site Composite Curves for Minimum Fuel Requirement (MFR) and

Minimum Utilities Cost (MUC) 11

Figure 2-4: The construction of the Site Utility Grand Composite Curve 12

Figure 3-1: Boiler specification on T-H diagram 15

Figure 3-2: The T-H diagram of steam 15

Figure 3-3: Typical heat loss plot for boilers (Pattison and Sharma. 1980) 16

Figure 3-4: The BHM accounts for the effect of boiler size, load and operating

conditions on efficiency

Figure 3-5: The THM of steam turbines

Figure 3-6: Typical data on the efficiency of condensing turbines

Figure 3-7: Simple gas turbine cycle

19

21

22

24

Figure 3-8: Typical data on the electrical efficiency of gas turbines as a function of size

(Marechal and Kalitventzeff, 1998) 26

Figure 3-9: The GTHM accounts for the effect of gas turbine size and load on

efficiency 28

Figure 4-1: Different operation scenarios can be represented by sets of total site profiles

32

Figure 4-2: Schematic showing the steam level optimisation strategy 33

Figure 4-3: Transhipment network representation of the total site heat flow 35

Figure 4-4: Heat flow pattern of the temperature intervals for steam level i 36

Figure 4-5: Heat flow pattern in each temperature interval of the heat source cascade 41

Figure 4-6: Heat flow pattern in each temperature interval of the steam level cascade 42

ix

Figure 4·7: Heat flow pattern in each temperature interval of the heat sink cascade 42

Figure 4·8: Schematic representation of the optimisation procedure 47

Figure 4·9: The total site profiles for the site of Case 1 49

Figure 4·10: Potential steam levels of Case 1 50

Figure 4·11: Transhipment network representation of case 1 51

Figure 4·12: Optimal structure for MUC case of Case 1 52

Figure 4·13: Optimal structure for MFR case of Case 1 52

Figure 4·14: Four operation scenarios for Case 2 53

Figure 4·15: Transhipment network representation for Case 2 56

Figure 4·16: The resulting SUGCCs corresponding to the optimal steam levels of Case

2 57

Figure 5·1: Schematic showing the configuration design optimisation strategy 62

Figure 5·2: Identification of steam turbines of a site by using the SCC 63

Figure 5·3: Total site profiles of a plant 65

Figure 5·4: Integration of the BBPT cycle 66

Figure 5·5: Integration of the GTWB cycle 67

Figure 5·6: Integration of the BCT cycle 69

Figure 5·7: Integration of the GTWBCT cycle 70

Figure 5·8: Integration of the SCT 71

Figure 5·9: The thermodynamic efficiency curve 72

Figure 5·10: Complex turbines are considered as a cascade of simple turbines 74

Figure 5·11: Decomposition of complex steam turbines 75

Figure 5·12: The candidate BP steam turbines for the case of two scenarios 75

Figure 5·13: The regenerative gas turbine 76

Figure 5·14: The effect of part load operation prevails over the increase of efficiency

with gas turbine size 77

Figure 5·15: Candidate gas turbines for the case of two scenarios 78

Figure 5·16: Superset of boilers 79

Figure 5·17: Candidate VHP condensing turbines for the case of two scenarios 80

Figure 5·18: Candidate surplus steam condensing turbines for the case of two scenarios

81

x

Figure 5·19: The SUGCC of a site 92

Figure 5·20: TECs for Case 1 94

Figure 5·21: Superstructure of Case 1 96

Figure 5·22: Optimal structure of Case 1 97

Figure 5·23: Superstructure of Case 2 99


Figure 6·1: Outline of debottlenecking and planning strategy 105

Figure 6·2: Identification of debottlenecking turbines of a site by using the SCC 107

Figure 6·3: Decomposing a complex turbine into different sizes of cylinders in each

expansion zone 107

Figure 6·4: Typical TEC for debottlenecking 108

Figure 6·5: The boiler and back-pressure turbine cycle for debottlenecking 109

Figure 6·6: The gas turbine and waste heat boiler cycle for debottlenecking 110

Figure 6·7: The gas turbine and waste heat boiler and condensing turbine cycle for

debottlenecking 110

Figure 6·8: The boiler and condensing turbine cycle for debottlenecking 111

Figure 6·9: Surplus condensing turbines for debottlenecking 111

Figure 6·10: Debottlenecking superstructure 112

Figure 6·11: Decomposition strategy 121

Figure 6·12: The existing utility system of Case 1 122

Figure 6·13: TECs for different operation periods for Case 1 126

Figure 6·14: Debottlenecking superstructure of Case 1 128


Figure 6·16: The existing utility system of the industrial case 131

Figure 6·17: Thermodynamic Efficiency Curves for the industrial case 135

Figure 6·18: Debottlenecking superstructure of the industrial case 136

Figure 6·19: Optimal structure of the industrial case 137

Figure 7·1: Total site optimisation 141

Figure 7·2: The configuration of a total site 152

Figure 7·3: Optimal maintenance and operation schedule of all units 155

xi

Figure 7·4: Optimal profile of steam consumed by processes 156

Figure 7·5: Optimal power consumption profile of processes 156

Figure 7·6: Optimal boiler operation 156

Figure 7·7: Optimal turbine operation 157

Figure 7·8: Optimal power export profile 157

Figure Bl: Regression parameter AC as a function of inlet saturation temperature 171

Figure B2: Regression parameter BC as a function of inlet saturation temperature 172

xii

List of Tables

Table 4·1: Cost data of utilities 48

Table 4·2: Candidate saturation temperatures for each steam level of Case 1 49

Table 4·3: Heat provided by the process heat sources in each temperature interval of

C~1 ~

Table 4·4: Heat required by the process heat sinks in each temperature interval of Case

1 50

Table 4·5: Candidate temperatures for each steam level of Case 2

Table 4·6: Heat enthalpy changes of processes of Case 2 (Scenario A)

Table 4·7: Heat enthalpy changes of processes of Case 2 (Scenario B)

Table 4·8: Heat enthalpy changes of processes of Case 2 (Scenario C)

Table 4·9: Heat enthalpy changes of processes of Case 2 (Scenario D)

53

54

54

55

55

Table 4·10: Heat required of process sinks above temperature interval (1,1) for Case 2

55

Table 4·11: Surplus heat of process sources below temperature interval (I,J) for Case 2

55

Table 4·12: Optimal steam levels for single and mUltiple scenarios

Table 5·1: PIH Characteristics of gas turbine cycles

Table 5·2: Capital cost data (Bruno et al., 1998)

Table 5·3: Summary of operating conditions

Table 5·4: Utility data

Table 5·5: Power demands of Case 1

Table 5·6: Steam amount across each expansion zone of Case 1 (t/h)

Table 5·7: Power outputs of possible SCT and BBPT cycles of Case 1

Table 5·8: PIH characteristics of Case 1

Table 5·9: Power outputs of the OTWB cycles of Case 1

Table 5·10: Candidate sizes of BP turbines of Case 1 (t/h)

Table 5·11: Candidate sizes of condensing turbines of Case 1 (t/h)

xiii

57

76

89

91

91

92

93

93

94

94

95

95

Table 5-12: Candidate sizes of gas turbines of Case 1 (MW) 95

Table 5-13: Optimal loads of the units of Case 1 98

Table 5-14: Power demands of Case 2 99

Table 5-15: Optimal loads of the units of Case 2 101

Table 6-1: Summary of Operating Conditions of Case 1 123

Table 6-2: Utility demands of Case 1 123

Table 6-3: Utility data of Case 1 123

Table 6-4: Maximum power generation of the existing system of Case 1 (MW) 124

Table 6-5: Steam amount across each expansion of Case l(tIh) 124

Table 6-6: Capacities of simple turbines in every expansion zone of Case l(tIh) 125

Table 6-7: Capacities of potential steam turbines of Case l(tIh) 125

Table 6-8: The capacities of potential GTWB cycles (MW) of Case 1 127

Table 6-9: Capacities of candidate steam turbines of Case 1 (tIh) 127

Table 6-10: Capacities of candidate GTWB cycles of Case l(MW) 127

Table 6- 11: Summary of the problem size 128

Table 6-12: Optimal capacities of the new units of Case 1 130

Table 6-13: Optimal operation of all units of Case 1 130

Table 6-14: Summary of operating conditions of the industrial case 132

Table 6-15: Utility demands of the industrial case 132

Table 6-16: Power demands of the allocated turbines of the industrial case 133

Table 6-17: Utility cost data in different periods for the industrial case 133

Table 6-18: Maximum power generation of the existing system of the industrial case

(MW) 133

Table 6-19: Total steam flowrates across expansion zones for the industrial case (tIh)

134

Table 6-20: Capacities of existing turbines in every expansion zone for the industrial

case (tlh) 134

Table 6-21: Capacities of potential steam turbines for each period for the industrial case

(tlh) 135

Table 6-22: Capacities of GTWB cycles for different periods for the industrial case 136

Table 6-23: Optimal operation of all turbines of the industrial case (MW) 138

xiv

Table 6-24: Optimal operation of all boilers of the industrial case (tlh) 138

Table 6-25: Optimal operation of all gas turbines of the industrial case (MW) 138

Table 7-1: Summary of operating conditions of the utility system 152

Table 7-2: Utility demands of process units in nonnal operating conditions 153

Table 7-3: Utility cost data 153

Table 7-4: Maintenance times of all units (days) 153

xv

Chapter 1 Introduction

Chapter 1

Introduction

1.1 Problem Description

A typical chemical plant usually consists of several chemical production processes,

which consume heat and power to make products in order to obtain maximum profit

(Figure 1-1). The heat and power are supplied by a site utility system. The site utility

system consumes fuel in boilers and gas turbines, supplies the necessary steam to

chemical processes via several steam mains and produces power via steam turbines and

gas turbines. The processes may also generate steam at various levels. The steam

generated by the processes can be supplied to the steam mains, and eventually

consumed in other processes.

It is often the case that considerable changes exist in the chemical processes as a result

of fluctuating demand and prices of products, feed compositions, ambient temperatures

and so on. The changes in the operation of chemical processes result in fluctuating heat

and power demands between the site utility system and chemical processes.

Most of the research conducted on the analysis and optimisation of total site utility

systems has given little attention to the operational variations and strong interactions

between the site utility system and site processes. Above all, no systematic methodology

for the analysis and optimisation of total site utility systems under operational variations

has been suggested.

1

Chapter i introduction

p;:;o~

c:> I Process 11 Demand and prices I Process 21 TIme c:> ~ I Process 31 Feed specifications

c:> I Process n 1

~ TIme

TIme

UHeat U Power Utility demands

b:: TIme

Figure 1-1: Schematic of a total site under operational variations

1.2 Scope of the Thesis

In this thesis, three types of issues are addressed for total site utility systems:

1.2.1 Design of Total Site Utility Systems

In design situations the objective is to design the site utility system that will meet

fluctuating utility demands of site processes. The main decisions involved are the

selection of the steam levels with respect to their temperatures and pressures and the

determination of the configuration of the operating units with respect to type, number,

capacity and connections among the units. The best practical site utility system design

will feature a minimum total cost.

2


1.2.2 Debottlenecking and Planning Optimisation of an Existing Site

In debottlenecking and planning situations, the objective is to make sure the site utility

system satisfies the changing utility demands of site processes in a long-term horizon in

order to minimise the total cost. It involves the following two tasks: the selection of the

new units to be added to the current system, and the determination of the optimal

operational strategies of all units with respect to operating conditions and on/off status.

1.2.3 Total Site Maintenance Scheduling

As both site process units and site utility units have to go through shutdown and start-up

changes, steam and power demands gradually increase or decrease. Strong interactions

exist between the site processes and the site utility system. In maintenance scheduling

situations the objective is to determine the optimal operation and maintenance schedules

of the total site. The total site maintenance scheduling approach simultaneously

considers the maintenance and operation of the site utility system and site processes so

that the total operating cost is minimised.

1.3 Objective of the Thesis

The objective of the thesis is to propose systematic analysis and optimisation

methodologies to tackle total site utility system problems under operational variations.

Grassroots design, debottlenecking and planning of site utility systems, as well as

maintenance scheduling of a total site are addressed.

The procedures use total site analysis, thermodynamic analysis and mathematical

optimisation techniques. The work aims at using previous total site analysis tools and

developing new thermodynamic tools which can help engineers to scope and screen

promising design options. Mathematical optimisation techniques are then proposed to

find the optimum solution.

3


1.4 Outline of the Thesis

The next chapter presents a review of previous techniques for the analysis and

optimisation of total site utility systems. The hardware models for steam turbines, gas

turbines and boilers are introduced in chapter 3. A systematic methodology for the

design of total site utility systems is proposed in chapter 4 and chapter 5. Chapter 4

introduces the method for steam level optimisation and chapter 5 introduces the method

for configuration optimisation of site utility systems. A systematic methodology for

debottlenecking and planning optimisation of an existing site is presented in chapter 6.

Chapter 7 deals with maintenance scheduling problem for a total site. The last chapter

presents major conclusions of the work, along with the possible future research on the

topic.

4

Chapter 2 Review of Previous Work

Chapter 2

Review of Previous Work

2.1 Introduction

Previous approaches to the synthesis and design of site utility systems will be

introduced first. This will be followed by a discussion on the available techniques for

the debottlenecking, and planning and scheduling of site utility systems. Finally, due to

their relevance to the concepts that will be developed in the following chapters, a

description of total site analysis approaches is provided.

2.2 Previous Approaches to the Synthesis and Design of Site Utility

Systems

A well-designed site utility system should be able to match the plant heat and power

variations and keep its total costs to a minimum. Design decisions are mainly concerned

with the selection of the optimum steam levels and the determination of the

configuration of the site utility system.

Several methods have been presented previously to address the problem of synthesis

and design of utility systems. These methods generally follow three basic approaches:

those based on thermodynamic targets, those based on pinch analysis targets, and those

based on optimisation techniques. Examples of the first group are papers presented by

Nishio et ai. (1980), EI-Masri and Magnusson (1984) and Chou and Shih (1987). The

traditional way of designing utility systems using thermodynamic methods is to

maximise the thermal efficiency of the system. Thermodynamic analysis reveals the

5


thermal inefficiencies of the various subsystems. Once the inefficiencies have been

identified, heuristic rules are applied to obtain the design structure. Although there is no

question that thermodynamic targets and heuristics provide a good understanding of the

processes, they do not take into account the complex interactions that take place

between the subsystems, nor do they guarantee optimality. Furthermore, the capital cost

hasn't been taken into account.

Townsend and Linhoff (1983) explained the concept of "appropriate" heat engine and

heat pump placement in process networks. They also introduced procedures for

preliminary design, involving heat engine, and heat pump equipment selection and

performance assessment. Dhole and Linnhoff (1992) introduced the concept of "Total

Site Profiles" for the analysis of an entire total site. They used thermodynamic insights

to graphically represent a total site on a Carnot factor-enthalpy diagram. In order to

target the Minimum Cost of Energy Requirements (MCER), Marechal and Kalitventzeff

(1996) proposed a concept of integrated composite curves for the integration of utility

systems.

In order to address the problem of selecting the pressures of the steam mains, Morton

and Linnhoff (1984) proposed the use of Grand Composite Curves. By using total site

analysis method, Raissi (1994) studied the optimum placement of steam levels and

identified the two extreme cases of the Minimum Fuel Requirement (MFR) and the

Minimum Utilities Cost (MUC) for single operation scenarios. The target model of

steam turbines in this work cannot account for the efficiency variation with load,

operating conditions and capacity, and the exhaustive enumeration algorithm was used

to find the optimal solution. Mavromatis and Kokossis (1998a) proposed a new Turbine

Hardware Model (THM) for steam turbines and an exhaustive enumeration method to

search for the optimal levels. The cases they studied were only based on the shaft-work

target. However, it is very difficult to get the optimal levels in large problems by using

exhaustive enumeration methods because of the huge computation requirement. In

addition, neither Raissi nor Mavromatis has taken into account the boiler target model to

calculate the fuel cost in order to determine the minimum utility cost. Finally,

systematic methods for generating potential steam levels have not been accounted for.

6


It is also possible to use mathematical optimisation techniques to synthesise and design

site utility systems. Most of the publications dealing with the synthesis and design of

utility systems have focused on fixed utility demands or specified header pressure

levels. Nishio (1977) appears to be the first to consider the problem of selecting optimal

header pressure levels and presented a direct search approach coupled with

simultaneous solution of the balance equations. Papoulias and Grossmann (1983a)

proposed an MILP method for the structural and parametrical optimisation of utility

systems under fixed steam and power demands. The work was subsequently extended to

account for the synthesis and design of chemical processes (Papoulias and Grossmann

1983c). Iyer and Grossmann (1998) have presented a multi-period MILP approach for

the synthesis of utility systems operating under multiple periods. However, steam level

optimisation is not considered in this work. Petroulas and Reklaitis (1984) used a

dynamic programming method to optimise the steam conditions as continuous variables

and a linear programming method for the optimum allocation of drivers with the

common objective of minimising the real work loss. A non-linear programming strategy

was applied by Colmenares and Seider (1989) for the design of utility systems

integrated with the chemical process. The interaction of steam level selection and steam

demand for each level is not accounted for in this work, and the steam raised by

chemical processes is not considered. A simulated annealing algorithm has been used by

Maia and Qassim (1997) for the synthesis of utility systems with variable utility

demands. Most recently, Mavromatis and Kokossis (1998b) have presented an MILP

approach for the optimal design of steam turbine networks. This approach is only

limited to the back-pressure steam turbine network design. An MINLP model for the

synthesis and design of utility plants has been presented by Bruno et al. (1998).

Wilkendorf et al. (1998) also proposed an MINLP model for the synthesis of complete

utility systems. In practice, however, there are several drawbacks in the approach. If all

the candidate options are included in the superstructure, the number of candidate

structures should be enormous and the size of the problem would become too large to be

handled even for moderate problems. The consideration of multiple operation scenarios

results in a further increase of the design options to an extent. Secondly, the formulation

of utility systems is inherently non-linear with respect to the efficiencies for the units,

which gives rise to complex models. Therefore it is essential to find a systematic

7


methodology which can build a superstructure including all the promising alternatives

without being too large, and to develop new modelling methods for the units.

Above all, we need a systematic methodology for the synthesis and design of site utility

systems, capable of considering the realistic efficiency trends of units, operational

variations and the interaction between the site utility system and site processes. One of

the objectives of this thesis is to present a systematic optimisation approach for the

synthesis and design of total site utility systems under operational variations.

2.3 Previous approaches to the debottlenecking, planning and

scheduling of site utility systems

A number of approaches have been reported for the debottlenecking and planning of site

utility systems. Iyer and Grossmann (1998) recently addressed the synthesis and

operational planning problem for utility systems that they formulated as an MILP

problem. A recent survey can be found in Iyer and Grossmann (1997) in which the

operational planning problem for utility systems is formulated as an MILP program.

The optimisation of steam production network under uncertainty has been reported by

Papalexandri and Pistikopoulos (1996). Nath and Holliday (1985) have proposed an

MILP model which can be used for the long term planning of plant utility systems. A

multi-period utility system model has been presented by Hui and Natori (1996) in which

an MILP model has been used to find out the best combination of new equipment to be

added. Yokoyama and Ito (1996) have proposed an MILP model for an operational

planning problem for a cogeneration system under a complex utility rate structure. A

planning method can be found in Ito et al. (1990) in which the operational policy of

each piece of constituent equipment has been decided so as to minimise the operational

cost. Makwana (1997) proposed a debottlenecking method for utility systems by using

top level analysis. The trend of assuming constant efficiencies for the gas turbines,

steam turbines and boilers appears to be a limiting assumption in these developments.

Furthermore, no systematic methodology has been addressed to target and scope for the

debottlenecking options for the utility systems under operational variations. An

alternative approach is reported by Yokoyama et al. (1994) in which an NLP+MILP

8


model is used. The shortcoming is that it can only optimise the fixed structure and there

is only one steam header in the approach. The approach is often limited in the size of

problems that they can handle. Olsbu et ai. (1988) proposed an MINLP model for the

design and planning of power systems which accounts for variable production profiles

and the availability of the system over a given time horizon.

Various maintenance-scheduling methods have been proposed. Dopazo and Merrill

(1975) described an integer programming approach that minimises the unit maintenance

costs. An MILP model has been proposed by AI-Khamis et al. (1992) to determine unit

maintenance schedules with fuel constraints. Chattopadhyay et ai. (1995) also proposed

an MILP model for least-cost generating unit maintenance scheduling for

interconnected power systems. Most recently, Moro and Ramos (1999) have presented a

mixed integer approach to maintenance scheduling of generating units in large scale

power systems. A simulated annealing method has been presented by Satoh and Nara

(1990) for the maintenance scheduling problem. Chen and Toyoda (1990) have

proposed a method to levelize the incremental risks, which results in a minimum Loss

of Load Probability (LOLP) maintenance schedule. Recently, an application of a

generic evolved fuzzy (GEF) system for the maintenance scheduling of generating units

can be found in Huang (1998), in which the fuzzy system was formulated with respect

to multiple objectives and soft constraints. Above all, all these approaches do not

consider the interactions between the site utility system and site processes. It results in a

local optimum maintenance schedule for the site utility system instead of an optimum

maintenance schedule for the total site.

2.4 Total Site AnalysiS

Dhole and Linhoff (1993) introduced a graphical representation of all process heat

sources and heat sinks in the site, that need to be connected to the utility system, termed

the "Total Site Profiles" (TSP) shown in Figure 2-1. It is used in this paper to represent

the chemical processes and extract the information required for the analysis of site

utility systems. By integrating the utility system, especially the steam system with the

total site profiles, the optimal steam level operating conditions and loads can be

9


detennined to minimise the utility cost, or to minimise the fuel requirement. It should be

noted that in the total site profiles, the steam demand at each steam level is expressed as

heat load, namely, the amount of heat can be used for heating at the saturation

temperature. The Total Site Profiles provide site-wide targets for fuel and co-generation.

The targets can be used for screening possible design options of site utility systems.

HP site heat

H H

Figure 2-1: Total Site Profiles (TSP)

In order to understand the interactions between fuel demand, heat recovery and co

generation, Raissi (1994) proposed "Site Composite Curves" (SCC). These are

constructed by shifting the Total Site Profiles towards each other (Figure 2-2).

T

HP

H H cw H

Total Site Profiles Site CompOSite Curves

Figure 2-2: The construction of the Site Composite Curves

10


The Site Composite Curves provide targets for fuel and co-generation, in a similar way

to the original Total Site Profiles. More importantly, the Site Composite Curves can

visually represent the steam flow in the utility system in addition to heat flow between

processes and utilities.

Raissi (1994) discussed the trade-offs between the fuel requirement and the

cogeneration potential when the steam levels under selection for one operation scenario.

Two extreme cases of Minimum Fuel Requirement (MFR) as shown in Figure 2-3a and

Minimum Utilities Cost (MUC) as shown in Figure 2-3b were studied.

VHP

MP

CW

a. MFR

Increased fuel

Increased cooling utility

b.MUC

Cogeneration

Figure 2-3: The Site Composite Curves for Minimum Fuel Requirement (MFR) and Minimum

Utilities Cost (MUC)

The costs of fuel and power determine the optimal steam levels for the MUC case. The

work boiler efficiency and the steam turbine efficiency are assumed constant. For the

utility system operating under operational variations, the steam load raised by VHP

boilers and steam amount passing steam turbines should not be constant. As the steam

raised by boilers varies for different steam level selection, as well as for different

operation scenarios, it requires a model for the boiler that is able to account for the

variation of steam boiler efficiency with the load and the size, as well as the operating

conditions. The shaftwork-targeting model of steam turbine should account for

11


efficiency variation with load, capacity and operating conditions as well . If the models

that fail to address these effects are used to select the steam levels, the selection of

steam levels will not be the optimum.

T T VHP

HP

MP

IP

H H

Site Composite Curves Site Utility Grand Composite Curve

Figure 2-4: The construction of the Site Utility Grand Composite Curve

In order to provide the net steam balance for each steam header of site utility systems,

Raissi (1994) proposed a Site Utility Grand Composite Curve (SUGCC) (Figure 2-4) by

plotting the steam generation load towards the right and the steam use load towards to

the left for each steam level. The site-wide targets for fuel and co-generation can also be

identified by SUGCC in a similar way by TSP and SCC. Figure 2-4 illustrates steam

turbines placed on the Site Utility Grand Composite Curve. The characteristics of steam

turbines are easily identified.

12

Chapter 3 Hardware Models

Chapter 3

Hardware Models

3.1 Introduction

In the synthesis and design of the total site utility systems under operational variations,

the loads and operating conditions of the units vary for different operation scenarios.

Their efficiencies vary and the unit capacities influence the efficiencies. Most of the

publications dealing with the synthesis and design of site utility systems simplify the

problem with linear mass/energy balances whereby the units are assumed of constant

efficiencies. A new approach for the targeting models of the units is proposed in this

chapter. The targeting models account for the variation of efficiency with load and

capacity, as well as changes in the operating conditions.

In the first part of this chapter a new Boiler Hardware Model (BHM) is developed to

describe the performance of boilers. The BHM exploits the basic thermodynamic

principles relating to the operation of boilers. Next, the development of a new Gas

Turbine Hardware Model (GTHM) is proposed which is based on thermodynamic

principles, hardware data and engineering knowledge. The Turbine Hardware Model

(THM) proposed by Mavromatis and Kokossis (1998a) is introduced to describe the

performance of the back-pressure steam turbines. Finally, the THM is extended towards

a Condensing Turbine Hardware Model (CTHM) to describe the operation of

condensing turbines.

13


3.2 The Boiler Hardware ModeJ

Most of the conventional applications dealing with the synthesis and design of site

utility systems have either simply focused on the balance calculations associated with

boilers or assumed the constant boiler efficiency. In order to address the problems of the

optimisation of total site utility systems under operational variations, a new boiler

model is proposed, termed the Boiler Hardware Model (BRM). The model makes use of

basic thermodynamic principles related to the operation of steam boilers. As a result, the

model is capable of accounting for the efficiency trends of realistic steam boilers.

3.2.1 Model Development

The BRM relies on the principle of the calculation of boiler efficiency. Figure 3-1

shows us the relation between steam load (Qsteam), heat losses (Qloss) and fuel

requirement (Qfuel). The numerical expression for this relation is:

Q fuel = Qloss + Qsteam

The definition of steam load yields:

where:

hI : the enthalpy of boiler inlet water

h2 : the enthalpy of steam raised by boiler

M: the steam load raised by boiler

14

(3-1)

(3-2)


T T,

Steam

T.

H

~'

QIuoI

Figure 3·1: Boiler specification on T-H diagram

Figure 3·2: The T -H diagram of steam

In terms of the thermodynamic principle as shown in Figure 3-2, gives:

(3-3)

where:

Tin : the temperature of inlet water

Tout sat : the saturation temperature of outlet steam

15


Cp : the specific heat of saturation water between Tin and Tout sat

~Tsat : the temperature difference between Tin and Tout sat

q : the specific heat load of the steam, namely, the heat that can be used for

heating at saturation temperature

The efficiency is defined by:

It follows that:

Substituting Equations (3-2) and (3-3) into Equation (3-1) yields:

Qjue/ = (C p~Tsal + q)M + Q/oss

35~----------------------------~

30

Q[oss (%) 25 QSleam

20

15+-~--~--~~--~--~~--~--~~

o 10 20 30 40 50 60 70 80 90 100

Figure 3-3: Typical heat loss plot for boilers (Pattison and Sharma, 1980)

(3-4)

(3-5)

(3-6)

In order to define the boiler model, the Qloss needs to be known. The Qloss originates

mainly from two parts: the external boiler surface losses and the flue gas losses. Typical

16


data on the total heat loss can be found in the form of plot over a range of loads as

shown in Figure 3-3 (pattison and Sharma, 1980). The plot shows the heat loss percent

QIOSS versus steam load percent ~. Q Mmax

steam

where:

Qsteam : the steam heat load

M : the steam load

Mmax : the maximum steam load

On the basis of the data as shown in Figure 3-3 (Passison and Sharma, 1980), the

following equation is regressed within the range between 10% and =100% of~: M max

Qloss ~=a+b~, Q Mmax M max

steam

M 10% 5 -- 5100%

M max (3-7)

Where a and b are regression parameters. The regression over the data provided by

Pattison and Sharma (1980) yields a=0.0126 and b=0.2156 for the plot in Figure 3-3. It

should be noted that both ~ and Qloss vary within the above range of ~. The M~ Q M~

steam

expression estimates the heat loss within 2% throughout the operating range.

Substituting Equations (3-2) and (3-3) into Equation (3-7) gives:

(3-8)

As a result of this expression, the operation of a boiler can be fully defined, once its size

is known in terms of the maximum steam load Mmax. Substitution of Equation (3-8) into

Equation (3-6) gives:

(3-9)

17


The Equation (3-9) constitutes the core of the new boiler model. It relates the fuel

requirement of the boiler to the boiler size, the steam load and its operating conditions.

Given a set of expected conditions, the performance of the boiler is a function of its

size. Most notably, while the non-linear variation of the efficiency is accounted for, the

relation of the fuel requirement to the steam load is linear. The predicted boiler

efficiency from Equations (3-5) and (3-9) is:

M MOlaX

11 = ---=-=-----M

(1+b)--+a M max

(3-10)

Equation (3-10) accounts for the variation of efficiency with load and capacity. If we

define the efficiency 11b as the ratio of the heat load of steam (the heat that can be used

for heating at the saturation temperature) to the heat of fuel, gives:

M q MOlaX

11b=------=~----M-----

(CpllTsat +q)«1+b)--+a) MOlaX

(3-11)

By plotting the efficiency Tlb predicted by the above expression versus M~X for

different working conditions, the attributes of the new model are best revealed. As seen

in Figure 3-4, the new model accounts for the variation of efficiency Tlb with the effect

of load, capacity and operating conditions, as would be required by a realistic model. In

the remaining of the dissertation, the model will extensively be used for the

optimisation and analysis of total site utility systems in order to minimise the total

utility cost.

18

Chapter 3

80

75

llb (%) 70

65

60

55

50

45

40

0

h 7f:-)( )(

20 40 60 80 100

M --(%) M max

Hardware Models

-+- Tin= 144, P=88bar, q=2005kj/kg

~ Tin=144, P=88bar, q=1383kj.kg

Tin=144, P=48bar, q=2005kj/kg

Tin: 144, P=48bar, q=1651kj/kg

Figure 3-4: The BHM accounts for the effect of boiler size, load and operating conditions on

efficiency

3.2.2 Summary

The Boiler Hardware Model is based on basic thermodynamic principles and the typical

heat loss plot proposed by Pattisson and Sharma (1980). The thermodynamic principles

describe the operation of boilers and the relation between fuel requirement and steam

generation. The plot of heat loss against load represents typical operation of boilers.

Againist the published data (Pattisson and Sharma (1980» , the BHM provides estimates

within 2% error. In addition to size, load and operating conditions, the heat loss of a

boiler depends on a series of other factors, such as its type, technology and age. Hence,

it is not realistic to expect all boilers to fit in the same curve. To get plots for the

particular classes of boilers , it is sensible one revises the regression parameters to

accurately reflect on the particular case.

19


3.3 The Condensing Turbine Hardware Model

The Turbine Hardware Model (THM) presented by Mavromatis and Kokossis (1998a)

is only valid for back-pressure steam turbines. In order to address the optimisation and

analysis problem of total site utility systems, the THM is extended towards a

generalised Condensing Turbine Hardware Model (CTHM).

3.3.1 The Turbine Hardware Model

The THM is based on the Willans Line which depicts steam turbine performance as

shown in Figure 3-5. Where Wmax is maximum power output and n is incremental shaft

work generation against a unit of steam change. The THM relies on the size of the

steam turbine and describes the operation of the unit over its entire range. The turbine

shaftwork is given by (Mavromatis and Kokossis, 1998a):

W 6 1 (A lJ A)( 1 max =-- UIIis - M --M ) 5B M max 6

(3-12)

The isentropic efficiency can be predicted by (Mavromatis and Kokossis, 1998a):

_6~(1_ A )1_1Mmax

llis - 5 B MlisM max ( 6 M ) (3-13)

where:

W : the shaft-work of the steam turbine

A, B : the regression parameters

Ml is : the isentropic enthalpy change

M : the steam flowrate

Mmax : the steam turbine capacity

llis : the isentropic efficiency

20

Chapter 3

Throttle Flow (M)

M Willans line

wmax Shaftwork (W)

Figure 3·5: The THM of steam turbines

Hardware Models

W

The THM accounts for a maximum steam flowrate through a simple turbine, an

isentropic enthalpy change between the turbine inlet and outlet, and a set of regression

parameters. The isentropic enthalpy change and the regression parameters can be

calculated using saturated temperatures of the steam at the turbine inlet and outlet (see

Appendix A). The maximum steam flowrate is derived from the heat demands and

specific heat load at the turbine exhaust. The THM takes into account changes in

isentropic efficiency with the turbine load and working conditions.

3.3.2 The Condensing Turbine Hardware Model

It is assumed that the Willans Line applies to condensing turbines (Church, 1950). The

Condensing Turbine Hardware Model (CTHM) pursues similar calculations for the

shaftwork:

(3-14)

where:

W : the shaft-work of the condensing turbine

AC, BC

: the regression parameters

Mi i., : the isentropic enthalpy change

21


M : the steam f10wrate

Mm3x : the steam turbine capacity

The isentropic efficiency is similarly predicted by:

c =~_1 (1 1]/.1 5 Be

Ae 1 M max =:----)(1----) ~isMmax 6 M

(3-15)

The differences between the CTHM and theTHM relate to the regression parameters AC

and BC• Typical data on the efficiency of condensing turbines are found from plots of

the maximum efficiency, as shown in Figure 3-6 (Peterson and Mann, 1985). The

regression parameters are derived from the data on Figure 3-6. By definition, the

maximum efficiency is:

hence:

E max

rh·.max = MI . M max /.1

E max ~i.\· Mmax = __

77 ;s ,max

0.85 ..,.-------------------

0.75

11 is , max 0.65 ____ 28bar

41bar

0.55 62bar

X 83bar

0.45 +---------,,-------,------~

0.1 10 100

Emax(MW)

Figure 3-6: Typical data on the efficiency of condensing turbines

22

(3-16)

(3-17)


The curves in Figure 3-6 are represented by an expression of the following equation for

each inlet pressure:

E max

Ml isM max = __ = A C + B C E max (3-18) l]is.max

The regression parameters AC and Be are derived as functions of the inlet pressure or the

respective saturation temperature Tsat (see Appendix B):

(3-19)

Be = be +be Tsar 1 2 (3-20)

3.3.3 Summary

The Condensing Turbine Hardware Model follows similar principles with the THM. It

has the capacity to accurately consider the effect of turbine size, load and operating

conditions on the efficiency of typical condensing turbines.

The plots of maximum efficiency represent typical condensing turbines. Compared to

such plots, the CTHM provides estimates within 3% error by conducting two segments'

regression (see Appendix B). More accurate estimates can be obtained by applying

more segments' regression analysis.

3.4 The Gas Turbine Hardware Model

Most of the previous applications dealing with the synthesis and design of site utility

systems assume constant efficiency for the gas turbine and disregard the effect of

capacity and partial loading. With a purpose to address the problems of the synthesis

23


and design of total utility systems under operational variations, a Gas Turbine Hardware

Model (GTHM) is proposed here. The GTHM makes use of the basic thermodynamic

principles, exploits available information for gas turbine equipment, and accounts for a

realistic model to use in synthesis and conceptual calculations.

3.4.1 Model Development

Figure 3-7 illustrates us the basic structure of a gas turbine cycle. The power output

(W), the total power loss of the gas turbine cycle (WIOSS), the fuel flowrate (F\ the fuel

temperature (Tf) , the air flowrate ~), the air temperature (Ta) and the outlet

temperature rout are related by:

(3-21)

where,

Cpa : the specific heat of air

Cpf : the specific heat of fuel

cpg : the specific heat of flue gas

MIf : the specific enthalpy of fuel reaction

W10ss : mechanical losses, heat loss and so on.

Ft, Tt

r6 Combustor

Compressor Turbine

Figure 3-7: Simple gas turbine cycle

24


If we define f = Ff ,Equation (3-21) becomes: Fa

(3-22)

Let us define

(3-23)

Then, Equation (3-22) yields:

(3-24)

The parameters .1h and W10ss generally depend on the size of the gas turbine. For a gas

turbine, the overall electrical efficiency increases with size. Typical data on the

electrical efficiency against the turbine size are shown in Figure 3-8 (Marechal and

Kalitventzeff, 1998). The curve explores the impact of the turbine size on the basis of a

full-load efficiency; It does not provide information on the resulting efficiency from a

partly loaded unit. The curve is regressed in the form:

(3-25)

Where Ag and Bg are regression parameters (see Appendix C).

25


o.~~----------------------------------------~

0.4

0.35 l1e•max

0.3

0.25

0.2 +-----..,.------r-----.----r-----.---~--____"

o 10 20 30 40 50 60 70

Figure 3-8: Typical data on the electrical efficiency of gas turbines as a function of size

(Marechal and Kalitventzeff, 1998)

From the definition of the electrical efficiency:

It follows that:

It is assumed that:

Where n is a constant parameter.

w 11e = Ml Ff

f

wmax

11e.max = Ml F f .rnax f

26

(3-26)

. (3-27)

(3-28)


According to Equations (3-24) and (3-28) the maximum power output is equal to:

(3-29)

Substituting Equation (3-27) into Equation (3-25) yields:

(3-30)

By combining Equations (3-28), (3-29) and (3-30), the following expressions for the

parameters of the model are derived:

1 A g

ilh = (1+n)-(Ml j - f ) Bg F ,max (3-31)

and

(3-32)

Substituting Equations (3-31) and (3-32) into the Equation (3-24) gives:

(3-33)

According to Equation (3-23) and Equation (3-31), the outlet temperature Tout is given

by:

27


Equations (3-30) and (3-33) relate the power output of the gas turbine to the size and the

load of the turbine, as well as its operating conditions. Equation (3-34) relates the outlet

temperature of the gas turbine to the size of the turbine and its operating conditions,

expressed through r, Tf, f, .MIf. Given the expected operating conditions, the

performance of the turbine can be estimated merely on the basis of its size. While the

non-linear variation of the efficiency is accounted for, the relation of the power output

to the load is linear. The predicted electrical efficiency can be deri ved from Equations

(3-26) and (3-33):

1 A8 Ff.max

rtl' =-(1- f )«1+n)-n f) (3-35) B8 Ml fF ,max F

0.5

0.4 40MW 60MW

l1e 0.3

0.2

0.1

0 0 10 20 30 40 50 60

W(MW)

Figure 3·9: The GTHM accounts for the effect of gas turbine size and load on efficiency

By plotting the predicted efficiency against the fuel load Ff at various turbine size Ff,max,

Figure 3-9 shows the variation of the electrical efficiency with load and the effect of the

turbine size on the turbine efficiency as it would be expected by a reliable and realistic

model.

28


3.4.2 Summary

The GTHM is based on basic thermodynamic principles of gas turbine operations. It

considers a maximum efficiency plot and the assumption of fixed percentage of Wloss to

maximum power output. The thermodynamic principles ensure heat and mass balances

and the maximum efficiency plot accounts for a standard performance of a gas turbine.

The GTHM accounts for only 2% errors by conducting a two segments' regression (see

Appendix C). In addition to capacity, load and operating conditions, the efficiency of

gas turbine depends on a series of other factors, such as it's type, technology and age.

Consequently, it is not realistic to expect all gas turbines to fit in the same set of curves.

It is sensible to obtain plots for the particular class of turbines that are under

consideration and extract the corresponding regression parameters that will more

accurately describe the specific class.

3.5 Conclusions

A set of hardware models CTHM, BHM and GTHM are proposed. The use of the

models for the analysis and optimisation of site utility systems will be explained in the

following sections. The models combine thermodynamic principles, engineering

knowledge and performance data for condensing turbines, boilers and gas turbines.

They enable for an accurate prediction of unit efficiencies and embody the efficiency

trends of realistic units in terms of their variation with capacity, load and operating

conditions. These effects are accounted for in a simple and linear fashion, the

importance of which will be illustrated in the subsequent chapters.

The hardware models CTHM, BHM and GTHM provide results of good accuracy, by

considering the dependence of the efficiency on the capacity and operating conditions.

In view of operational variations, the effect of the part-load operation is well accounted

for all these models.

29


With respect to the analysis and optimisation problem, the CTHM, BHM and the

GTHM models provide the basis for modelling the condensing turbines, boilers and gas

turbines respectively in a manner that the efficiency trade-offs of the various design

alternatives can be considered. The linear relations of the power output to the steam

load of condensing turbines, the steam load to the fuel requirement of boilers and the

power output to the fuel requirement of gas turbines are essential for simple

formulations for the optimisation of site utility systems.

30

Chapter 4 Steam Level Optimisation

Chapter 4

Steam Level Optimisation

4.1 Introduction

In the design of process plants, the perfonnance of site utility systems directly

influences the operation of the plants, hence, the optimal design of site utility systems

often leads to significant savings. As there are strong interactions between the site

utility system and site processes, the design problem needs to consider the integration of

the site processes with the site utility system. The design usually involves two major

tasks:

1. the selection of steam levels with respect to their pressure or saturation

temperatures;

2. the development of a configuration for the operating units (ie, boilers, steam

turbines, gas turbines and the auxiliary units).

This chapter introduces a systematic optimisation methodology for the selection of

steam levels. In the next chapter a systematic methodology will be presented for the

optimal configuration of the utility system.

The placement of steam levels has a significant bearing on the utility demands, the

cogeneration potential of the processes and the operating conditions of the steam

turbines. The specific problem addressed in this approach assumes a given structure for

the chemical processes. Different operation scenarios are also given for the chemical

processes along with forecasts for prices of utilities over a finite number of time

periods. The different operation scenarios of the total site are described by the sets of

Total Site Profiles (TSP) shown in Figure 4-1. The process heat sources reject heat by

31


raising steam at different levels; the process heat sinks absorb heat also at different

levels. The total amount of steam raised by the process heat sources doesn't usually

match the amount required by the process heat sinks. Because of thermodynamic

constraints and heat transfer constraints, auxiliary cooling and heating are required.

These are available by the cold utility and the VHP steam raised by the boiler. The

timing of demands changes the profiles of heat sources and sinks over time and the

duration of each time period is usually different.

The objective of this chapter is to find the optimum locations for the steam levels

considering the total site. Single operations will be discussed first and subsequently be

generalised for multiple operation scenarios. As discussed by Petroulas and Reklaitis

(1984), if auxiliary fuel-boilers are required, they should operate at the highest-pressure

level. The optimisation problem then needs to determine the temperature of the VHP

steam, the saturation temperature (or pressure) of each steam level, the auxiliary boiler

duty, the cooling utility demand and the shaft-work produced by the steam turbine

network for each expansion zone. By using the THM and BHM models, one is able to

target the overall fuel requirement, the cooling utility demand and the co-generation

potential. In order to obtain the optimal solution for minimum utility cost, we need to

identify the correct compromise between heat recovery and co-generation.

Scenario A Scenario B

T T HP

MP

IP

LP

H H H H

Figure 4-1: Different operation scenarios can be represented by sets of total site profiles

32


4.2 The Strategy

Considering the drawbacks of the conventional techniques (see section 2.2) for the

selection of steam levels, the following strategy is proposed to determine the optimal

steam levels. The new strategy is shown in Figure 4-2. The strategy comprises two

stages:

1. The total site analysis is used to postulate a new transhipment network that describes

the heat integration of the steam levels with the process heat sources and heat sinks.

2. An optimisation model is developed based on the transhipment network and the

THM and BHM models. The model optimises by minimising the total annual cost

and is formulated as a multi-period Mixed Integer Linear Programming (Mll..P)

model.

Gal Analy~)-----t~~ I Transhipment Network Development I

G; and BHM m~)-----1~ ~r

~ I Optimisation I ~

I Optimal Steam Levels I Figure 4·2: Schematic showing the steam level optimisation strategy

4.3 The Transhipment Network of a Total Site

The transportation model determines the optimum transfer of commodities from sources

to destinations. The transhipment model has been widely used in the Operation

Research (Garginkel and Nemhauser, 1972) that deals with the optimum allocation of

resources and represents a variation of the transportation problem. Papoulias and

Grossmann (l983b) proposed a transhipment model for the synthesis of heat exchanger

33


networks. In this work, a transhipment network representation is developed for the total

site in order to get the optimal steam levels.

The total site heat flows can be represented by total site profiles. As seen in Figure 4-3,

heat is regarded as a commodity to ship from process heat sources to steam levels and

from steam levels to process heat sinks through temperature intervals. These intervals

account for thermodynamic constraints in the transfer of heat. In particular the second

law of thermodynamics requires that heat flows only from higher to lower temperatures,

and therefore these thermodynamic constraints have to be accounted for in the network

model. This is accomplished by partitioning the entire temperature range into

temperature intervals. For the total site profiles the interval temperatures are the

temperatures of turning points (critical points) of each heat source and heat sink. These

are all candidate locations of the optimum steam levels. The selected temperatures are

listed in descending order. The optimal steam levels are selected from all potential

steam levels denoted by their saturation temperatures.

As shown in Figure 4-3, the points A,B,C,D,E,F... are the turning points. This

partitioning method guarantees the feasible heat transfer of heat in each interval, given

the minimum temperature approach L\ T min. In this way as shown in Figure 4-3, the total

site heat flows are represented by the transhipment network. The network comprises

three cascades of temperature intervals:

• Heat source cascade.

• Steam level cascade.

• Heat sink cascade.

The heat source cascade represents that heat flows from process heat sources to the

corresponding temperature interval, and then to the steam level in the same temperature

interval with residual going to the next lower temperature interval. For the heat sink

cascade, it can be considered that heat flows from steam level to the corresponding

temperature interval, and then to the process heat sinks in the same temperature interval

with residual going to the next lower temperature interval. The steam level cascade

represents that heat flows from process heat sources to the corresponding steam level,

34

Chapter 4 Steam LeveL Optimisation

and then to the process heat sinks in the same temperature interval with residual passing

a steam turbine to the next stearns level.

T Heat source Steam Levels Heat sink cascade cascade cascade

A

8 --

Cooling Utility

H

Figure 4-3: Transhipment network representation of the total site heat flow

It is assumed that the total number of stearn levels for the site is I. The levels are

labelled from the highest level (i=l) down to the lowest level (i=I). The temperature

range for each level is partitioned into J temperature intervals which are labelled from

the highest interval (j=I) down to the lowest interval (j=J). In this way, the entire

temperature range of the total site is partitioned into IxJ temperature intervals. The

intervals are labelled from the highest interval (i=l, j=l) down to the lowest interval

(i=I, j=J).

The heat flow pattern of the temperature intervals for stream level i can be illustrated as

shown in Figure 4-4. It is represented by the three heat cascades:

35

Chapter 4 Steam Level Optimisatioll

Heat souce Steam level Heat sink

Site heat cascade cascade cascade Site heat

source

~ n. sink

~ i, j=1 (]--.I H it II

i, j=2 0--.1 H n: ~ JJ ~ ~

~ --------.. ~ ~

---------------

i, j=J-1 <l

i, j=J

Figure 4-4: Heat flow pattern of the temperature intervals for steam level i

(a) Heat source cascade:

(1) Heat flows into a particular interval from the process heat sources

contributing to the temperature interval.

(2) Heat flows out of a particular interval to raise steam with a temperature at the

lower bound of the interval.

(3) Heat flows out of a particular interval to the next lower temperature interval

or the cooling utility. The heat is the residual heat that can't be utilised in the present

interval, and consequently has to flow to a lower temperature interval or the cooling

utility.

(4) Heat flows into a particular temperature interval from the previous interval

that is at higher temperature. This heat is the residual heat that can't be utilised in the

higher temperature interval.

36


(b) Steam level cascade:

(1) Heat flows into a particular level from the heat source cascade in the same

temperature interval and VHP steam.

(2) Heat flows out of a particular level to the heat sink cascade in the same

temperature interval.

(3) Heat flows out of a particular level passing a steam turbine to the next lower

temperature steam level.

(4) Heat flows into a particular level from the higher temperature steam level.

This heat is the residual heat out of steam turbines.

(c) Heat sink cascade:

(1) Heat flows into a particular interval from the steam level in the same

temperature interval and VHP steam.

(2) Heat flows out of a particular interval to the process heat sinks within the

temperature interval.

(3) Heat flows out of a particular interval to the next lower temperature interval.

This heat is the residual heat that can't be utilised in the present interval, and

consequently has to flow to a lower temperature interval.

(4) Heat flows into a particular temperature interval from the previous interval

that is at higher temperature. This heat is the residual heat that can't be utilised in the

higher temperature interval.

Different operations are favoured by different sets of steam levels. Since it is

impractical to vary the conditions of steam levels between different operation scenarios,

the optimisation is searching for the conclusions that minimise the total utility cost over

the entire set of scenarios. For mUltiple scenarios the temperature intervals are extracted

from each individual scenario following the previous analysis that is based on a single

scenario; a general model is constructed next whereby intervals are listed in descending

order. The selection of steam levels is made out of all possible cases.

37


4.4 Optimisation Model

In this section, the postulated transhipment representation is modelled as a multi-period

MILP model. The model minimises the utility cost for the total site utility system under

multiple operation scenarios and incorporates the BHM and THM models that predict

the reliable equipment performance against a wide range of operating conditions. In

order to develop the mUlti-period MILP model continuous and binary variables are

associated with the transhipment network presented in Figure 4-3. The binary variables

assigned to steam levels represent the existence or non-existence of the corresponding

steam level at a given condition. The binary variables associated to units define the

operating status of boilers and steam turbines for each scenario. The continuous

variables represent the heat flows across temperature intervals, the boiler duty, the fuel

requirement, the cooling utility demand, the power output of each steam turbine and so

on.

The optimisation problem involves the following sets, parameters and variables:

Sets

IS = { i=I,2 .. .11 steam level}

I is the total number of steam levels.

1S = (j =1,2 ... 1 or jm=1,2 ... 1 I temperature intervals}

1 is the total number of temperature intervals for each steam level.

K = { k=I,2 ... Nk I operation scenarios}

Nk is the total number of operation scenarios.

V = { v=1,2 ... Nv I operating conditions of VHP steam }

Ny is the total number of candidate operating conditions of VHP steam.

Parameters

a,b regression parameters of BHM

Ai,j, Bi,j: regression parameters of THM for the steam turbine using steam in interval

(i,j)

Ay,By regression parameters of THM for the VHP steam turbine

38


Ci,j,k : total heat required by all process heat sinks in temperature interval (i, j) under

scenario k

CHk : total heat required by all process heat sinks above temperature interval (1,1)

under scenario k

Cp specific heat of saturation water between Tin and Tout sat

E1Si,j,jm: isentropic enthalpy change between the steam level in intervals (i, j) and the

steam level in interval (i+ 1, jm)

EISV v,j: isentropic enthalpy change between the VHP steam level at condition v and

the steam level in interval (1, j)

H operating hours per year

Hi,j,k total heat provided by all process heat sources in temperature interval (i, j)

under scenario k

HLk : total heat provided by all process heat sources below temperature interval (I, J)

under scenario k

Mimax

: capacity of the steam turbine locating between the steam level i and the steam

level i+l

Mmax : capacity of the VHP steam turbine

MBmax: capacity of the boiler

qv specific heat load of the VHP steam at operating condition v

qi,j specific heat load of the steam level in interval (i, j)

Ti,j lower bound temperature of interval(i, j). The intervals are labelled from the

highest interval (Tl,I) down to the lowest interval (TJ,J). The saturation temperature of

the steam level in interval (i, j) equals Ti,j

TkS time fraction of scenario k

~Tsat temperature difference between Tin and Tout sat

TVH saturation temperature of the VHP steam

U/ unit cost of fuel under scenario k

Ukc unit cost of cooling utility under scenario k

UkP unit cost of electricity under scenario k

Wkd electricity demands of the site under scenario k

39


Binary variables

Yi,j variable to denote the steam level in interval (i,j) is selected (Yi,j=1) or not

(Yi,j=<»

ytij,k variable to denote the steam turbine using steam in interval (i,j) works under

scenario k (ytj,j,k=1) or not (ytij,k=<»

Xv : variable to denote the operating condition v of the VHP steam level is selected

(xv=!) or not (xv=<»

xbv,k : variable to denote the boiler works at operating condition v under scenario k

(xbv,k=1) or not (xbv,k=O)

Xtv,k : variable to denote the VHP steam turbine works at operating condition v under

scenario k (Xtv,k=!) or not (xtv,k=1)

Continuous variables

RHi,j,k : residual heat flowing out of interval (i,j) of the heat source cascade under

scenario k

RCij,k : residual heat flowing out of interval (i,j ) of the heat sink cascade under

scenario k

Di,j,k : heat flowing out of interval (i,j) of the heat source cascade to the steam level

cascade under scenario k

Sjj,k : heat flowing into the steam level in interval (i,j) from a steam turbine under

scenario k

QSTv,j,k: heat flowing into the steam level in interval (l,j) from the VHP steam level at

operating condition v under scenario k

QSv,k : heat flowing out of the VHP steam level at operating condition v to the VHP

steam turbine under scenario k

Fj,j,k : heat flowing out of the steam level in interval (i,j) passing a steam turbine to

next steam level under scenario k

Ei,j,k : heat flowing out of the steam level in interval (i,j) to the heat sink cascade

under scenario k

FTj,j,jm,k: heat flowing out of the steam level in interval (i,j) passing a steam turbine to

the steam level in interval (i+l,jm) under scenario k

40


Wj,k : power output of the steam turbine locating between steam levels i and i+ 1

under scenario k

WVHk: power output of the VHP steam turbine under scenario k

steam load raised by the boiler at operating condition v under scenario k

fuel required by the boiler under scenario k

heat flowing out of the VHP steam level at operating condition v to process

heat sinks under scenario k

QVk : heat flowing into interval (1,1) of the heat sink cascade from the VHP steam

level under scenario k

CC: total cost of cooling utility

Cf: total cost of fuel

cp,tot total cost of electricity

4.4.1 Model Formulation

The previous sections explained the transhipment representation of the total site (as

shown in Figure 4-3) and the temperature intervals of the system (Figure 4-4). The heat

flows across the intervals of the heat source cascade, the steam level cascade and the

heat sink cascade can then be represented by Figures 4-5, 4-6 and 4-7 respectively.

RH,j-l.k RHi-I.J.k

RH'j.k

i=I.2 •.. .I, j=2,3,,,.J, k=I,2,,,.K i=I,2,,,.I, j=l, k=I,2,,,.K

Figure 4-5: Heat flow pattern in each temperature interval of the heat source cascade

41


S'J.k

F'J.k

Figure 4·6: Heat flow pattern in each temperature interval of the steam level cascade

RC..I).k

E.J.k

i=1,2 .... 1. j=2.3 ... .J. k=I.2 .... K i=I.2 ... .I. j=l. k=I.2 .... K

Figure 4·7: Heat flow pattern in each temperature interval of the heat sink cascade

Given the sets, the parameters and the variables introduced above, the mathematical

model includes:

Heat balances for each temperature interval (i,j) in the process heat source cascade:

H. k + RH . . 1 k = D .. k + RH . . k' i E IS, J' ~ 2, k E K I.J. I.J- • I.J. I.J. (4-1)

Hi.J.k + RHH.J.k = Di.J.k + RHi.J,k' i :t 1, j = 1, k E K (4-2)

H. k = D . k + RH . k' i = 1, j = 1, k E K I.J. I.J. I.J. (4-3)

42


Heat balances for each temperature interval (i,j) in the steam level cascade:

D"k +S""k =E."k +F. Ok' iE IS,jE JS,kE K I,j, I,j, I,j, I,j,

Heat balances for each temperature interval (i,j) in the process heat sink cascade:

E;,j,k + RCi,j_I,k = Ci,j,k + RCi,j,k ' i E IS, j ~ 2, k E K

Ei,j,k + QV k= Ci,j,k + RCi,j,k ' i = 1, j = 1, k E K

Ei,j,k + RCH.J ,k = Ci,j,k + RCi,j,k' i::l: 1, j = 1, k E K

Heat balances of the process heat sink cascade above the temperature interval (1,1):

CRk +QVk = LQCV,k' kE K veV

For each steam level exactly one operating condition can be selected. Therefore,

~y" " = 1, iE IS ~ I,j

jeJS

VHP steam also works at a single condition. Therefore,

(4-4)

(4-5)

(4-6)

(4-7)

(4-8)

(4-9)

(4-10)

If a steam level in interval (i, j) is not selected, the steam turbine cannot use steam from

the steam level, the following logical models apply:

Lyti,j,k ~ Yi,j' iE IS,jE JS (4-11) keK

43


To ensure that the input and output flowrates of each level are eliminated if the

corresponding level doesn't exist, the following inequalities must be included:

Si,j,k -UYi,j ~ 0, ie IS, j e JS,ke K (4-12)

Ei,j,k ~UYi,j :SO, ie IS,je JS,ke K (4-13)

Dj,j,k -UYi,j ~ 0, i e IS,j e JS,k e K (4-14)

F;,j,k - UYi,j :S 0, i e IS, j e JS, k e K (4-15)

A single steam turbine is assumed for every expansion zone. The shaft-work of the

steam turbines employs the THM:

[6 1 ( A r FT k 1 J] = __ EIS ... __ ,_,j_ I,j,jm, __ M.max t ..

Wi,k LL 5 B . I,j,jm M max . . 6 I Y I,j,k ' JEJS "nEJS I,j I q',j

ie IS,k e K

(4-16)

~ FT .. k = F .. k' i E IS, J' E JS, k E K L.J I,j,jm, I,j, (4-17) jmeJS

~ IT 1 .. k = S. . k' i ~ 2, J'm E JS, k E K L.J 1- ,j,jm, I,jm, (4-18) jEJS

The fuel consumption employs the BHM:

Q! = L ((C pD.Tsa, + qv X(1 + b )MBv'k + aMBrnax

Xbv,k )~ k E K (4-19) veV

If no VHP steam is available at condition v, the operation of the boiler at condition v is

also excluded. Therefore, the following logical inequalities apply:

44

Chapter 4

Lxbv•k ~ Xv' VE V keK

MBv•k -Uxbv•k ~ 0, vE V,k E K

Steam Level Optimisation

(4-20)

(4-21)

The heat balance for the VHP steam level is fonnulated as follows:

The power output of the VHP steam turbine is gi ven by:

where:

LQSTv.j •k = QSv.k' VE V,kE K jeJS

Lxtv•k ~ xv' VE V keK

QSv.k -Uxv.k ~O, vE V,kE K

LQSTv•j.k = Sl.j,k. jE JS,kE K lEV

The annual cost of the fuel required by the boiler is:

c f = LU! Q!T/ H keK

(4-22)

(4-24)

(4-25)

(4-26)

(4-27)

(4-28)

As the heat of cooling utility required by the process heat sources is RI,J.k + HLk under

scenario k, the annual cost of cooling utility is:

45


CC = 'LU%(R1,J,k + HLk)TkS H (4-29)

kEK

The savings from the power cogeneration are:

ct = LU:Wi,kT/ H, iE IS (4-30) keK

CVH = 'LU!WVHkT/H (4-31) kEK

The annual cost of electricity is:

cp,tot = 'LU[W/T/ H - 'LC/-CVH (4-32) kEK iE/S

The objective function used minimises the annual utility cost that includes the cost of

fuel and cooling utilities, as well as the cost of power. It is given by:

(4-33)

It should be noted that the proposed MILP model can also be used to find the optimal

steam levels for total site utility systems in order to minimise the fuel requirement. This

can be accomplished by replacing the above objective function by:

minMFR=C f (4-34)

Normally, these two objectives define different steam levels and this can be illustrated

by Case Study 1 which will be introduced next.

46

Chapter 4 Steam LeveL Optimisation

4.4.2 Remarks on the Optimisation Model

The above fonnulation consists of linear constraints of continuous and integer variables.

It comprises a multi-period Mixed-Integer Linear Programming (MILP) model. The

problem of synthesising a total site utility system given by the objective function and

the proposed set of constraints in Section 4.4.1, corresponds to a model whose

development requiring the following infonnation:

(a) Data on the total site profiles for each operation scenario.

(b) Specific heat load of VHP steam for each working condition; it is assumed that the

specific heat load of steam expanded through a turbine remains approximately

constant for all exhaust pressure values. The assumption is based on the observation

by Mavromatis and Kokossis (1998a), Raissi (1994) and Salisbury (1942).

(c) Cost correlations for the available utilities.

Total site profiles generation

Temperature intervals partition

Transhipment superstructure

Optimisation

Optimal solution

Figure 4-8: Schematic representation of the optimisation procedure

The steps are presented in Figure 4-8. The total site profiles for each operation scenario

are generated from the procedure proposed by Dhole and Linhoff (1993). The

temperature range is partitioned following the propositions of Section 4.3. The

transhipment representation is developed as explained in Section 4.3. The optimisation

determines the optimal structure of the steam levels and the operating condition of the

47


VHP steam. It also provides the steam load and power output of each steam turbine, the

heat duty of the boiler and the cooling utility demand for each operation scenario.

4.5 Case Studies

The methodology is illustrated with two different cases. Case 1 is a steam level

optimisation problem under a single operation scenario. The second case considers

multiple scenarios. The cost data of the available utilities are given in Table 4-1.

Cooling Water Fuel (Natural Gas) Electricity

Tout-Tin=20°C LfrV: 13856kWhlTon

Cost: O.0185$ffon Cost: 223$ffon Cost: O.12$/kWh

Table 4-1: Cost data of utilities

4.5.1 Case 1: Steam Level Optimisation under a Single Scenario

The total site profiles are given in Figure 4-9. The steam system comprises a boiler, the

four steam levels shown on the TSPs, and a single cooling utility. It is assumed that a

single steam turbine is placed at each steam expansion zone. The very high-pressure

(VHP) steam is raised in the boiler house at 500°C and 90 bar (Tsat =302°C). The

temperature of inlet water is 245°C. The specific heat load of the VHP steam is

0.557MWhlt at 500°C and 90bar. The HP, MP and LP steam are raised against process

heat sources and consumed by process heat sinks. On the basis of the total site profiles,

the objective is to find the optimal placement of the intermediate steam levels HP, MP

and LP in order to minimise the utility cost and minimise the fuel requirement

respecti vel y.

48


ToCi

Fuel __ ~

300 ----~--------~~ VHP

HP

MP

LP

Cooling Utility

---' ___ l •

. H(MW) H(MW)

Figure 4-9: The total site profiles for the site of Case 1

Based on the total site profiles and the temperature partition rule, the candidate

saturation temperatures for each level are obtained as shown in Table 4-2.

HPCOC) MPeC) LPCOC)

275 210 130

260 200 120

250 190 110

Table 4-2: Candidate saturation temperatures for each steam level of Case 1

The total heat provided by the process heat sources and total heat required by the

process heat sinks for each temperature interval (i,j) are obtained by targeting the heat

loads with the help of Figure 4-10 as shown in Table 4-3 and Table 4-4. The heat

requirement of the process sinks above the temperature interval (1,1) is 3MW. The

surplus heat of the process heat sources below the temperature interval (3,3) is 9MW.

49


=-::_ .. ===_--=~~~~_:_= ___ =-::=:: _____ :-__ -_-=--__ -_fC-__

H(MW)

-+ =====;::.;;.:;:::::====-==-=--t~. -fic>==-------.-.-.. --.---=----... --.... -...

Figure 4·10: Potential steam levels of Case 1

I.

H(MW)

H(I,j) MW 1 sl interval 2na interval 3r<1 interval

1 sl level 18 2 3

2D<1level 9 3 10

3r<1 level 9 5 2

Table 4·3: Heat provided by the process heat sources in each temperature interval of Case 1

C(I,j) MW 1 sl interval 2Da interval 3r<1 interval

1 sl level 1 2 3

2nd level 2 37 9

3rd level 3 3 6

Table 4·4: Heat required by the process heat sinks in each temperature interval of Case I

After the partition of the temperature intervals, the transhipment representation is set up

on the basis of Figure 4-11.

The proposed MILP model is applied to minimise the total utility cost. The model is

developed using the general algebraic modelling system (GAMS) (Brooke, etc., 1992)

and the optimisation has been conducted by employing the OSL solver. The

50


corresponding MILP model involves 92 continuous variables, 24 binary variables and

125 constraints.

302

270 260 250

210 200 190

130 120 110

Fue:..:..I_~ VHP

. . .-.~:-~:~~:~.~ ::~!~. f==5::::::+:;tl=~~ HP .... ..

- - - +- L-··=:·····:;:·· ~+:t~::::;;~ ... :~ .... + .~ .... -=: +- I . ....... ....... -=<.:........-. ................. ,...... -........ _ . ., .... _ .. _._ ..... _._ ... _ ..... ~----- MP

--+-

LP

Cooling Water

Figure 4-11: Transhipment network representation of case 1

The optimal steam levels for the Minimum Utility Cost (MUC) case are shown in

Figure 4-12. The optimisation determines the saturation temperature of each steam

level, the heat load balance of each steam level, the heat load of each steam turbine, the

power output of each steam turbine, the heat duty and fuel requirement of the boiler and

the cooling utility requirement. The optimal temperature levels are 260°C for HP, 200°C

for MP and 110°C for LP. The total utility cost is 68.5 k$/year, out of which the fuel

cost is 6618.7 k$/year, the cooling utility cost is 63.1 k$/year and the power saving is

6613.3 k$/year. The site pinch is located at the MP level.

The same MILP model can be used to minimise the fuel requirement. The optimal

steam levels for the Minimum Fuel Requirement (MFR) case are shown in Figure 4-13.

The optimal steam levels are 270°C for HP, 200°C for MP and 130°C for LP. Even

though the MFR case has the same total site profiles as the MUC case, their optimal

steam levels are apparently different. The fuel cost for the MFR case is 4280 k$/year

51


which is less than the MUC case. However, the power output is zero and there IS no

power saving.

302

270 260

250

Fuel 47_2MW

210 ------/--200 190

130 120 110

302

270 260

250

210 200 190

130 120 110

Cooling Water

Figure 4-12: Optimal structure for MUC case of Case 1

~ 22~ Fuel 30MW l5-~----r"

19MW _ --------------------------------- ------~ --------- ------....I.----'r:::--- ----. ---- -:=;------.--.-.--.. -.--... -.--.. --.-.--.... -.--...... -- -.... . ==:===:==~~=:==::::::::::=~:_==~ :====: =~==:====:::::::::::::::::====~M:W ----.- -=+-.------ ----.---.. --------- .--

- -14MW 17MW

:=~==:=:===::::===-....:-~===:==~ ~i~~: =:=~-.-.--.-.-.----.. ---.-.-.==:= J~~ ~:=::::========::::==~-.-~===: ---.. -.--..... ------.------.- ... -.--. -·_--·---··-·--·--··---i7MW -.---.. - -.-.. --.. --.-.-. --.-----.--.--.---... --.----.-.-

19MW OMW -.... ,,-..•.. -~.- ---..... -.--.----... ---.---.---.-.-.. -.------.-.. ----.

-- ... _------------_ .. _----------:=+ ---- -··---·-·1:2MW ---- .=+.- --.. -... -.. --.--... -------.-... ---.---.. --.-.-.-

16~

Cooling Water 7~

Figure 4-13: Optimal structure for MFR case of Case 1

52

VHP

HP

MP

LP

VHP

HP

MP

LP


4.5.2 Case 2: Steam Level Optimisation under Four Scenarios

The site of Case 1 is now considered with three additional scenarios, scenarios B, C and

D. The total site profiles for each scenario are shown in Figure 4-14. Each scenario

spans for a period equal to one-fourth of the year.

L '. -=r-= '.

H(MW)

T oe

--

T oe

:: =--=- ---:: -------

:: ::::::-:. =-==---

H (MW)

T oe Scenario A Scenario B

/ LP

H(MW) H(MW) H(MW)

Scenario C Scenario D

H(MW ) H(MW) H(MW)

Figure 4-14: Four operation scenarios for Case 2

Based on the total site profiles and the temperature partition, four candidate saturation

temperatures are obtained for each level as shown in Table 4-5.

HP(OC) MP(OC) LPeC)

280 210 140

270 200 130

260 190 120

250 180 110

Table 4-5: Candidate temperatures for each steam level of Case 2

53


For each temperature interval, the total heat provided by the process heat sources and

the total heat required by the process heat sinks are obtained by targeting the heat loads

and using Figure 4-14. Results are summarised in Tables 4-6, 4-7, 4-8 and 4-9, where

H(i,j) represents the heat provided by the heat sources and C(i,j) represents the heat

required by the heat sinks. The heat requirement of process heat sinks above

temperature interval (1,1) for each scenario is shown in Table 4-10. The surplus heat of

the process heat sources below temperature interval (3,3) for each scenario is shown in

Table 4-11.

H(i,j) MW 1 st interval 2na interval 3ra interval 4tn interval

1 st level 3 15 2 3

2nd level 9 3 10 1.5

r d level 6 1.5 5 2

C(i,j) MW 1 st interval 2na interval 3ra interval 4 tn interval

1 st level 3 1 2 3

2nd level 2 37 1.5 6

3rd level 1.5 3 3 6

Table 4-6: Heat enthalpy changes of processes of Case 2 (Scenario A)

H(i,j)MW 1 st interval 2nd interval 3rd interval 4tn interval

1 st level 3 15 2 3

2nd level 9 3 10 1.5

3rd level 6 1.5 5 2

C(i,j) MW 1 st interval 2nd interval 3rd interval 4tn interval

1 st level 3 1 2 3

2nd level 2 12 1.5 6

3rd level 1.5 3 3 31

Table 4-7: Heat enthalpy changes of processes of Case 2 (Scenario B)

54


H(i,j)MW 1 st interval 2nd interval 3rd interval 4th interval

1 st level 3 10 6 3

2ha level 9 3 5 3

3rd level 6 3 5 2

C(i,j) MW 1 st interval 2nd interval 3rd interval 4th interval

1 st level 6 8 8 3

2nd level 2 15 4 6

3ra level 13 5 3 6

Table 4-8: Heat enthalpy changes of processes of Case 2 (Scenario C)

H(i,j) MW 1 st interval 2na interval 3ra interval 4th interval

1 st level 5 4 2 3

2na level 9 3 10 1

3ra level 6 8 5 2

C(i,j) MW 1 st interval 2nd interval 3ra interval 4th interval

1 st level 3 1 2 3

2nd level 2 10 9 6

3ra level 6 3 9 10

Table 4-9: Heat enthalpy changes of processes of Case 2 (Scenario D)

Scenario A Scenario B Scenario C Scenario D

O(MW) O(MW) 3(MW) 2MW

Table 4-10: Heat required of process sinks above temperature interval (1,1) for Case 2

Scenario A Scenario B Scenario C Scenario D

9(MW) 9(MW) 5(MW) 7MW

Table 4-11: Surplus heat of process sources below temperature interval (1,1) for Case 2

55

Chapter 4 Steam Level Optimisatioll

The transhipment network is set up on the basis of Figure 4-15.

302 Fuel '----_.

280-------- -. 27()---- .-+---= 260-'·-- '0

250 - -- - -.------ -.~-- -- ... -.-.. - .. ·+· .. I-~----I~-+-~

U

., ~

5 _OJ

VHP

HP

MP

==t~±==t:::::=:::I==5t:::t:t:~:::::;;;:::::~::::-:. :::::;=:= .=: : :==::=:::::=:::::::~ ... -. :=:~~==::::==== ....L.--+-L--_~-- - + -.---- . ~-.-. - .... --- .. - ... - LP

..... ,. ........................... _ .. _ ... :g .... _ ............ _ ...... __ ............ _ .......... .

Cooling Water

Figure 4·15: Transhipment network representation for Case 2

The Mll...P model is applied to minimise the total annual utility cost. The mathematical

model in GAMS involves 513 continuous variables, 88 binary variables and 628

constraints. The model employs the OSL solver.

The optimal saturation temperatures are 260°C for HP, 200°C for MP and 140°C for

LP. Figure 4-16 shows the Site Utility Grand Composite Curves for the four scenarios.

The total utility cost is 150.6 k$/year, out of which the fuel cost is 5252.8 k$/year, the

cooling utility cost is 126.1 k$/year and the power saving is 5228.3 k$/year.

4.5.3 Summary

The results of Table 4-12 illustrate different optimal steam levels between single and

multiple scenarios. Figure 4-16 shows that the site pinch of scenario A is at the MP. The

site pinches of the other three scenarios are at the LP. The illustration explains that:

• The optimal levels in considering isolated scenarios are generally different from the

case more scenarios are considered simultaneously

56


• Each scenario favours a different set of steam levels.

• Results may yield not only different levels but also different location of the site

pinch.

Scenario A 47,3MW

T VHPF===~~~~~~

HP 7MW

15MW MP ~--------~------~-------

58MW

17,5MW LP J------,

VLP 17,5MW

cw

H

Scenario C

2,2MW

15MW

CW H

Scenario B

Q,5MW

2,5MW

15MW MP ----

19,5MW

17,5MW LP J-----"---'-----

38,5MW

17,5MW

cw

Scenario D

T Q,86MW

HP

MP 15MW

'----r-r---_ 1, lMW

LP

22MW

CW

2,2MW

H

H

Figure 4-16: The resulting SUGCCs corresponding to the optimal steam levels of Case 2

Optima steam levels Single scenario (Case 1) Multiple scenarios (Case2)

lIP (OC) 260 260

MP (OC) 200 200

LP (OC) 110 140

Table 4-12: Optimal steam levels for single and multiple scenarios

57


4.6 Conclusions

As shown with the presented case studies, the proposed optimisation methodology is

powerful to address the needs of the preliminary steam levels design for the total site

system under operational variations. By exploiting engineering knowledge, the BHM

and THM models are capable of predicting the real efficiency trends of units, by

considering the dependency of the efficiency on load and operating conditions. The

application of the two models are particularly important in the case of multiple

operation scenarios, where the steam loads and the respective efficiencies may vary

significantly. By exploiting total site analysis techniques, a new transhipment network

is developed to represent the total site system. It can be used to describe the interaction

between the placement of steam levels and steam loads of site processes. Based on the

transhipment representation and combined with the BHM and THM models, a multi

period MILP model is applied to minimise the total utility cost for the total site under

multiple operation scenarios. Major decision variables include the overall fuel

requirement, the cogeneration potential and the cooling utility demand. The MILP

model is a general model which can not only be used for the Minimum Utility Cost

(MUC) case but also for the Minimum Fuel Requirement (MFR) case.

58

Chapter 5 Layout Screening and Optimisation

Chapter 5

Layout Screening and Optimisation

5.1 introduction

A typical chemical plant consists of several chemical production processes, which

consume heat and power to make products. The chemical processes usually operate in

different scenarios. Heat and power are supplied by a central site utility system and the

design should be able to adjust efficiently to variations in demand for heat and power.

The design decisions include the selection of the optimum steam levels and the layout

of the site utility system. The system consists of available steam turbines, gas turbines,

boilers and other auxiliary units. The optimal selection of steam levels has been

discussed in chapter 4.

Once the steam levels are determined, the design can proceed with the development of

the best structure to produce utilities. This task comprises a large combinatorial

problem. Candidate systems involve layouts of the following units:

1. simple and/or complex back-pressure turbines.

2. simple and/or complex condensing turbines.

3. reheat cycles.

4. simple and/or regenerative gas turbine cycles.

5. boiler networks.

Each alternative configuration results in a different overall efficiency and a different

capital cost. The consideration of multiple operation scenarios results in a further

increase of the design options to an extent that is difficult to handle even for moderate

problems. As the utility demands vary with time, it is important the utility system

59

ChapterS Layout Screening and Optimisation

maintain high efficiency over the entire variation range. On the other hand, the optimum

trade-off between flexibility and capital cost needs to be identified. In order to evaluate

the alternative design options and distinguish amongst the associated efficiencies, the

effects of the unit size, as well as load and operating conditions on the unit efficiencies

need to be taken into account. These effects generally involve non-linear relations that

give rise to complex models and formulations.

The problem addressed in this chapter assumes given structures of existing chemical

processes and fixed steam levels whose optimisation has been separately addressed in

chapter 4. Also given are the power and steam demands at each level. The time

associated with each operation scenario can be different. Then the design problem is to

determine the structure of the site utility system to minimise the total cost, subject to the

satisfactory of the utility demands over the available operation horizon.

The following boilers are considered in the analysis:

1. Very High Pressure (VHP) boilers fired by fuel.

2. Heat Recovery Steam Generators (HRSG) which recover heat contained in the gas

turbine or the furnace exhaust gases. Supplementary firing is allowed for these units.

3. Waste heat boilers recovering heat from chemical processes.

4. Medium pressure boilers fired by fuel, which reheat steam in reheat cycle.

The capacities of the boilers should be determined, and the boiler efficiencies are

variable and depend on the boiler capacity, heat load and the operating conditions.

Steam is collected and distributed to chemical processes, steam turbines, reheat cycles

or to the next low pressure steam level through letdown valves.

Power can be generated by gas turbines, steam turbines and diesel engines or by

importing electricity from the utility grid.

For gas turbines, the following configurations are considered:

1. Simple gas turbine cycles.

2. Regenerative gas turbine cycles.

60


The gas turbine efficiencies are variable and depend on the gas turbine size, load and the

operating conditions. The exhaust gas may be used by a HRSG to generate steam.

For steam turbines, the following configurations are considered:

1. Back-pressure (BP) steam turbines.

2. Extraction BP steam turbines.

3. Condensing turbines.

Steam turbine efficiencies vary with the turbine capacity, type of exhaust, i.e.,

condensing or non-condensing, load, and the operating conditions. If a condensing

turbine is selected a condenser and a vacuum header have to be selected.

Steam can be returned as condensate. The return of condensate is collected in a

condensate header at a given pressure and saturated condition. Auxiliary units include

deaerator and pumps.

5.2 The Strategy

Systematic techniques are required to address the optimal configuration design of total

site utility systems under operational variations. The strategy that is proposed in this

work is schematically shown in Figure 5-1.

The approach combines the benefits of total site analysis, thermodynamic analysis and

optimisation techniques. The total site analysis technology is used to screen and identify

all possible design options. The thermodynamic analysis is applied to reduce the size of

the optimisation problem. Since the energy cost of a utility system is an overwhelming

factor in the analysis of each year's cost, the thermodynamic efficiency is used to guide

the selection of the main utility structures. This strategy has been applied successfully in

utility system design (Chou and Shih, 1987) and heat exchanger network design

(Linnhoff and Turner, 1981). The proposed strategy comprises the following five

stages:

61


1. The total site analysis is used to screen and identify all possible design options

2. The thermodynamic analysis is employed to screen among various design

alternatives and identifies the most promising design options that are passed on to

the next stage.

3. Based on the promising design options, this stage is to develop the detailed design

components for the superstructure that is much smaller than the conventional

superstructures. The components will be concerned with back-pressure steam

turbine network, condensing steam turbine network, reheat cycles, gas turbine

network, boiler network and auxiliary units.

4. The superstructure is optimised so as to minimise the total cost. The optimum model

is a result of the BHM, THM, CTHM and the GTHM applications and is formulated

as a multi-period MILP model.

5. The component back-pressure and condensing turbines are synthesised into practical

and complex turbines.

c;; site ana~)-----I.~ Possible design options

G;;odynamiC a~r----i.~ Promising design options

Superstructure generation (reduced size)

Synthesis of complex turbines

Figure 5-1: Schematic showing the configuration design optimisation strategy

62


5.3 Total Site Analysis

There are enormous number of candidate structures which include steam turbine cycles,

condensing turbine cycles, simple gas turbine cycles, regenerative gas turbine cycles,

combined steam and gas turbine cycles with or without condensing turbine, diesel

drivers, and all of their djfferent combinations.

The synthesis and design problem is to find a site utility system that satisfies the

chemical processes ' varying heat and power requirements, subject to minimum energy

consumption and capital investment. The method discussed in this work proposes that

the process heat requirements are satisfied first and the heat and power requirements are

matched exactly. This is particularly desirable for those industties that use a very large

amount of thermal energy such as the petrochemkal , food processing and the paper &

pulp (Chou and Shih, 1987).

VHP

HP

CW

Figure 5-2: Identification of steam turbines of a site by using the SCC

The Site Composite Curves (SCC) reflect on the integration opportunities between

chemjcal production processes and the site utjlity system. The curves can represent the

steam flow in the utility system as well as the heat exchange between site processes and

utilities (Figure 5-2). The enclosed shaded area between the steam levels is proportional

to the potential for power cogeneration . The curves also reveal the heat recovery, fuel

63

ChapterS Layout Screening and Optimisation

requirement and cooling utility demands of the site. Therefore, the see can be used as a

conceptual tool to screen and target the possible design options for the site utility

system. Figure 5-2 illustrates a possible allocation of back-pressure turbines with the

use of the see. The sizes and positions of the turbines can be identified using the

curves.

5.4 Thermodynamic Analysis

The objective of the thermodynamic analysis is to screen out the infeasible and

inefficient options. As it will be shown later in the chapter, The size and complexity of

the optimisation problem is reduced dramatically.

Heat and power represent energy of different quality. The thermodynamic efficiency is

defined by a relationship that determines the ratio of the useful part of the energy to the

total fuel input. The thermodynamic efficiency of a typical utility unit is defined by:

(5-1)

W is the shaft-work generated. L Qt is the sum of the steam heat loads required by the

chemical processes at different levels. Qfuel is the net fuel heat input. The

thermodynamic efficiency indicates fuel utilisation efficiency.

In the proposed work, the thermodynamic analysis is used to calculate the

thermodynamic efficiency of each potential utility structure and lead to the construction

of an overall efficiency curve. The curve accounts for all possible structures, assuming

that heat demands of the processes are satisfied first. The efficiency curve explains the

most appropriate combinations of the utility structures to be selected as the candidate

structures.

64

Chapter 5 Layout Screenillg alld Opti/'/'lisation

5.4.1 Thermodynamic Efficiencies and Utility Structures

Figure 5-3 illustrates the total site profiles of a pl ant. The possi ble utility structures

which satisfy the heat and power demands of the site processes are identified. T he

thermodynamic efficiencies of the corresponding utility structures are provided.

VHP

cw

Figure 5-3: Total site profiles of a plant

5.4.1.1 Integration of the Boiler and Back-Pressure steam Turbine (BBPT) cycle

The stearn crossing each expansion zone can be used by bac k-pressure steam turbines to

generate power (Figure 5-4). The VHF steam is raised by the VHF boiler. The

thermodynamjc efficiency is defined by the ratio of the useful energy (power outputs

and steam heat loads to processes) over the fuel consumption :

I wi + IQ/ I Q;" eI, i

(5-2)

where Wi is the shaft-work generated by the stearn turbine, Q/ is the steam heat load of

the steam turbine to processes and Q;',el,i is the net fuel heat input in boiler i.

65


Q ,

cw

Figure 5-4: Integration of the BBPT cycle

As shown in Figure 5-4, the exhaust heat of BP steam turbines can be used as process

heat, therefore the VHP steam load equals:

(5-3)

Substituting Equation (5-3) into Equation (5-2) gives:

(5-4)

where Tl rB is the thermodynamic efficiency of the boilers.

5.4.1.2 Integration of the Gas Turbine and Waste heat Boiler (GTWB) cycle

The GTWB cycle is shown in Figure 5-5.

66


F'

WB

GT

+ VHP

Figure 5-5: Integration of the GTWB cycle

The gas turbine is integrated with the waste heat boiler to generate power, and the waste

heat boiler is used to raise steam. It is assumed the gas turbine works at full load (i.e. ,

maximum efficiency load). The thermodynamic efficiency of the GTWB cycle is

defined as the ratio of the useful energy (the power output of gas turbine and the steam

load raised by the waste heat boiler) over the fuel consumption. It is calculated by:

(5-5)

where WG is the power output, QG is the steam load generated in the waste heat boiler

and pf is the fuel consumption . On the basis of the GTHM, the fuel consumption is

given by:

(5-6)

As presented by Cohen et al. (1987), the stack temperature is assumed as 170°C.

Therefore, the useful waste heat from the gas turbine to the boiler is:

67


(5-7)

T'ut can be calculated by using Equation (3-34).

The steam load of the boiler is given by:

G BQ Q = 11, waste (5-8)

where 1]/8 is the thermodynamic efficiency of the waste heat boiler.

5.4.1.3 Integration of the Boiler and Condensing Turbine (BCT) cycle

The BCT cycle is shown in Figure 5-6. As the exhaust heat of the condensing turbine is

lost to cooling water, the thermodynamic efficiency is defined by the ratio of the useful

energy (the power output of the condensing turbine) and the fuel requirement. It is

calculated by:

BCT We 11, =-QB

fuel

(5-9)

where We is the power output of the condensing turbine and Q~e1 is the fuel

consumption.

It is assumed that the condensing turbine works at full load. Hence, on the basis of the

CTHM, the relation between the power output and the steam load crossing the

condensing turbine is:

(5-10)

68

Chapter 5

The fuel requirement is given by:

a 1 Q juel =-a qM

'fit

Layout Screen.ing and Optimisation

(5-11)

where q is the specific heat load of the steam and 'fIta is the thermodynamic efficiency of

the boiler.

Combining Equations (5-9), (5-10) and (5-11), the thermodynamic efficiency of the

BCT cycle is given by:

(5-12)

Boiler

VHP VHP

+

VAC

Figure 5-6: Integration of the BeT cycle

5.4.1.4 Integration of the Gas Turbine, Waste heat Boiler and Condensing Turbine

(GTWBCT) cycle

The GTWBCT cycle is shown in Figure 5-7. When the gas turbine and waste heat boiler

cycle produces the amount of steam more than the steam requirements from the

processes, a condensing turbine can be integrated to the gas turbine and waste heat

boiler cycle to generate additional power by using the surplus heat. The thermodynamic

efficiency for the GTWBCT cycle is defined as the ratio of the useful energy (power

69


outputs of the condensing turbine and the gas turbine) over the fue l requirement. It is

calcul ated as follows:

GTWBCT We + W G

T] =----( F J t1H

J

(5-13)

where WC and WG are the power outputs of the condensing turbine and the gas turbine

respecti vely. WC is calculated by applying the CTHM and WG is calcul ated by the

GTHM.

F'

WB

Fa

GT VHP

+

VAC

Figure 5-7: Integration of the GTWBCT cyc le

5.4.1.5 Integration of the Surplus steam Condensing Turbine (SCT)

The SCT is defined as the condensing turbine using surplus steam from chemical

processes as shown in Figure 5-8. Condensing turbines can be integrated to the site

utility systems to generate power with the use of surplus heat.

As the SCT uses surplus heat, it should be considered as the first priority choice fo r

power generati on in the design problem provided that chemical processes have surplus

heat. In order to compare efficiencies of different SCT units, the thermodynamic

70

Chapter 5 Layout Screening and Optimisatioll

efficiency of the SCT is defined as the ratio of the power output to the surplus heat of

the processes. It is calculated as follows:

w surp surp _

llr - Q surp (5-14)

where Wsurp is the power output of the condensing turbine and Q surp is the surplus heat

of the chemical processes. The W urp can be calculated by using the CTHM.

VHP

ew~ VAC VAC

Figure 5-8: Integration of the SCT

5.4.1.6 Import of Power (lP)

There is always an option to import power from a utility grid. In order to compare the

efficiencies of the site utility systems with imported power, a thermodynamic efficiency

for importing power is included based on the principle of the Top Level Analysis

(Makwanna, 1997). It is assumed that the cost of Qrucl fuel can buy Wimp! power. The

imp0l1ed power efficiency is defined as:

. W impr C F

rJ"1Jpt = --= _ Q cP

fuel

(5-15)

where C F is the unit fuel price and cP is the unit power price.

71


The concept defined above provides us an efficiency for importing power, which can be

directly used for comparison with the thermodynamic efficiencies of utility structures.

5.4.2 The Thermodynamic Efficiency Curve

In order to identify the most efficient candidate structures, a Thermodynamic Efficiency

Curve (TEC) is constructed. The efficiency relates the utility structures of Section 5.4.1.

The efficiencies are computed following the discussions in Section 5.4.1. Given the

steam demand for each level, the calculations yield the thermodynamic efficiency and

the maximum power output for each possible design option. The TEC is presented

graphically in Figure 5-9. The vertical and horizontal axes respectively represent the

thermodynamic efficiency and the power requirement. The TEC is constructed by first

plotting the efficiency curve of units using surplus heat from chemical processes (SCT

in this case), whose length equals the maximum power capacity. The curve follows with

the other designs plotted one by one in a step downwards in terms of efficiency until

completion of options. In this case, the SCT and the BBPT cycles are the preferable

options, the GTWB cycle follows next and the GTWBCT cycle is itself followed by the

BCT cycle and the option to import power.

BBPT

GlWBCT I

I SCT I IP t-- [-~-' f~ ~-I(--J f[~~_~I ___ PB8PT~f'~~_}~_J _~~ __ Iuuu~

Ll ---------------�r-----~!--------+I----~I---------------~ ~ ~ Pc Po Power (MW)

Figure 5-9: The thermodynamic efficiency curve

The power requirement of the site determines the utility systems to consider. The

corresponding sizes of the units are identified and targeted with the use of the TEC; the

72


inefficient options are screened out. Superstructures are developed only using the

options enabled by the TEC. Figure 5-9 explains the case. Assuming a power

requirement P A, the SCT and the BBPT cycles are only allowed. The other inefficient

options are excluded. Assuming the power requirement from PA to PB, additional

considerations include a gas turbine and waste boiler cycle. The other options are

similarly screened out. The power capacity of the gas turbine is equal to the difference

between the power requirement and P A. Additional power requirement from PB to Pc

introduces the GTWBCT cycle. The power capacity of the cycle is equal to the

difference between the power demand and PB. Extending the power requirement from

Pc to PD includes the option for the BCT cycle. The capacity in power of the cycle is

equal to the difference between the power requirement and Pc. Beyond the power

requirement PD, the residual power has to be imported from the utility grid.

It should be understood the TEC is a screening tool based on thennodynamics and in

particular based on energy efficiency. Alternative tools can be designed to replace the

focus on energy efficiency by a focus on fuel to power ratios or other economic criteria.

In all cases, one should ensure the screening tool considers second and third-best

options. Alternatively, the TEC procedure can be relaxed by shifting the cut-off line of

the synthesis screening and let synthesis options with slightly lower efficiencies to also

become part of the superstructure.

So far, the TEC is discussed on the basis of a single operation scenario. Changes in the

steam and power demands will affect the TEC and suggest different utility structures.

For mUltiple operation scenarios, a systematic methodology is presented that makes use

of superstructure development.

5.5 The Generation of the Superstructure

The TEC is constructed for each operation scenario. The curves are applied to identify

candidate structures and capacities of the utility units. A systematic method is presented

to generate the superstructure for the site utility system and optimise for the best option.

73


5.5.1 Superset of Back-pressure Steam Turbines

The cogeneration potential available between the steam levels can be exploited through

a lot of combinations of turbine networks and layouts such as complex turbines,

multistage turbines, single turbines and so on. As discussed by Mavromatis and

Kokossis (1998b), both complex turbines and multistage turbines are equivalent to a

cascade of simple turbines, each taking up potential from a single expansion zone, as

shown in Figure 5-10. On the grounds of the equivalence, all possible combinations of

turbine layouts are reduced to a single superset of component cylinders as illustrated by

Figure 5-11. It is only this superset of design components that is required in order to

derive the optimum structure of back-pressure steam turbine network.

Figure 5-10: Complex turbines are considered as a cascade of simple turbines

The sizes of component turbines for each scenario are determined at the thermodynamic

analysis stage. For multiple operation scenarios the number and sizes of the simple

component cylinders for each expansion zone are identified by using the discretisation

method proposed by Mavromatis and Kokossis (1998b). The method suggests that the

turbines are sized to match the loads of every scenario as well as all their possible

combinations.

74


Figure 5-11: Decomposition of complex steam turbines

The case of two scenarios with the steam flows across an expansion zone is illustrated

in Figure 5-12. The first combination involves the select jon of turbine TI sized to the

scenario B, while operating at part load under scenario A. This option features the

lowest capital cost, but lower part load efficiency for scenario A. Alternatively, turbine

T2 can be installed to size scenario A. This option achieves the highest overal l

efficiency but requires the highest capital cost. In option 3, turbine T2 can be se lected,

along with turbine T3 sized to take up the remaining load for scenario B. The efficiency

for scenario B will be smaller than the first two options, but achieves the highe t

efficiency for scenario A and requires lower capital cost than the second option.

14--- Scenario B ScenarioA ~

HP E}gg § HP

Q MP MP

Superset of BP steam turbines

n 11 11 . .

""m'~"" ""'; " ""'~"""""" " ' '''''''''2?T~'''''''' '' ' :'' "" '[' "''' '''' '''' '' '' '' '''' '' 'Y'r''''''''' :·fi .. .. · .. ·j .. 1 : : T1 :: 2: T3:

· . . . . . · . . . . . · . . . . . · . . . . . l...-__ -'-. _---'-. -+ .. . .

Q Q Q

Option 1 Option 2 Option 3

Figure 5-12: The candidate BP steam turbines for the case of two scenarios

75


5.5.2 Superset of Gas Turbines

The capacity of the gas turbine for each scenario is determined by using the TEC. For

multiple operation scenarios the number, sizes and types of candidate gas turbines of the

superset depend on the specific problem, as explained in the following section.

5.5.2.1 Types of Gas Turbines in the Superset

The types of the gas turbine cycles are concerned with simple and regenerative gas

turbine cycles. The major difference between the simple and regenerative gas turbine

cycles is the addition of a recuperator for heat exchange between the turbine outlet and

the compressor outlet as shown in Figure 5-13. Following Chou and Shih (1987), the

types of the gas turbines are screened by the characteristic value of power to heat ratio,

PIH. Table 5-1 shows the ratio corresponding to each gas turbine cycle.

Heat -exchanger

Air

Compressor Turbine Power

Figure 5·13: The regenerative gas turbine

Gas turbine cycle PIH ratio

Simple gas turbine cycle 0.65

Regenerative gas turbine cycle 0.85

Table 5-1: P/H Characteristics of gas turbine cycles

76


5.5.2.2 Number and Sizes of Gas Turbines in the Superset

The GTHM relates the power output to the fuel load and the size of the gas turbine as

shown in Equation (3-33). As both the load and size of the unit need to be optimised,

straightforward modelling would result in an MINLP formulation. The discretisation

method follows next, however, reveals an MILP problem could be solved as the

economic analysis of the gas turbine operation suggests the discrete sizes and number of

the candidate gas turbines.

0.5

0.4 40MW 60MW

0.3 TJe

0.2

0.1

0 0 10 20 30 40 50 60

W(MW)

Figure 5·14: The effect of part load operation prevails over the increase of efficiency with gas

turbine size

As the electrical efficiency increases with size but decreases at part load, the highest

efficiency is obtained when a gas turbine is sized to operate at full load under the

specific power demands. This is shown in Figure 5-14. Hence, in terms of efficiency,

the optimum turbine size for each scenario is that which exactly matches the power

demand for each scenario. For multiple operation scenarios, the maximum efficient

sizes may not be the optimal sizes if capital cost is considered. Following the

discretisation scheme used for BP steam turbines, a discretisation method is proposed

whereby gas turbines are sized to match the power demand of every scenario as well as

all their possible combinations. The case of two scenarios with the power demands is

illustrated in Figure 5-15.

77


There are three combinations and three component gas turbines are identified. The first

option features the lowest capital cost, but lower part load efficiency for scenario A. The

second option achieves the highest overall efficiency but requires the highest capital

cost. In option 3, The efficiency for scenario B will be smaller than the first two

options, but achieves the highest efficiency for scenario A and requires lower capital

cost than the second option.

~ PB (MW) --+j t4- PA (MW) ~ I

DO PA D=cJo PB

G~

. . . . . . .

n .... j/ .................. ~ ... ~ ......... nr~ 1...-____ : __ + : : : :

PA PB P(MW) PA PB P(MW) PA PB P(MW) Option 1 Ootion 2 Option 3

Figure 5-15: Candidate gas turbines for the case of two scenarios

5.5.3 Superset of Boilers

The BHM is used to describe the performance of each fired boiler and waste heat boiler.

It is reminded that the BHM relies on the size of the boiler Mmax• The design model is

given by:

Qfuel = (C p!1Tsa, + q)«1 + b)M + aM max) (5-16)

The above expression relates the fuel flowrate with the steam load and the boiler size.

As both the steam load and the size of the boiler need to be optimised, the model results

in an MILP formulation by converting the bilinear model to a linear model.

78


Waste heat

Fuel . . .

VHP

Figure 5-16: Superset of boilers

The superset of the boilers is shown in Figure 5-16. The waste heat is the waste heat

from gas turbine cycles. The number, sizes and fuel requirements of the boilers are

detennined by the optimisation.

5.5.4 Superset of VHP Condensing Steam Turbines

The power output of the VHP condensing turbine for each scenario is determined with

the use of the TEes. In terms of efficiency, the optimum turbine size is the one that

exactly matches the power demand for a single scenario. For the mUltiple operation

scenarios, the maximum efficient sizes may not be the optimal sizes if the capital cost is

considered. The number and sizes of candidate condensing turbines of the superset for

multiple operation scenarios are determined by the discretisation scheme followed for

the gas turbines. The discretisation method is proposed for multiple operation scenarios

so that condensing turbines are sized to match the power demand of every scenario as

well as all their possible combinations.

The case of two scenarios is illustrated in Figure 5-17. There are three combinations and

three component condensing turbines. The first option features the lowest capital cost,

but lower part load efficiency for scenario A. The second option achieves the highest

overall efficiency but requires the highest capital cost. In option 3, The efficiency for

scenario B is smaller than the first two options, but achieves the highest efficiency for

scenario A and requires lower capital cost than the second option.

79


VHP

VAH

Superset of VHP condensing turbines

n

.. ··m~;,uu.T~ "~C~T ! uT'1····~CT~········ i·A····C···T·j·· : : CT: : : i : : 1; : : : · . . . . . · . . . . . · . . . . .

'------'----'--+

PA PB P(M'N) PA PB P(MW) PA PB P(M'N) Option 1 Option 2 Option 3

Figure 5-17: Candidate VHP condensing turbines for the case of two scenarios

5.5.5 Superset of Surplus Steam Condensing Turbines

The surplus heat of the processes for each level is obtained by total site analysis. The

optimum turbine size for each scenario exactly matches the surplus heat load. The

number and sizes of candidate surplus steam condensing turbines of the superset for

multiple operation scenarios are determined by the discretisation scheme followed for

the back pressure steam turbines. The discretisation method is proposed for mUltiple

operation scenarios so that condensing turbines are sized to match the surplus heat loads

of every scenario as well as all their possible combinations. The case of two scenarios

with the surplus heat loads is illustrated in Figure 5-18. There are three combinations

and three component surplus condensing turbines are identified.

80

Chapter 5

O~rp 0aurp P(MW)

Option 1

Layout Screening and Optimisation

IP

VAH

Superset of VHP condensing turbines

O~urp O~urp P[MW)

Option 2

O~urp 0Burp P(MW)

Option 3

Figure 5-18: Candidate surplus steam condensing turbines for the case of two scenarios

5.5.6 Reheat Cycles

In a reheat cycle, steam is first expanded to some intermediate pressure and then

reheated in the boiler. It next expands in the turbine to the exhaust pressure. Following

Chou and Shih (1987), the reheat cycle can improve the overall thermal efficiency only

if the thermal efficiency contributed by the reheat part is greater than that of the

remaining parts. The required large heat-exchange area and the increased complexity in

system design detract from the gain in efficiency due to reheating. The reheat cycle,

therefore, will be of interest to site utility system design only when a lot of heat is

exhausted to cooling water.

5.6 Optimisation Model

In thi s section , a mUlti -period MILP model is presented for the minimisation of capital

investment and operating cost. The model incorporates the BHM, THM, CTHM and the

GTHM models. The optimisation is a screening tool for the selected alternative design

81


options by using the thermodynamic analysis, rather than for the exhaustive structures.

The binary variables account for the selection of units and their operation status at each

scenario. The continuous variables relate to the stream flowrates (steam, fuel), the

power outputs and the operating and capital costs.

The optimisation problem involves the following definitions for sets, parameters and

variables:

Sets

IB = { ib I candidate boilers }

IT = { it I candidate BP steam turbines }

IC = { ic I candidate condensing turbines }

VC = { vc I candidate VHP condensing turbines }

p = { pi I power generation units }

I = { i I selected units}

IG = { ig I candidate gas turbines }

K = { k I operation scenarios}

Z = { z I expansion zones}

Parameters

a, b : regression parameters of BHM for boilers

Aic, Bic : regression parameters of CTHM for condensing turbines

Ag, Bg : regression parameters of GTHM for gas turbines

Az, Bz : regression parameters of THM for BP steam turbines of expansion zone z

Cp : specific heat of saturation water between Tin and Tout sat

cpg : specific heat of flue gas

Cpa : specific heat of air

ci : specific heat of fuel

EISic : isentropic enthalpy change of condensing turbine ic

EISz : isentropic enthalpy change of BP steam turbines of expansion zone z

F/,max : maximum fuel load of gas turbines Ig

H : operating hours per year

82


M-/i : specific enthalpy of gas turbine fuel reaction

LB : lower bound of boiler capacities

M i!'max : maximum steam load of boiler ib

M :.Tt·max : maximum steam load of BP steam turbine it of expansion zone z

M i?"'max : maximum steam load of condensing turbine ic

M ~.k : total steam load across each expansion zone z under scenario k

q : specific heat load of steam

r : temperature of inlet air of gas turbines

P : temperature of gas turbine fuel

AT:at : temperature difference between Tin and Tout sat

T/ : time fraction of scenario k

cf1 : upper bound of boiler capacities

U { : unit cost of fuel for boilers under scenario k

UfT,i : unit cost of fuel for gas turbines under scenario k

w/em : power demand of site processes under scenario k

Binary variables

Yi!·e : integers to denote the selection of boilers

y B•o : integers to denote the operation of boilers ib.k

yBT.e : integers to denote the selection of BP steam turbines Z.II

yBT.o : integers to denote the operation of BP steam turbines z.lI.k

Yi?,·e : integers to denote the selection of condensing turbines

/7.0 : integers to denote the operation of condensing turbines ic.k

ygT.e : integers to denote the selection of gas turbines

yGT.o : integers to denote the operation of gas turbines ig.k

83



eE! : annual fuel cost of boilers

(fiT! : annual fuel cost of gas turbines

C·tot : total capital cost of selected units

C{ : capital cost for each unit

(;'01 : total annual cost

M i~.k : steam load of boiler ib under scenario k

M BT : steam load of BP steam turbine it under scenario k z.it.k

M i~ : steam load of condensing turbine ic under scenario k

M;:k : steam load of VHP condensing turbine vc under scenario k

M ;,k : amount of steam throttled through the let down valve of expansion zone z

under scenario k

Q B,J : fired fuel load of boiler ib under scenario k ih.k

QB.w : waste heat load from gas turbines to boiler ib in scenario k ih.k

QGT.w : waste heat load of gas turbine ig under scenario k ig,k

Fi{k : fuel load of gas turbine ig under scenario k

W BT : power output of BP steam turbine it of zone z under scenario k z.it,k

W/U)' : power import under scenario k

Wi;]' : power output of condensing turbine ic under scenario k

wi~I : power output of gas turbine ig under scenario k

5.6.1 Model Formulation

Given the parameters, sets and variables above, the design model includes consideration

for the following models:

84


(a) VHP boilers

The BHM yields:

The above bilinear model is replaced by the following mixed integer linear model:

(5-18)

Constraints include:

The above logical constraint denotes X i:.k equals M i:·rnax while the boiler is operating.

LB Y B.o < X B < U B B.o ib.k - ib.k - Y ib.k ' ib E IB, k E K (5-20)

The above logical constraint denotes X i:.k =0 while the boiler is not in operating status.

M~'rnax _y~.eUB <0 ibE IB ,b ,b -, (5-21)

(5-22)

The above logical constraints denote the boiler capacity should be zero if it is not

selected and the boiler capacity should be larger that its lower bound and smaller than

its upper bound.

(5-23)

The above logical constraint denotes the load of the boiler should be zero if it is off.

85


(5-24)

The above constraint denotes the load of the boiler shouldn't be larger than its capacity.

(5-25)

The above logical constraint denotes the boiler can't operate if it is not selected.

(b) Back-pressure steam turbines

The THM applied for the power output of a back-pressure steam turbine in zone z under

scenario k yields:

Z E Z, it E IT, k E K

(5-26)

If the turbine is not selected, it can't operate:

BT,o _ BT,e < 0 Z' IT k K Yz,it,k Yz,it - , ZE ,ltE ,E (5-27)

The load of the steam turbine shouldn't be larger than its capacity:

M HT _ Hr,oM HT,max < 0 Z' IT k K z.it.k Y z.it.k z,it -, Z E ,It E ,E (5-28)

( c) Condensing steam turbines

The CTHM applied for the power output of a condensing turbine under scenario k

yields:

86


W CT 6 1 (ElS Aic )(MCT 1 MCTmax era) ic k = -- if - CT ,'c t - - ic' Yit t' , , 5 B M. ,max '6 '

Ie Ie

iCE [C,kE K (5-29)

If the condensing turbine is not selected, it can't operate:

cr,o _ cr,e < 0 . IC k K Yic,k Yic -, ICE ,E (5-30)

The load of the condensing turbine shouldn't be larger than its capacity:

MCT - CT,oM CT•max < 0 . IC k K ic.k Yic,k ic -, IC E ,E (5-31)

(d) Gas turbines

The GTHM applied for the power output of a gas turbine under scenario k yields:

ig E IG,k E K (5-32)

Where the maximum fuel flowrate F;{maX can be calculated by Equation (3-30).

If the gas turbine is not selected, it can't operate:

GT.o _ yf?T,e < 0 ig E [G k E K Y,g,k 19 -, , (5-33)

The load of the gas turbine shouldn't be larger than its capacity:

Ff _yGT,OFf,max <0 igE [G kE K ,g.k 'g.k 'g -, , (5-34)

The waste heat from the gas turbine is given by:

87


GT,w _ [1 a a f f 1 1 ( A g ] f Qi k - -CpT +Cp T +Ml f -( +n)- Ml f - f ) Figk , igEIG,keK g, f Bg F ,max , Ig

(5-35)

(e) Steam mass balances

The mass balance across each expansion zone z for scenario k involves the steam

through the turbines and the steam throttled through the let down valves (in case the

installation of a turbine is not cost effective). The mass balances give:

L M :'Tr,k + M ~,k = M ~,k Z E Z, k e K (5-36) iteff

The VHP steam requirement is equal to the sum of the amount of steam across the first

expansion zone plus the amount of the steam through the VHP condensing turbines,

LMi!,k =Mtk + LM;:k' kE K ibelB vceVC

(j) Power balance

The electricity balance under scenario k is expressed as:

~w. +W buy =W dem kE K £.J pl,k k k' piEP

(g) Costs

The annual fuel cost of boilers is:

CB,f = LU! Qi!:{T/ H keK ibelB

88

(5-37)

(5-38)

(5-39)


The annual fuel cost of gas turbines is:

(5-40)

The capital cost incurred for the installation of the equipment is:

cc,tot = L CjC

jei (5-41)

The capital costs of the units are calculated using the functions presented by Bruno et

al. (1998). They are given in Table 5-2 along with linearized expressions for the boiler

cost. It is important to note that the discretisation methods (Section 5.5.2) treat the

capacities of the steam turbines, the gas turbines and the electric generators as

parameters in the optimisation model. Therefore, the nonlinear capital cost functions for

these units are applied.

Unit Type of Cost Function Investment Cost ($/year)

Large package boiler Nonlinear 4954p'·77fp2

F: steam flowrate (t/h) fp2=1.3794-0.5438P+0.1879p2

P: Pressure (MPa) Linear (9Mpa) 495384+13861F

Heat Recovery Boiler Nonlinear 941Ffgu.7)

Ffg: flue gas flowrate (t/h) Linear 6996+211.5Ffg

Steam turbine Nonlinear 2237WstU.41

W st: power (kW)

Gas turbine Nonlinear 952WgtU./b

Wgt: power (kW)

Electric generator Nonlinear 176Wegu.49

Weg: power (kW)

Deaerator Nonlinear 904FBu.Cll

FB: BFW Flowrate t/h

Table 5-2: Capital cost data (Bruno et al. t 1998)

89


(h) Objective function

The objective function minimises the total annual cost:

(5-42)

The total annual cost consists of the capital cost and the fuel cost.

5.6.2 Remarks and Discussion

The optimisation model consists of linear constraints and integer variables, and

comprises a multi-period MILP model. The structure and the operation strategy are

optimised to minimise the total cost consisting of capital cost and operating cost. The

development of the MILP model requires the following information:

(a) steam level specifications

(b) data on total site profiles for each scenario

(c) power demand for each scenario

(d) cost correlations for the utilities

(e) capital cost correlations for the units

It should be noted that the original problem is a Mixed Integer Non-Linear

Programming (MINLP) formulation with a very large number of variables. The use of

total site analysis and thermodynamic analysis has reduced the problem into a

reasonably sized.

5.7 Synthesis of Complex Steam Turbines

The outcome of the optimisation stage is a set of simple steam turbines and condensing

turbines. The simple turbines can be used to synthesise practical complex or multi-stage

90


turbines. The synthesis of the complex turbines relies on the operation schedule of the

simple turbines as provided by the optimisation stage. For two cylinders to merge into a

complex unit, they both have to be loaded during the same scenario. Depending on

whether the steam flow through the upper cylinders of a complex turbine is larger or

smaller than that in the lower sections, the turbines can be of an extraction or induced

type.

5.8 Case Studies

Two case studies are selected to illustrate the capabilities of the methodology. The

operating conditions of the four steam levels, the vacuum header and the de aerator are

shown in Table 5-3. The steam used for heating can be returned as condensate. The

difference between the two case studies relates to the utility demands. The cost data of

the utilities used are given in Table 5-4. The capital costs are given in Table 5-2.

Unit Operating Conditions

VHPHeader Saturation Temperature: 303°C

HPHeader Saturation Temperature: 275°C

MP Header Saturation Temperature: 210°C

LPHeader Saturation Temperature: 140°C

Vacuum Header Temperature: 60°C, Pressure: 0.02MPa

Deaerator Vent Ratio: 0.0015

Table 5·3: Summary of operating conditions

Demineralized Water Fuel (Natural Gas) Electricity

Temperature: 27°C LHV: 13856kWhffon

Cost: 0.24${fon Cost: 223${fon Cost: O.I$/kWh

Table 5·4: Utility data

91

Chapter 5 LAyout Screening and Optimisation

5.8.1 Case Study 1

The Site Utility Grand Composite Curves (SUGCC) of Figure 5-19 reflect the steam

demand/generation of the site under three operation scenarios. The power demands for

the scenarios are given in Table 5-5. On the basis of the SUGCC, the aim is to find the

optimal configuration of the site utility system that satisfies the utility demands and

minimises the annual total cost.

Scenario B ScenarlOC ScenorloA 260

180 VHP VHP HP

HP

VHPI==="""""-~~-..., HP

MP MP 130

30 50

LP LP

MPI-----=-=30=-=-0-------1

lP 60

VAC VAC VAC

HUh} H !h} H !h}

Figure 5·19: The SUGCC of a site

Scenario A Scenario B Scenario C

Power demand (MW) 22 35 42

Table 5·5: Power demands of Case 1

5.S. 1. 1 Total Site Analysis

The SUGCC are given in Figure 5-19. The steam across each expansion zone is

obtained in Table 5-6. LP steam is in surplus and used by the condensing turbines.

Back-pressure turbines are installed in the steam expansion zones VHP-HP and HP-MP.

The power outputs for the possible SCT and BBPT cycles are calculated and shown in

Table 5-7.

92



VHP-HP 180 220 260

HP-MP 130 260 300

MP-LP

LP-Vacuum header 30 50 60

Table 5-6: Steam amount across each expansion zone of Case 1 (tIh)


SCT(MW) 2.5 4.1 5

BBPT(MW) 13 22.9 26.7

Table 5-7: Power outputs of possible SCT and BBPT cycles of Case 1

5.8.1.2 Thermodynamic Analysis

The characteristic values of power to heat ratio of the site for the three scenarios are

presented in Table 5-8. The PIH values are lower than the characteristic value of the

simple gas turbine cycle. A simple gas turbine cycle is then employed instead of a

regenerative gas turbine cycle. By calculating the efficiency and the maximum power

output for every potential cycle, the TEC is constructed starting with the most efficient

option with the corresponding power capacity limit. The TECs for the three operation

scenarios are shown in Figure 5-20. On the basis of the TECs and the utility demands,

the promising candidate utility structures include the Boiler and Back-Pressure steam

Turbine (BBPT) cycles, the Surplus Condensing steam Turbine (SCT) cycles and the

Gas Turbine and Waste heat Boiler (GTWB) cycles. All the other design options are

screened out because of their lower efficiencies. By using the TECs, the power outputs

of the GTWB cycles are obtained for all scenarios as shown in Table 5-9.

93

Chapter 5

seT

2.5

,....

'JMW

lAyout Screening and Optimisation


PIH ratio 0.22 0.285 0.29

Table 5-8: PIH characteristics of Case 1

Sconarto A

, I , , I

~ ~ I=q ~ 6.5MN I

seT I--~l-. l

Scenario 8

GTWB

GTWIICT

IICT

~ I.~ ····_··········1 22.9MIN "l ....................... ~ ..... .

PIIAW)

ScenaloC

B8PT GT'M!

I GlWIICT

IICT

_G' .. 26,1WNI f---- --·-1 1 OJMW ~.

Figure 5-20: TECs for Case 1


Power output (MW) 6.51 7.98 10.32

Table 5-9: Power outputs of the GTWB cycles of Case 1

5.8.1.3 Generation of the Superstructure

On the basis of the steam amount across each expansion zone for each scenario,

candidate sizes of the BP steam turbines expressed as maximum steam capacities can be

obtained for each zone. The sizes are given in Table 5-10.

94


BTl BT2 BT3 BT4 BTs

VHP-HP 180 220 260 40 80

HP-MP 130 260 300 30 170

Table 5·10: Candidate sizes ofBP turbines of Case 1 (tIh)

Similarly, for every scenario the surplus heat provided by the processes determines the

candidate sizes of the condensing turbines. These are given in Table 5-11. The simple

gas turbines are used. Expressed in terms of power capacities, the candidate sizes of the

gas turbines are given in Table 5-12.

CTl CT2 CT3 CT4 CTs

Size (tJh) 30 50 60 10 20

Table 5·11: Candidate sizes of condensing turbines of Case 1 (tIh)

OTl OT2 OT3 OT4 OTs OT6

Capacity (MW) 6.51 7.98 10.32 1.47 3.81 2.34

Table 5·12: Candidate sizes of gas turbines of Case 1 (MW)

VHP boilers are fired by fuel and heated by the waste heat from the gas turbine cycles.

An HP waste heat boiler and an MP waste heat boiler recover surplus heat from the

processes. Without heat exhausted to cooling water, the reheat cycle is excluded as an

option. The superstructure of the site utility system is shown in Figure 5-21.

95


VHP

HP • __ -r ---.-.-.-----.-.. - ....

MP

LP

~~~-I Deaerator L-___ .

'-------"

--,......:I-__ ... __ ....z... CONDo

Figure 5·21: Superstructure of Case 1

5.8.1.4 Optimisation

The superstructure is formulated as an MILP model. The optimisation minimises the

total annual cost. The model is developed using GAMS and the optimisation is

conducted by employing the OSL solver. The model involves 195 continuous variables,

92 binary variables and 242 constraints.

The optimum configuration is given in Figure 5-22. The selected units include three BP

steam turbines, one condensing turbine, one gas turbine, a VHP boiler, an HP waste

heat boiler, an MP waste heat boiler and the de aerator. The HP and MP waste heat

boilers are selected to produce HP and MP steam respectively. One of the back-pressure

turbines operates between the VHP and HP levels. The other two back-pressure turbines

96


operate between the HP and MP levels. They supply power by exploiting the

cogeneration potential. The condensing turbine is employed to generate power by using

surplus heat from the site processes. The back-pressure turbines and the condensing

turbine do not meet the power demands. The gas turbine is installed to supply the

remaining power. The total annual cost is 33.341 MM$. The annual fuel cost is 27.718

MM$ and the annual capital cost is 5.623 MM$. The capacities of the selected units are

given in Figure 5-22.

Max360tfrl

I

I UDeoeratO'

Max lO.32MN

VHP

Max6.91MW

HP

Max 19.78MN

LP

Max4.99MW

.&...,... _________ VAC.

.....,...lIr..-_ ...... r..-__ .z.. COND.

Figure 5-22: Optimal structure of Case 1

The optimal loads of the units are obtained under each scenario. These are given in

Table 5-13. The back-pressure turbine BTl (HP-MP) operates during A, but not during

Band C. Turbine BT3 (HP-MP) operates during Band C, but not during A. During A

turbine BTl (HP-MP) is more efficient than turbine BT3 (HP-MP) and during Band C

97


turbine BT3 (HP-MP) is more efficient than turbine BTl (HP-MP). The HP waste heat

boiler shuts down during B and C because there is no waste heat during these periods.

All other units operate for all three scenarios.

Unit Scenario A Scenario B Scenario C

BT3 (VHP-HP) 180tlh 220tlh 260tlh

(steam load! power output) 4.36MW 5.64MW 6.91MW

BTl (HP-MP) 130tlh Otlh Otlh

(steam load! power output) 8.38MW OMW OMW

BT3 (HP-MP) Otlh 260tlh 300tlh

(steam load! power output) OMW 16.61MW 19.78MW

CT3 30tlh 50tlh 60tlh


GT 3 (power output) 7.26MW 8.76MW 1O.32MW

VHP BI (steam load) 180tlh 220tlh 260tlh

HP WB (steam load) 50tlh Otlh Otlh

LP WB (steam load) 30tlh 50tlh 60tlh

Deaerator (water load) 21O.3t1h 31O.5t1h 360.5t1h

Table 5-13: Optimal loads of the units of Case 1

5.S.1.5 Synthesis of Complex Turbines

As shown in Table 5-14, no steam turbines have the same operation schedule.

Therefore, no complex turbines can be synthesised.

98


S.8.2 Case Study 2

The SUGCC account for the steam demand/generation of the site under the three

operation scenarios of Case 1. These are shown in Figure 5-19. The power demands for

this case are given in Table 5-14.


Power demand (MW) 12 25 30

Table 5-14: Power demands of Case 2

Based on the TECs of Figure 5-20 and the power demands, the candidate utility

structures include the Boiler and Back-Pressure steam Turbine (BBPT) cycles and the

Surplus Condensing steam Turbine (SCT) cycles. The other power units are not

economic and are excluded. The superstructure is shown in Figure 5-23 and is smaller

than the one studied in Case 1. The candidate sizes of the turbines are apparently the

same.

L---

I

~.~

;Deoeralor

VHP

HP

MP

LP

...:...._ ... .-.lI ..... __ .....&_ ..... _ VAC .

....,.-.lI ..... _--l'--__ .L CONDo

Figure 5-23: Superstructure of Case 2

99


The MILP model is optimised against the total annual cost. The model involves 97

continuous variables, 60 binary variables and 157 constraints.

The optimum configuration is shown in Figure 5-24. It includes two BP steam turbines,

one condensing turbine, one VHP boiler, one HP waste heat boiler, one MP waste heat

boiler and the deaerator. One back-pressure turbine operates between the VHP and the

HP steam levels. Another one operates between the HP and the MP steam levels. The

condensing turbine generates power using surplus heat from the site processes. There is

no need for a gas turbine. The total annual cost is 30.751 M$. It is lower than Case 1

because of the lower power demand. The annual fuel cost is 26.325 M$ and the annual

capital cost is 4.426 M$. The capacities of the units are given in Figure 5-24. The

optimal loads for each scenario are given in Table 5-15.

VHP t-::--, Max 5.78MN ~

HP

Max19.78MN

MP

LP

Max5.0MN

..z...,... ____ ..... ____ VAC.

--,......lI ____ .... __ ..&.. COND.

Figure 5-24: Optimal structure of Case 2

The back-pressure turbine BT2 (VHP-HP) and the turbine BT3 (HP-MP) maintain

identical operation schedules as shown in Table 5-15. Therefore, the two turbines can be

synthesised as a single complex turbine.

100


Unit Scenario A Scenario B Scenario C

BT 2 (VHP-HP) 180tlh 220tlh 220tlh


BT3(HP-MP) 119t1h 243t1h 300tlh


CT3 30tlh 50tlh 60tlh


VHP B, (steam load) 180tlh 220tlh 260tlh

HP WB (steam load) 50tlh Otlh Otlh

LP WB (steam load) 30tlh 50tlh 60tlh

Deaerator (water load) 21O.3t1h 31O.5t1h 360.5t1h

Table 5·15: Optimal loads of the units of Case 2

5.8.3 Discussion

Although the SUGCC of the two studied cases are the same, the optimal configurations

of the site utility systems are different because of the different power demands. It

implies that different PIH ratios assume different optimal structures. By using the

proposed thermodynamic analysis, the reduced superstructure is obtained.

For Case 2, the MILP model is also optimised by integrating the gas turbine cycles into

the superstructure. The same optimal solution is obtained. However, the model involves

195 continuous variables, 92 binary variables and 242 constraints, which is much bigger

than the proposed method. If other possible design options are integrated with the

superstructure, the size of the optimisation problem should be even much bigger.

101


5.9 Conclusions

A systematic methodology is presented for the optimal design of site utility systems

under operational variations. The methodology combines the benefits of total site

analysis, thermodynamic analysis and optimisation techniques. The approach accounts

for the interactions between the site utility systems and the site processes. The design

task is addressed in view of the anticipated variations in the process demands and the

effect of the unit capacities and varying loads on the efficiencies of the selected units.

These aspects normally give rise to highly complex and large problems. The proposed

methodology utilises total site analysis and thermodynamic analysis to reduce the size

and complexity of the design problem. The total site analysis is employed to screen and

identify all possible design options. A thermodynamic curve is proposed in this

approach. It is a useful tool to identify the promising candidate design options to be

included in the superstructure by screening among all alternative design options. The

size of the optimisation problem can be reduced by screening out the uneconomic

design options.

By using the engineering knowledge and analytical insight, a discrete scheme is

proposed to identify the sizes of the candidate steam turbines, condensing turbines and

gas turbines. The optimisation problem is formulated as a mUlti-period MILP model that

relies on the THM, CTHM, GTHM and the BHM to describe the performance of the BP

steam turbines, condensing turbines, gas turbines and boilers. The models account for

the efficiency variations with operating conditions and capacity. It should be

emphasised that, had conventional models for the units been applied, the use of an

MINLP formulation would be inevitable.

102

Chapter 6 Debottlenecking and Planning Optimisation of an Existing Site

Chapter 6

Debottlenecking and Planning Optimisation of an Existing Site

6.1 Introduction

Industrial plants are in need for debottlenecking technology and planning techniques to

accommodate with the best investment scheme and their process operations (Hirsheld

1987). There are additional incentives and challenges for site utility systems. First, one

has to assess the potential for the purchase of new equipment. The challenge has to

consider a dynamic environment with changes in utility demands and prices, changes in

technology and changes in markets and regulations. The site utility system addresses a

particularly dynamic market. Changes consider the operation of the chemical processes,

changes in the feed/product specifications and the modifications in the schedule of

production.

The purpose of this chapter is to present a systematic debottlenecking and planning

methodology for site utility systems. The objective is to determine the best investment

scheme for an existing site and the optimal operational strategies to adopt. Options

consider the minimisation of the total cost so that utility demands are met by the

utilities.

The problem assumes a given utility system. Also given are forecasts for the prices and

demands of utilities, the ambient conditions and the regulations over a finite number of

time periods. The problem identifies a number of time periods of different duration. The

heat requirements are satisfied in preference to the power requirements. A

superstructure is developed that considers existing processes and potential new

equipment. The candidates for debottlenecking are generated with the use of total site

103


analysis and thermodynamics. The superstructure is formulated as an optimisation

problem that minimises the total cost over the given time horizon and determines:

• the new equipment to purchase: equipment include boilers, steam turbines,

condensing turbines, gas turbines, waste heat boilers and auxiliary units.

• optimal operational strategies over the considered period. The units are possible to

tum on and off and the approach considers different operating levels in the plant.

• the amount of fuel, the appropriate type of fuel, the amount of water and assesses

available options to import power.

Non-linear and bilinear models are converted to MILP models by using piecewise

linearisation and integer programming techniques. Non-linear cost models are used for

the steam and gas turbines.

Potential steam boilers include:

1. Heat recovery system generators (HRSG) for recovering heat contained in gas

turbine or furnace gases and for generating super heated very high-pressure (VHP)

steam. Supplementary firing is allowed in these units.

2. Fuel fired units for generating VHP steam.

3. Waste heat units for recovering heat from process flue gases or from process units

such as chemical reactors.

The approach makes use of the BHM, so that capacities of the boilers can be

determined, and the boiler efficiency appears to be a variable of capacity, heat load and

operating conditions.

Gas and steam turbines are considered as potential electricity generators. Options for

steam turbines include:

1. Back-pressure steam turbines exhausting to lower pressure levels.

2. Extraction back-pressure steam turbines exhausting to medium and low pressure.

3. Condensing steam turbines.

4. Multi-stage simple turbines.

104


Complex turbines are decomposed into simple turbines and the use of the THM and

CTHM enables the turbine efficiency to vary with the turbine capacity, its load, the

operating conditions and the type of exhaust.

Options for gas turbines include:

(1) Simple gas turbines.

(2) Regenerative gas turbines.

By using the GTHM, the gas turbine efficiency remains variable and depends on the

turbine size, its load and the operating conditions. The exhaust flue gas is possible to

use by a HRSG to generate steam.

6.2 Optimisation Strategy

Efficient methodologies are required to address debottlenecking and planning

challenges for total site utility systems under operational variations. In this chapter, a

systematic strategy is proposed whose outline is schematically shown in Figure 6-1.

Optimisation of existing system

cr;;i site ana~)-----I •• Possible debottlenecking options

~odynamiC~ Promising debottlenecking OPtions

Superstructure generation (Existing system + promising debottlenecking options)

Synthesis of complex turbines

Figure 6-1: Outline of debottlenecking and planning strategy

105


The strategy comprises the following stages:

1. Optimise the existing system.

2. The total site analysis identifies the debottlenecking options that meet the variable

utility demands for the different periods.

3. The thermodynamic analysis screens out uneconomic options. A superstructure is

postulated out of the remaining candidates and includes the existing and new units.

4. The superstructure is formulated as an MILP model. The model minimises the total

cost and identifies the structure and the operational strategies to adopt. The

component back-pressure and condensing turbines are synthesised into practical and

complex turbines.

6.3 Stage I: Optimisation of the Existing System

The existing system is optimised for the maximum power output of the system over the

considered periods.

6.4 Stage II: Total Site Analysis

The Site Composite Curves account for integration between the site processes and the

site utility systems. Figure 6-2 shows the representation of a total site utility system that

uses the SCC. The shaded units are the candidates need to be installed; the others are

existing units. The capacities and the placement of the debettlenecking units are

possible to identify using the Sec.

In order to target the capacities of the potential steam turbines, one has to identify the

capacities of the existing complex turbines for each expansion zone. It is accomplished

by decomposing the complex turbines into sets of simple turbines with specific

capacities. A decompose strategy is presented following Chou and Shih (1987). Figure

6-3 illustrates a decomposition problem. The decomposition produces individual simple

turbines aJ, a2 and a3 which are of the same capacity. Similarly, simple turbines bi and

106

Chapter 6 Debottlenecking alld Planning Optimisation of an Existillg Site

b2 are of identical capacities. The decomposition strategy reduces the analysis at a level

where si mple turbines are only used.

VHP

cw

Figure 6-2: Identification of debottlenecking turbines of a site by using the S

Figure 6-3: Decomposing a complex turbine into different sizes of cylinders in eac h expansion

zone

107


6.5 Stage III: Thermodynamic Analysis

The debottlenecking includes options for boiler and back-pressure steam turbine

(BBPf) cycles, gas turbine and waste heat boiler (GTWB) cycles, boiler and

condensing turbine (BCT) cycles, gas turbine, waste heat boiler and condensing turbine

(GTWBCT) cycles, diesel drivers and option to import power (IP) from a utility grid.

The thermodynamic analysis screens out the inefficient options and identifies sensible

scenarios to include in a superstructure representation. After the thermodynamic

analysis the size of the problem is reduced dramatically.

6.5.1 The Thermodynamic Efficiency Curve for Debottlenecking

The basic idea is to employ the TEC first on the existing utility system and next with the

consideration of additional options.

BBPT Exis1ing System

GlWBCT

IP

PelOsi II~f1 PG1W8 1+1 PGTWBCT I-~I- --CD PA

PB Pc PD PE Power (MW)

Figure 6-4: Typical TEe for debottlenecking

The construction of the TEC is based on the assumption the heat requirements from the

chemical processes are satisfied before the power demands are considered. Efficient

debottlenecking options are identified by comparing the thermodynamic efficiencies.

Given is the steam demand at each steam level. Then, the thermodynamic efficiency and

the maximum power output are calculated for the existing system. The maximum power

108

Chapter 6 DebottLenecking and PLanning Optimisation of an Existing Site

output of the exi ting system IS calculated by optimising the existing system.

Calculations of efficiencies for the debottlenecking options follow the propositions of

Section 5.4.1. The de elopment of the TEC is shown in Figure 6-4. The first part (i.e.

"existing system") excludes new equipment. Subsequent parts account for new units.

6.5.2 Identification of the Promising Debottlenecking Options

The superstructure is de eloped on the basis of the options suggested by the TEe. In

reference to Figure 6-4 for example, a power demand to P A would imply the existing

system is sufficient to satisfy it. Figure 6-5 explains scenarios with power requirements

above P A and up to PB , it is necessary to invest on a new BBPT cycle. The additional

power can be targeted wi th the hardware capacity. The capacity equals the difference

between power requirement and P A. It is inefficient to explore other debottlenecking

options.

Til BBPT E»sIlng~ GlWB

p. P,

cw

Figure 6-5: The boiler and back-pressure turbine cycle for debottlenecking

Fi gure 6-6 exp lain cases of power requirements above PB and up to Pc. The gas turbine

and waste boiler c c le i required to consider as an additional option . The capacity of

the gas turbine hould be consi dered from the difference between the power requirement

and PB.

109


'l' bistro~S!em

P-

P,

66PT GTWB

GTWBCT

IP

P- P~~ ~ P, Po p. Ft>wer (MW)

F'

+ ~ ........ .

~",,"",,!;;=9 VHp:

HP

. .

........................................... . ........... •••• 1

Figure 6-6: The gas turbine and waste heat boiler cycle for debottlenecking

WB

Between Pc and Po as shown in Figure 6-7, the additional power should be available

from a GTWBCT cycle. The power capacity of the cycle should equal the difference

between the power requirement and Pc.

n.

WB

GT

BBPT ......................................................... GTWBCT

Fuel

BCT

VHP I:::::::::::.

-'~ I HP

~ ...................... .. .... ... ... ..................... 0.:

+

VAC

Figure 6-7: The gas turbine and waste heat boiler and condensing turbine cyc le for

debottlenecking

110

Chapter 6 Deboulellecking and Planning Optimisation of an Existillg Site

Similarly Figure 6-8 explains the picture between PD and PE. A BeT cycle should

produce the additional power. The power capacity equals the difference between the

power requirement and PD. Beyond PE, power should be imported from the utility grid.

BCT

r .......... ·~~~; .... · .. · ...... · .... · ...... · .. · .. · .. · ·~ WB

~ Fuel VHP!.

F"";;;;;;;!;=i +

GTWBCT VHP

HP

Iff Power (MW)

: C : ... ....................................... ................ : VAC

Figure 6-8: The boiler and condensing turbine cycle for debottlenecking

Figure 6-9 shows that if the chemical processes generate surplus steam, the surplus

condensing turbines can be integrated to generate additional power using surplus steam

for diffe rent levels.

VHP

I SSPT 11 E.omg $vslem

SCT

IP

~-[~} P, P, Power IMW)

VAC

Figure 6-9: Surplus condensing turbines for debottlenecking

III

Chapter 6 Debottlellecking and Planning Optimisation of all Existing Site

So far, the TEC is discussed to identify the most efficient debottlenecking options for a

single period operation . The discrete scheme presented in Section 5 .5 is applied to

generate the debottlenecking superstructure.

6.5.3 The Debottlenecking Superstructure

The superstructure consists of existing units and new units. The superstructure

development is schematically shown in Figure 6-10. The capacities of the

debettlenecking options are identified with the use of the TEC for each single operation

period and the discretisation schemes. The superstructure is modelled over all operation

periods.

+

Figure 6-10: Debottlenecking superstructure

112

Period n •.

Period 2

Pe riod 1


6.6 Stage IV: Optimisation

The postulated superstructure is formulated as an optimisation problem. It yields a

multi-period Mll..P model that is optimised for the minimum capital investment and

operating cost. The model incorporates the BHM, THM, CTHM and the GTHM

models. The MILP model is a screening tool with binary variables to represent the

selection of the new units and the operation mode of the units. The continuous variables

relate to the stream flowrates (steam, fuel), the power outputs and the operating and

capital costs.

The optimisation problem involves the definitions for sets, parameters and variables:

Sets

EB = { eb I existing boilers }

IB = { ib I candidate new boilers }

IT = { it I all BP steam turbines }

NT = { nt I candidate new BP steam turbines }

IC = { ic I all condensing turbines}

NC = { nc I candidate new condensing turbines }

VC = { vc I all VHP condensing turbines }

p = { pi I power generation units}

I = { i I selected new units }

IG = { ig I all gas turbines}

NG = { ng I candidate new gas turbines }

K = { k I operation periods }

Z = { z I expansion zones}

Parameters


A ic, Bic : regression parameters of CTHM for condensing turbines

Ag, Bg : regression parameters of GTHM for gas turbines

Az, Bz : regression parameters of THM for BP steam turbines of expansion zone z

113


Cp : specific heat of saturation water between Tin and T outsat

Cp : specific heat of flue gas

Cpa : specific heat of air

Cp : specific heat of fuel

ElSie : isentropic enthalpy change of condensing turbine ic

ElSz : isentropic enthalpy changes of BP steam turbines in expansion zone z

F/'max : maximum fuel loads of gas turbines Ig

H : operating hours per year

Mlf : specific enthalpy of gas turbine fuel reaction

LB : lower bound of boiler capacities

M !.max : maximum steam load of boiler eb

M BT,'max : maximum steam load of BP steam turbine it in expansion zone z Z.I

M i;r·max : maximum steam load of condensing turbine ic

M ;,k : total steam load across each expansion zone z in period k

q : specific heat load of steam

r : temperature of inlet air of gas turbines

P : temperature of gas turbine fuel

!:IT:al : temperature difference between Tin and Tout sat

T/ : time fraction of period k

if : upper bound of boiler capacities

U f : unit cost of fuel for boilers in period k

U~T,J : unit cost of fuel for gas turbines in period k

w/em : power demand of site processes in scenario k

Binary variables

y!',~ : integers to denote the operation of boiler eb

yj~'O : integers to denote the operation of boiler ib

yB.e : integers to denote the selection of boiler ib ib.k

114


Y BT.e : integers to denote the selection of BP steam turbine nt z.nI

y:::;:~ : integers to denote the operation of BP steam turbine it

y;;.e : integers to denote the selection of condensing turbine nc

yCl'.o : integers to denote the operation of condensing turbine ic ie.k

y~T.e : integers to denote the selection of gas turbine ng

yGT.o : integers to denote the operation of gas turbine ig ig.k

Continuousva~ks

cH! : annual fuel cost of boilers

cGT! : annual fuel cost of gas turbines

C·lot : total capital cost of the selected units

C{ : capital cost for each unit

Cot : total annual cost

M i!.k : steam load of new boiler ib in period k

M i!'rnax : maximum steam load of new boiler ib

M !.k : steam load of existing boiler eb in period k

M BT : steam load of BP steam turbine it in period k z.it.k

M i~ : steam load of condensing turbine ic in period k

M ;;:k : steam load of VHP condensing turbine vc in period k

M ~.k :amount of steam throttled through the let down valve of expansion zone z in

period k

QB,J : fired fuel load of new boiler ib in period k ib.k

Q B,J : fired fuel load of existing boiler eb in period k eb.k

QB.w : waste heat load from gas turbines to new boiler ib in period k ib.k

QB.w : waste heat load from gas turbines to existing boiler eb in period k eb.k

QGT.w : waste heat load of gas turbine ig in period k ig.k

115

Chapter 6 Debottlenecking and PLanning Optimisation of an Existing Site

Fi:,k : fuel load of gas turbine ig in period k

W BT : power output of BT steam turbine it in period k Z,il,k

W/UY : power import in period k

Wi;:I : power output of condensing turbine ct in period k

Wi~r : power output of gas turbine ig in period k

Wp~ : power output of power generation unit pi in period k

6.6.1 Mathematical Formulation

Given the parameters, the sets and the variables above, the model includes consideration

for the following models:

(a) VHP boilers (existing boilers and debottlenecking boilers)

Using the BHM, the fuel requirement of an existing boiler in period k is given:

The BHM is applied for the fuel requirement of a new boiler. As the boiler is optimised

both load and size, straightforward modelling with the BRM would result in the bilinear

tenn:

The above bilinear tenn is modelled instead as a mixed integer linear tenn:

116


Logical constraints include:

M i!'max - U B (1- Y!::) :S X !,k 5 M !,max - LB (1- Yi!::)' ib E IB, k E K (6-5)

The above constraint denotes X :,k equals M ;!,max while the boiler is operating,

L B B ,0 < X B < U B B ,0 Y ib ,k - ib ,k - Y ib ,k ' ib E IB, k E K (6-6)

The above constraint denotes X :,k =0 while the boiler is not in operating status,

(6-7)

The above constraint denotes the boiler capacity should be zero if it is not selected.

(6-8)

The above constraint denotes the load of the boiler should be zero if it is off.

(6-9)

The above constraint denotes the load of the boiler shouldn't be larger than its capacity.

(6-10)

The above constraint denotes the boiler can't operate if it is not selected.

117


(b) Back-pressure steam turbines (existing and debottlenecking turbines)

Using the THM, the power output of a back-pressure steam turbine in zone z in period k

yields:

BT 6 1 W.I'I. =--(EIS. ... ~ 5 B

z -

A: )(M BT _'!"M BT•max BT.O) M BT.max :.it.k 6 :.il Y:.it.k'

Z,ll

Z E Z, it E IT, k E K

(6-11)

The logical constraints that relate the above model are:

Y:::: _y::e SO, zE Z,itE NT,ntE NT,kE K (6-12)

M BT BT.oM BT.max < 0 Z't IT k K :.i1.1: - Y:.il.k ;;.il -, Z E ,I E ,E (6-13)

(c) Condensing steam turbines (existing and debottlenecking turbines)

The power output of a condensing turbine in period k is given by the CTHM:

CT 6 1 S Aic )(M CT 1 M CT.max CT,o) Wid = ST(EI ic - M CT.max ic,k - 6 ic Yic.k'

Ie IC

iCE IC,kE K (6-14)


YLT.·o - y;:.e ~O, iCE NC,nCE NC,kE K IC.~

(6-15)

M cr _ M cr.max cr ,0 < 0 . E IC k E K ie,/( ic Yie,k - ,IC , (6-16)

(d) Gas turbines (existing and debottlenecking turbines)

The power output of gas turbine ig in period k is given by the GTHM:

118


GT 1 W· k =-(Mlf Ig, Bg

The logical constraints relating to this model are:

GT.o GT,e <0 NG' NG k K Yig.k -Yng - ,nge ,lge ,e (6-18)

F' - F"max GT.o <0 . 1G k K ig.1: ig Yig.k - , 19 e I' , E (6-19)

The waste heat from the gas turbine can be obtained by:

(6-20)

(e) Steam mass balances

The mass balance across each expansion zone z in period k involves the steam through

the turbines and the steam throttled through the let down valves (in case the installation

of a turbine is not cost effective). The mass balances yield:

"LM:';;.k +M~,k =M~,k zE Z,ke K (6-21) ilErr

The VHP steam requirement is the sum of the amount of stream across the first

expansion zone plus the amount of steam through the VHP condensing turbines:

"LMi!.k + "LM!,k = Mtk + "LM;:k' kE K (6-22) ibEIB ebEEB vceVC

119


(f) Power balance:

The electricity balance in period k is expressed as:

~w W buy Wdi!m ~ pi.k + k = k ' kE K (6-23) pieP

(g) Costs:

The costs include the fuel cost of the utility system and the capital cost incurred for the

installation of the new equipment.

The annual fuel cost of boilers is:

CBJ = ~UIQ.BJr,sH+ ~UfQBJT,sH ~ k ib.k k ~ k eb.k k (6-24)

keK keK ibelB ebeEB

The annual fuel cost of gas turbines is:

CGT.! = ~ U GT.! pi r,s H ~ k Ig.k k (6-25)

keK igelG

The total capital cost of all new units is:

Cc,tot = Lct (6-26) iel

The capital costs of the units are calculated using the functions presented by Bruno et

al. (1998). They are given in the Table 5-2.

(h) Objective junction:

The objective function minimises the total annualised cost:

120


min C IOI = C B./ + CGT./ + ec,lol (6-27)

The total annual cost consists of the capital cost and fuel cost.

6.6.2 Solution Methods

The proposed model is an MILP problem and can be solved using a full space LP based

Branch and Bound method. A large number of the time periods however automatically

increases the size of the MILP model. The alternative approach followed in this work

solves the large MILP model using a decomposition algorithm such as the one proposed

by Iyer and Grossmann (1998). The algorithm is schematically shown in Figure 6-11.

The multi-period MILP is decomposed into a debottlenecking problem (Master

problem) and an operation-planning problem (Operation problem). Both problems are

formulated as MILPs. The master problem is a relaxed version of the original problem

in that it contains only a subset of its constraints and debottlenecking options. Its

solution provides a lower bound on the objective. The solution of the master problem is

used to set up the operation problem. The operation problem involves the

debottlenecking design options as they are fixed from the master problem. Its solution

provides an upper bound on the objective. Successive solution of these problems is

repeated until convergence criteria are met.

Original MILP model

1 .1 Master problem 1

~~"I (MILP) II---.-~

Structure cuts Tnal new structure

Operation problem (MILP)

Figure 6-11: Decomposition strategy

121


6.7 Cllse Studies

The methodology is illustrated with two examples. The first example considers a

debottlenecking and operation-planning problem. The second example considers an

industrial application.

6.7.1 Case Study 1

Figure 6-12 shows the configuration of an existing system. The current system consists

of a main boiler (Bl), two complex steam turbines (Tl and T2) and the de aerator. The

capacities of the units are shown in Figure 6-12. There are four steam levels (VHP, HP,

MP and LP). The operating conditions of the levels and the de aerator are shown in

Table 6-1. The steam is used for heating and can be returned as condensate. The utility

system should satisfy the heat requirements in preference to the power requirements.

Letdown steam from higher levels is available. There is no option to sell power. Ten

operating periods are considered, each one occupying 0.1 year. The utility demands are

shown in Table 6-2. The cost data are given in Table 6-3. The objective is to find the

optimal debottlenecking options and the operational planning for the site utility system.

VHP

HP

MP

LP

+ ,~Io-----

L-___ -..J

....,....&. __ :..-_--1. CONDo

i OeaeralOl , ,

Figure 6-12: The existing utility system of Case 1

122


Unit Operating Conditions

VHPHeader Saturation Temperature: 303 °C,

Specific heat load: 0.557MWhlt

HPHeader Saturation Temperature: 270°C,


MPHeader Saturation Temperature: 210°C,


LP Header Saturation Temperature: 110°C,


Deaerator Vent Ratio: 0.0015

Table 6-1: Summary of Operating Conditions of Case 1

Period 1 2 3 4 5 6 7 8 9 10

Power(MW) 25 35 50 55 45 60 55 60 63 56

VHP (tIh) 0 0 0 0 0 0 0 0 0 0

HP (tIh) 100 100 130 130 190 130 180 130 130 80

MP (tIh) 100 130 160 210 110 180 170 170 180 220

LP (tIh) 100 120 150 150 190 230 190 190 230 190

Table 6·2: Utility demands of Case 1

Fuel (Natural Gas) Electricity

LHV: 13856kWhlTon

Cost: 223$ffon Cost: O.1$IkWh

Table 6-3: Utility data of Case 1

123


6.7.1.1 Optimisation of the Existing System

The existing system is optimised for maximum power over the operation periods. The

results are given in Table 6-4.

Period 1 2 3 4 5 6 7 8 9 10

Power 28.2 35.5 46.4 46.4 45.4 46.4 46.4 46.4 46.4 46.4

Table 6-4: Maximum power generation of the existing system of Case 1 (MW)

6.7.1.2 Total Site Analysis

The amount of steam for each expansion zone is calculated from the steam demand data

of Table 6-2. The amount of steam across each expansion zone is given in Table 6-5.

Period 1 2 3 4 5 6 7 8 9 10

VHP-HP 300 350 440 440 490 540 540 490 540 490

HP-MP 200 250 310 360 300 410 360 360 410 410

MP-LP 100 120 150 150 190 230 190 190 230 190

Table 6-5: Steam amount across each expansion of Case l(tlh)

There is no surplus of steam at the available levels. Therefore, surplus condensing

turbines (SeT) are not considered for debottlenecking. The capacities of the

debottlenecking back-pressure turbines require the capacities of the existing turbines.

Turbine TJ is decomposed into Til and T)2. Turbine T2 is decomposed into T2J. T22 and

T 23. The capacities of the simple turbines are given in Table 6-6.

124


Expansion zone Tll Tl2 T2l T22 T23

VHP-HP 80 90 50 70 150

HP-MP 90 70 150

MP-LP 150

Table 6-6: Capacities of simple turbines in every expansion zone of Case l(tlh)

The sizes of the potential steam turbines are determined by comparing the maximum

steam loads of the existing turbines and the total amount of steam across each expansion

zone. The capacities are given in Table 6-7.

Period 1 2 3 4 5 6 7 8 9 10

VHP-HP 0 0 0 0 50 100 100 50 100 50

HP-MP 0 0 0 50 0 100 50 50 100 100

MP-LP 0 0 0 0 40 80 40 40 80 40

Table 6-7: Capacities of potential steam turbines of Case l(tlh)

6.7.1.3 Thermodynamic analysis

Once the capacities are determined, efficiencies are calculated for the existing system

and the system with new units. The TECs are constructed for all periods. These are

given in Figure 6-13. On the basis of the TECs and the power demands, the options

should consider boiler and back-pressure turbine (BBPT) cycles and gas turbine and

waste heat boiler (GTWB) cycles. The capacities of the back-pressure turbines are given

in Table 6-7. The capacities of the GTWB cycles are given in Table 6-8.

125

Chapter 6

Period 1 '1. ExJsIing....-

-j 2S.2MW -, ' (MW]

Period 2

'1. Exlltrog .... _

--j ~~.~ f--_2

' (MW]

Period 3

'1. EJdIIIrQ .........

G1W1I

, G1W8CT H I I acT ~ : ,

'P

46.4MW 3.6MW

_3 P(MW]

Period 4

'1. EJdIIIrQ .........

4b.4MW

P(MW]

PeriodS

--j 46._ f- _._, _5 P(MW]

Debottlenecking and Planning Optimisation of an Existing Site

1].

1].

'1.

1].

Exlltrog .... _

'6._

ExIo1IrQ .... _

.•. -ExIatIrQ .... '.."

-- ~ '6._

ExIltIrQ .... _

46.4MW

Period 6 B6P!

, , , , , ,

b -.'(MW]

Period 7 asP!

, , , , , , , I 19.7MW I

!-TO-I _ 7 P(MW)

Period 8

, ,

i ~o_, d ~T ' , , , 7.'l'lMW H 'P , ,

~ ""TO ' 6 .61MW

, , , , , ,

_8

Period 9

asP!

Period 10

asP!

P(MW]

.---4"'6--:._=----,.10 ,,~ ~========~~~--~ _ '0 P(MW]

Figure 6-13: TECs for different operation periods for Case 1

126


Period 1 2 3 4 5 6 7 8 9 10

Capacity 0 0 3.58 5.81 0 0 0 5.61 0 0

Table 6-8: The capacities of potential GTWB cycles (MW) of Case 1

6.7.1.4 Superstructure Development and Optimisation

The discretisation procedure (Section 5.5.1) is applied to determine the capacities and

number of the back-pressure turbines for debottlenecking. The capacities are given in

Table 6-9.

Zone BTl BT2

VHP-HP 50 100

HP-MP 50 100

MP-LP 40 80

Table 6-9: Capacities of candidate steam turbines of Case l(tIh)

From Table 6-8, the capacities of the gas turbines in periods 4 and 8 are close.

Therefore, the size 5.61 is dropped from the superset. The discretisation procedure

(Section 5.5.2) is used to determine capacities of the potential gas turbine and waste

heat boiler cycles. These capacities are given in Table 6-10. Hence, resulting

superstructure is generated and shown in Figure 6-14.

GTWB GT I GT2 GT3

Capacity 3.58 5.81 2.23

Table 6-10: Capacities of candidate GTWB cycles of Case l(MW)

The MILP model minimises the total annual cost. The model is developed using GAMS

(Brooke et al .• 1992) and the optimisation has been conducted by using the full space

search (Branch and Bound) as well as the proposed decomposition method (Section

6.6.2). The optimisation yields identical solutions. However the full space search

127


appears less efficient. Table 6-11 summaries the size of the original problem and the

decomposition result with respect to the subproblems discussed earlier.

Max2.23MW

VHP

HP

MP

LP

~I""""I-__ ..L.. __ -I.. CONDo

Figure 6-14: Debottlenecking superstructure of Case 1

Original problem Debottlenecking Operational planning

problem problem

0-1 variables 170 70 160

Cont. variables 379 370 379

Constraints 479 419 479

Table 6- 11: Summary of the problem size

128


The optimal structure is shown in Figure 6-15. It consists of three new back-pressure

steam turbines, one new gas turbine and a new waste heat boiler. The back-pressure

turbines exploit the cogeneration potential and since they are unable to generate enough

power the gas turbine and waste heat boiler are employed to address the remaining

power demands. The total annual cost is 59.77 M$. The annual fuel cost is 56.95 M$

and the annual capital investment cost is 2.82 M$. The resulting optimal capacities are

given in Table 6-12.

VHP

HP

Max90t/h Max 70tJh MP

Max l5Ot1h LP

COND.

Figure 6·15: Optimal structure of Case 1

129


Unit Capacity

VHP-HPBT2 2.88MW

HP-MPBT\ 2.77MW

MP-LPBT2 8.20MW

Gas turbine GT2 5.81 MW

Boiler B2 100t/h

Table 6-12: Optimal capacities of the new units of Case 1

The optimal loads of all units are given in Table 6-13. Boilers Bl and B2 are operating

to raise steam in all periods because of the high steam demand from the site processes.

The steam turbines are employed to fully use the potential for cogeneration and generate

power to meet the demand of the site processes. The gas turbine is shut down unless the

power outputs of the steam turbines are unable to meet the demand for power.

Period 1 2 3 4 5 6 7 8 9 10

Til (t/h) 0 80 0 0 0 80 80 80 80 80

TI2 (t/h) 90 90 90 90 90 90 90 90 90 90

T2\ (t/h) 0 0 0 30 0 50 50 0 50 0

Tn (t/h) 0 0 70 70 70 70 70 70 70 70

T23 (t/h) 87 120 150 150 140 150 150 150 150 150

BT 2 (VHP-HP) (t/h) 100 60 100 100 100 100 100 100 100 100

BT I (HP-MP) (t/h) 23 40 0 50 0 50 50 50 50 50

BT 2 (MP-LP) (t/h) 13 0 0 0 50 80 40 40 80 40

BJ (t/h) 200 250 340 340 390 440 440 390 440 390

B2 (t/h) 100 100 100 100 100 100 100 100 100 100

GT2 (MW) 0 0 4.13 5.73 0 0 0 5.81 1.73 1.87

Table 6·13: Optimal operation of all units of Case I

130


6.7.2 An Industrial Case Study

The methodology is illustrated as it has been applied to an industrial complex. The

configuration of the site utility system is shown in Figure 6-16. The current system

consists of three main boilers (BI, B2, B3), two local boilers (PI and P2), six steam

turbines (Tl to T6, where TI, T5 and T6 are allocated turbines which are allocated to

some specific units of processes), one BFW pump and the deaerator. The capacities of

the units are given in Figure 6-16. There are five steam levels (VHP, HP, MP, LP and

VLP) and one vacuum level. Steam can be generated at two levels: very high pressure

(Bl, B2, B3 and P2) and high-pressure (PI). The operating conditions of the steam

levels and the de aerator are shown in Table 6-14. The steam used for heating is returned

as condensate. Letdown steam from higher levels is also available.

¢Jc;D . I .

I Condenser I

Figure 6-16: The existing utility system of the industrial case

131


The site utility system is connected with several chemical processes. There is no option

to sell power. The chemical processes are expanded in three periods and the utility

demands for each period are given in Table 6-15. The three periods span over 0.4, 0.3

and 0.3 year respectively. The power demands of the allocated turbines for each period

are given in Table 6-16. The cost data of the utilities are given in Table 6-17. The load

on the local boilers PI and P2 are 50tlh and 59.6 tIh respectively for all periods.

The current utility system can't satisfy the increasing heat and power demands of the

chemical processes. The optimum investment scheme for new units to be added into the

current system and the operational strategies are optimised so that the utility demands

are met at a minimum cost.

Unit Operating parameters

VHPheader Pressure: 12.1 Mpa, Temperature: 550°C

lIP header Pressure: 3.1 Mpa, Temperature: 236°C

MP header Pressure: 1.4 Mpa, Temperature: 195°C

LP header Pressure: 0.4 Mpa, Temperature: 144°C

VLPheader Pressure: 0.11 Mpa, Temperature: 110°C

Condenser level Pressure: 0.01 Mpa, Temperature: 50°C

Deaerator Pressure: 0.14 Mpa, Vent rate: 0.15

Table 6-14: Summary of operating conditions of the industrial case

Period Period 1 Period 2 Period 3

Electricity (MW) 168.6 239.1 338

VHP steam (tIh) 0 0 0

lIP steam (tIh) 171 181 220

MP steam (tIh) 133 183 267

LP steam (tIh) 108 159 170

VLP steam (t/h) 54 94 120

Table 6-15: Utility demands of the industrial case

132



Power demand of T 1 (MW) 1.6 5.4 0.0

Power demand of T5 (MW) 9.0 0.0 9.0

Power demand of T6 (MW) 30.8 35.5 43.0

Table 6-16: Power demands of the allocated turbines of the industrial case


Demineralized water 0.47 $/ton 0.47 $/ton 0.47 $/ton

Electricity O.I$/kWh O.I$/kWh O.I$/kWh

Fuel cost of boiler 1 11.05 $/mmkcal 11.05 $/mmkcal 11.05 $/mmkcal



Fuel cost of gas turbine 245 $/ton 245 $/ton 245 $/ton

Fuel cost of new boiler 16.1 $lMWh . 16.1 $IMWh 16.1 $IMWh

Table 6-17: Utility cost data in different periods for the industrial case

Once the existing utility system is optimised, maximum power outputs and total steam

flowrates across expansion zones are determined for all operating periods. The results

are given in Table 6-18 and Table 6-19.


Power output 172 172 172

Table 6-18: Maximum power generation of the existing system of the industrial case (MW)

133


Steam zone Period 1 Period 2 Period 3

Zone 1 1204 1509 1852

Zone 2 991 1262 1538

Zone 3 748 939 1098

Zone 4 551 669 791

ZoneS 356 396 450

Table 6-19: Total steam flowrates across expansion zones for the industrial case (t/h)

For our case there is no surplus steam for the available levels. Therefore no condensing

turbines are considered for debottlenecking. To determine the capacities of the potential

back-pressure turbines, the capacities of the existing turbines are required. The

suggested capacities of the existing turbines in each steam zone are given in Table 6-20.

Tl T2 T3 T4 T5 T6

Zone 1 0 215 420 568 0 0

Zone 2 0 215 400 214 48 0

Zone 3 0 112 270 214 48 0

Zone 4 0 0 8 214 48 400

Zone 5 80 0 8 0 48 400

Table 6-20: Capacities of existing turbines in every expansion zone for the industrial case (t/h)

The maximum steam loads across the existing turbines and the total steam across the

expansion zones determine the capacities of the potential steam turbines. The capacities

are given in Table 6-21.

134


Period 1 Period 2 Period 3

Zone 1 0 306 649

Zone 2 162 433 709

Zone 3 104 295 455

Zone 4 0 0 121

Zone 5 0 0 0

Table 6-21: Capacities of potential steam turbines for each period for the industrial case (tlh)

The discretization procedure of Section 5.5.1 suggests 3 candidate steam turbines in

zone 1 with capacities 306, 649 and 343 tlh. A total of 5 steam turbines are suggested

for zone 2 with capacities 162, 433, 709, 296 and 547 tlh. In zone 3 five turbines are

suggested with capacities 104, 295, 455, 351, 160 tlh. Zone 4 features a single capacity

of 121 tIh .

The development ofTECs is shown in Figure 6-17. The debottlenecking options include

the boiler and back-pressure turbine (BBPT) cycles and the gas turbine and waste heat

boiler (GTWB) cycles.

Perbd 1 Perbd 2 Period 3

'1. 1'1, ExIling.,.".", BBPI 1'1, ExlSr.g .,."""" 88P!

ExlSr.g .,."""" • GlWB ,

r I I I I I

H G1W8CT

I ~ ~T I I I I

:-, IP I I

InWi 1--1159 .4_ I'~ 7.7Wi --I 172 MIl In""" H

168.6_ P IMNj 239.1_ PI""")

Figure 6-17: Thermodynamic Efficiency Curves for the industrial case

The capacities of the GTWB cycles are presented In Table 6-22. The discretized

capacities include units of 6.6,62.1 and 55.5 MW.

135

PIWi)


Period 1 Period 2 Period 3

GTWB capacity (MW) 0 6.6 62.1

Table 6-22: Capacities of GTWB cycles for different periods for the industrial case

The synthesis superstructure is shown in Figure 6-18. The shaded units represent the

new units.

Figure 6-18: DebottIenecking superstructure of the industrial case

The MILP model minimises the total annual cost. The model consists of 166 binary

variables, 351 continuous variables and 462 constraints.

136


The optimal structure is shown in Figure 6-19. The solution includes seven new bac k

pressure steam turbines (NTI to NT7), two new gas turbines (OT1 and OT2) and one new

waste heat boiler (NB). The capacities of the units are given in Figure 6-19. As shown

in the Figure, two small gas turbines are selected instead of a bigger gas turbine. The

result contradicts conventional wisdom that would advocate a bigger turbine. For the

low power demands , the smaller gas turbine has higher efficiency than a big partly

loaded gas turbine. Simjlarly, in expansion zones VHP-HP, HP-MP and MP-LP two

small steam turbines are preferred instead of a bigger turbine. In periods 1 and 2 there is

not steam between the LP level and the VLP level and a single turbine is se lected to

exploit the cogeneration potential in period 3.

Max S7.SMW

Max20.3MW I

r.T • •

Max 6.1MW

[::j I

I Make-up wale, I

Figure 6·19: Optimal structure of the industrial case

137


The optimal loads are given in Table 6-23, Table 6-24 and Table 6-25. In period 1, the

existing system satisfies all power demand. The new steam turbines and the gas turbines

are all shut down. In period 2, some of the new steam turbines and the smaller gas

turbine are active. In period 3, the power demand reaches its maximum value. All

turbines are in use generating power to satisfy the additional power demand.

Unit Tl T2 T3 T4 IT5 T6 NT! NTz NT3 NT4 NT'! NT6 NT, Period 1 1.6 29.0 67.S 71.9 9.0 30.8 0.0 0.0 0.0 0.0 0.0 0.0 0.0

Period 2 5.4 0.0 67.S 63.2 0.0 35.5 0.0 57.0 0.0 20.1 0.0 IS.1 6.1

Period 3 0.0 0.0 67.S 67.0 9.0 43.0 26.6 57.0 7.S 20.3 5.2 IS.1 6.1

Table 6-23: Optimal operation of all turbines of the industrial case (MW)

Unit PI P2 Bl B2 B3 NB

Period 1 50 60 170 425 550 0

Period 2 50 60 170 425 588 266

Period 3 50 60 170 425 588 610

Table 6-24: Optimal operation of all boilers of the industrial case (t/h)

Unit GT! GT2

Period 1 0.0 0.0

Period 2 6.6 0.0

Period 3 6.6 55.5

Table 6-25: Optimal operation of all gas turbines of the industrial case (MW)

138

Cluzpter6 Debottlenecking and Planning Optimisation of an Existing Site

6.B Conclusions

The chapter presents a systematic optimisation methodology for the optimal

debottlenecking and planning of site utility systems. Given forecasts for the demands

and prices of utilities, the approach determines investment schemes and schedules the

operation for maximum efficiencies.

A straightforward modelling effort results in a highly complex and large problem. A

new strategy is employed that combines advantages of total site analysis,

thermodynamics and mathematical optimisation. The total site analysis screens and

targets possible debottlenecking options. The thermodynamics excludes inefficient

options and the mathematical optimisation finalises the best structure and operation

options. The proposed methodology has been successfully used to solve an industrial

application.

139

Chapter 7 Total Site Maintenance Scheduling

Chapter 7

Total Site Maintenance Scheduling

7.1 Introduction

Maintenance assumes an important part in the operation of a total site system. It reduces

the risk of capacity outrage and improves the availability of units. The maintenance

scheduling problem minimises the overall operating cost over the given operating

period subject to maintenance and system hardware and reliability constraints.

Scheduling methods have been proposed by Chattopadhyay et al. (1995) and Dapazo et

al. (1975), but they only considered power systems and assumed identical maintenance

needs for the system units. A typical chemical plant usually consists of several chemical

production processes that consume heat and power in order to make products. The

central utility systems supplies the heat and power of the processes that in tum have to

shutdown and start-up allowing, sometimes significant changes in the demands. By

product fuels of site process units can also be used to generate heat and power enabling

strong interactions between the site utility system and the processes. The optimal

maintenance schedule of the site utility system and the process units consequently

allows for a simultaneous consideration of the options, as it is schematically shown in

Figure 7-1.

This approach assumes given shutdown, start-up and maintenance periods for each unit

and applies a multi-period MILP model to develop the optimal maintenance schedule.

The optimisation further determines optimal switches for the fuel and economic

schemes for power import/export. The maintenance periods are allowed to be different,

the optimisation considers the maintenance of the chemical processes and the site utility

system, and the decisions are made to minimise the total operating cost.

140

Chapter 7

Time

TotaL Site Maintenance Scheduling

Site uti lity system

Figure 7-1: Total site optimisation

7.2 Mathematical Model

Sets, parameters and variables are defined as fo llows:

Sets

EB = { eb I set of boilers}

I = { u, p I set of all units }

Ie = { ic I set of condensing turbines }

IG = { ig I set of gas turbines}

IT = { it I set of BP steam turbines}

K = { k I set of operation periods}

L = { I I set of steam levels }

p = { p I set of process units}

U = { u I set of utility units}

UF = { uf I set of units consuming fuel}

141


Parameters


: regression parameters of CTHM for condensing turbines

CEPk

CESk

CFuk,k

Cp

Cp Cpa

ci CWk

DIp

D2p

D3p

EISit

: regression parameters of GTHM for gas turbines

: regression parameters of THM for BP steam turbines

: unit cost of purchased electricity in period k

: unit cost of sold electricity in period k

: unit cost of fuel for unit uk in period k

: specific heat of saturation water between Tin and T outsat

: specific heat of flue gas

: specific heat of air

: specific heat of fuel

: unit cost of water in period k

: shutdown duration of process unit p

: maintenance duration of process unit p

: start-up duration of process unit p

: maintenance duration of utility unit u

: isentropic enthalpy change of condensing turbine ic

: isentropic enthalpy change of BP steam turbine it

Fj{max : maximum fuel load of gas turbine ig

Mil : specific enthalpy of gas turbine fuel reaction

M !,max : maximum steam load of boiler eb

MBT,rnax : maximum steam load of BP steam turbine it II

Mj;r'max: maximum steam load of condensing turbine ic

MINu : earliest time unit u can be taken for maintenance

MAXu : latest time unit u can be taken for maintenance

MINp : earliest time process unit p can be shutdown for maintenance

MAXp : latest time process unit p can be shutdown for maintenance

qeb : specific heat load of steam

yo : temperature of inlet air of gas turbines

T : temperature of gas turbine fuel

142


T/ : time duration of period k

I1T sal : temperature difference between Tin and Tout sat

eb.1:

Binary variables

Xu = 1 denotes the unit i is in operation in period k, otherwise Xi.k = 0

Yu.k = 0 denotes the utility unit u is on maintenance in period k, otherwise Yu.k = 1

Y1p.k = 0 denotes the process unit p is shutting down in period k, otherwise Y1p,k =1

Y2p.k = 0 denotes the process unit p is starting up in period k, otherwise Y2p.k =1

Y!.k = 1 denotes the boiler eb is in operation in period k, otherwise Y:b.(~ =0

y/~.o = 1 denotes the BP steam turbine it is in operation in period k, otherwise

YBT.o=o II.k

YeT = 1 denotes the condensing turbine ic is in operation in period k, otherwise ic.k

YeTk=o IC.

Y GT = 1 denotes the gas turbine ig is in operation in period k, otherwise Yf~gT.k·() =0 ig.k

Zu.k = 0 denotes the utility unit u starts its maintenance in period k, otherwise 2u.k = 1

ZIp.k = 0 denotes the process unit p starts shutting down for maintenance in period k,

otherwise 21 pj = 1

Z2p•k = 0 denotes the process unit p starts starting up in period k, otherwise Z2p.k = 1


EDp.k : power demand of process unit p in period k

F f : fuel load of gas turbine ig in period k ig.k

FWk : water requirement of the utility system in period k

M B : steam load of boiler eb in period k "h.k

M B : steam load of boiler eb to steam level I in period k eh.l.k

Mi:~ : steam load ofBP steam turbine it in period k

M BT.I : steam load of BP steam turbine it to steam level I in period k it.l.k

M BT.O : steam load from steam level I to BP steam turbine it in period k if .I.k

143


M ft : steam load of condensing turbine ic in period k

M :.k : amount of steam throttled through let down valves to steam level I in period k

QB.! : fired fuel load of boiler eb in period k eb.k

QB.w : waste heat load from gas turbines to boiler eb in period k eb.k

QGT,W : waste heat load of gas turbine ig in period k ig,k

Quf,k : fuel requirement of unit uf in period k

SDp,l,k : I level steam demand by process unit p in period k

Wil~ : power output of BT steam turbine it in period k

W/UY : power import in period k

wi;,1' : power output of condensing turbine ic in period k

Wi~r : power output of gas turbine ig in period k

Wkexp

: power export in period k

7.2.1 Objective Function

The objective function minimises the total operating cost. The cost includes the fuel

cost, the boiler feed water cost and the electricity cost / revenue. It is expressed by:

min COST = L[ L CFuf.kQu/,k + LCWkFWk + LCEPkW:UY - LCESkWkexP 1r/ (7-1)

keK u/eUF keK keK keK J j

7.2.2 Performance Models

These include:

144


7.2.2.1 Utility Units

The utility models consist of:

(a) Boilers

The fuel requirement of each boiler in period k is provided by the Boiler Hardware

Model (Section 3.2):


M!.1c -M!,maxY!,k :::; 0, ebE EB,kE K (7-3)

(b) Back-pressure steam turbines

The power output of each back-pressure steam turbine in period k is provided by the

Turbine Hardware Model (Mavromatis and Kokossis, 1998a):

BT 6 1 W'le = --(EISil '. 5 B

/I

.4;, )(M BT _! M BT.max BT) • IT k K M BT,max i/.k 6 il YiI,k' It E , E .,

(7-4)


M BT BTMBT,max < 0 . IT k K i/.1e - Y iI.k il -, It E , E (7-5)

(c) Condensing steam turbines

The power output of each condensing turbine in period k is given by the Condensing

Turbine Hardware Model (Section 3.3):

145


WCT - 6_1_(ElS C _ A;~ )(M CT _.!..MCT,max CT) , IC k K ie,k - 5 Be ie M CT,max ie,k 6 ic Yic,k' IC E ,E

IC IC

(7-6)


M CT _MCT,max CT < 0 ' IC k K ic,k ic Yic,k - , ~CE ,E (7-7)

(d) Gas turbines

The power output of each gas turbine in period k is given by using the Gas Turbine

Hardware Model (Section 3.4):

W GT 1 (M! Ag

)«1 + )F! Ff,max GT) ig,k = B g ! - F1,max n ig,k - n ig Yig,k'

Ig

The logical constraints relating to this model are:

F ! F! ,max GT < 0 ' IG k K ig,k - ig Yig,k - ,lgE ,E

The waste heat from the gas turbine can be obtained by:

ig E IG,kE K (7-8)

(7-9)

QGT,,,,=[~caTa+C!Tf+M! -(I+n)_I_(Mf - Ag )]F.! igEIG,kEK Ig,t f P P ! B g ! FI,max Ig,k'

Ig

(7-10)

7.2.2.2 Process Units

The utility demands of the process units are formulated as general functions of the

operation conditions (i,e, start-up, shut down) as follows:

146


The steam demand function of process unit p in period k is:

(7-11)

The power demand function of process unit p in period k is:

EDp.k = !edp.k(Ylp.k,Y2p.k,Dlp,D2p,D3p), pe P,ke K (7-12)

The by-product fuel function of process unit p in period k is:

(7-13)

7.2.3 Steam Mass Balances

Steam inputs at each team level include steam raised by boilers, steam exhausted from

BP steam turbines and steam throttled through let down valves. Steam outputs at each

steam level include steam loads to BP steam turbines and condensing turbines, steam

throttled through let down valves and steam loads to site processes. The mass balances

of all steam levels give:

"LM/:J.: +M:.k + "L M!.I.k = LMi:;'~ +M:+l.k + "LSDp.l.k' Ie L,ke K(7-14) i/Err ebEEB i/Err peP

7.2.4 Power Balance

The power balance in period k is expressed as:

L W,:r + L Wc7.I + "L Wi~r + WkbUY = LED p.k + wtP , k E K (7-15)

IIErr eleCT ige/G peP

147


7.2.5 Maintenance Constraints

The maintenance constraints include:

1. Maintenance period constraints:

Within a given time period, each unit is scheduled for maintenance for a period of a pre

specified duration.

Within a given time period from M1Nu to MAXu, utility unit u needs to start its

maintenance:

MAXu

LZu,k =MAXu -MINu' UE U k=MIN.

(7-16)

Within a given time period from MINp to MAXp, process unit p needs to shut down for

maintenance:

MAXp

LZ1 p,k =MAXp -MINp' pE P k=MINp

(7-17)

After shutting down and maintenance, process unit p needs to start up for operation. The

start-up should start in a time period between MINp + Dlp+D2p and MAXp+ Dlp+D2p:

MAX p+D1p +D2p

LZ2p,k =MAXp -MINp' pE P (7-18) k=MIN p +D1p+D2p

Beyond the given time period from MINu to MAXu, utility unit u doesn't start its

maintenance:

Zu.k = 1, k < MINu or k > MAXu (7-19)

148


Beyond the given time period from MINp to MAXp, process unit p doesn't shut down for

maintenance:

Z1 p,t = 1, k < MIN p or k > MAX p (7-20)

Beyond the time period from MINp + DIp+D2p to MAXp+ Dlp+D2p, process unit p

doesn't need to start up for operation:

(7-21)

2. Maintenance completion constraints:

Additional constraints ensure maintenance times span over the pre-specified

maintenance slots without any interruption. Once the unit maintenance starts, it

automatically occupies the time required for its completion.

The constraints are formulated as follows:

k

Yu.* = 1- k + LZu,j, 1:5 k :5 Du ,u E U j=1

k

Yu,k = 1- Du + LZu,j' j=k+I-D.

N is the total number of time periods

3, Shut down/start up completion constraints:

(7-22)

The constraints ensure that start up and shut down times develop within the appropriate

time, This means once time is allocated for shut down or start-up operation, the

operation complete without interruption,

149


The shutdown completion constraints are formulated as follows:

I:

Yl p ,l: = l-k + LZlp,}, 1 ~ k ~ Dl p ,pe P j=1

I:

Yl p,l: = 1-Dl} + L Zl p,} ,

}=Ie+l-D1p

DI p ~ k ~ N, peP

The start-up completion constraints are formulated as follows:

k

Y2 p ,A: = l-k + LZ2 p ,j, 1 ~ k ~ D3 p ,pe P j=1

Ie

Y2 L = 1-D3 . + ~ Z2 ., P,A } £J P,} D3 p ~ k ~ N, peP j=le+l-D3p

4. Logical constraints:

Before they shut down, process units cannot start up. Therefore,

k-1

D1p(1-Z2p,k)~k-1- LY1 p ,j' pe P,ke K j=1

After the maintenance of process units is completed, the units start up immediately:

Units under maintenance cannot operate:

Xi,k ~ Yu,k' iE U,u E U,k E K

150

(7-23)

(7-24)

(7-25)

(7-27)

(7-28)


5. Co-ordination constraints:

There is a maximum number of units that can be maintained in each period. Therefore.

L (1 - Yu,k ) :5; UMAX, k e K (7-29) ueU

UMAX = Maximum umber of utility units can be put on maintenance in one period.

6. Resource constraints:

A separate set of constraints ensure the resources assigned for maintenance is not

exceeding available limits:

where:

L(1-Yu,k)Ru,m ~ RESm,k' ke K,m = 1,2, ... M ueU

Ru,m = amount of resource type m required by unit u

RESm.k = amount of mth resource available in period k

M = number of resources

7.3 Maintenance Case Study

(7-30)

The optimisation model that is used for maintenance scheduling is illustrated with a

case study. Figure 7-2 shows the configuration of a total site. The site consists of four

steam levels, four boilers, five steam turbines, the deaerator and one gas turbine. The

utility system serves four process units. The capacities of the utility units are given in

Figure 7-2. The operating conditions of steam levels are shown in Table 7-1. The steam

used for heating can be returned as condensate. The process units operate in normal

conditions and the utility demands from each unit are given in Table 7-2. The utility

151


plant is interconnected with the utility grid. Cost data for the utilities are given in Table

7-3.

~ . ~- ....... -- ... . -....••... --- .. .

~--

VHP

HP

MP

: ! I I I I I l I !

LP

---------------------------------r------ -- ----------r------- -- .---------r--- - -------------)

Export/,mpn,9ctricitY " .---.l.-.!..L.!.....L...,

COND.

Figure 7·2: The configuration of a total site

Steam levels Operating Conditions

VHP level Temperature: 550 °C, Pressure: 121Bar

HP level Temperature: 236°C, Pressure: 31Bar

MP level Temperature: 195 °C, Pressure: 14Bar

LP level Temperature: 144 °C, Pressure: 4Bar

Table 7·1: Summary of operating conditions of the utility system

Thirty-six operating periods are considered, each occupying 10 days . The total time

hori zon is one year. Process and utility units all undergo maintenance. Process P4 takes

longer times to start up and shut down and this all has been taken into account by the

model. It takes Process P4 10 days to start up and 10 days to shut down . Maintenance

times are given in Table 7-4. No more than 5 units can be maintained at a given period.

152


The optimisation simultaneously determines the optimal maintenance and the optimal

operating schedules for the utility system and the process plant.

Process unit PI P2 P3 P4

Power(MW) 20 65 35 100

VlIP steam (tJh) 40 240 0 300

lIP steam (tJh) 40 60 0 400

MP steam (tJh) 0 0 50 200

LP steam (tIh) 0 0 150 100

Table 7-2: Utility demands of process units in normal operating conditions

Fuel used by B 1 Fuel used by B2 Fuel Used by Purchased Sold

B3 andGT electricity Electricity

0.OO98$/KwH O.OI$IkWh 0.0 13$IkWh O.l$IkWh 0.085$/kWh

Table 7-3: Utility cost data

Unit BI B2 B3 TI T2 T3 T4 Ts GT PI P2 P3 P4

Duration 20 20 20 20 20 10 20 10 20 10 10 10 30

Table 7-4: Maintenance times of all units (days)

The scheduling MILP model involves 1200 integer variables, 1320 continuous variables

and 2453 constraints.

The optimisation results are given in Figures 7-3 to 7-8. The minimum operating cost is

78.3 M$. The optimal maintenance and operation schedule is shown in Figure 7-3,

where shaded M-bars account for maintenance, I-bars for idle, St-bars for start-up and

Sh-bars for shutdown times. Processes PI, P2 and P3 are shut down for maintenance in

periods 26, 29 and 27 respectively. Process P4 is shut down in period 25. It is

maintained during periods 26, 27 and 28 and starts up in period 29. Most utility units

are maintained during the time processes are maintained. For example, during periods

153


26, 27, 28 and 29, PI, P2. P3 and P4 are down for maintenance. The optimal profile of

steam consumed by processes is given in Figure 7-4. Figure 7-5 explains the optimal

power consumption of processes. Figure 7-6 shows the optimal boiler operation and

Figure 7-7 gives the optimal turbine operation. The optimal power export profile is

shown in Figure 7-8. The power export is quite stable except for the periods where the

process and utility units are shut down for maintenance. No electricity import is

required during maintenance.

7.4 Conclusions

A multi-period MILP model is presented for the total site. The model can obtain a

minimum cost maintenance and operation schedule. The optimisation method

simultaneously considers the maintenance and the operation of the site processes and

the site utility systems. It is shown that interconnection mode of the utility system and

the process plant can lead to substantial changes in utility demand decisions and the

overall operating costs are reduced significantly. As the site processes start up and shut

down gradually. the start-up and shutdown models of site processes are incorporated in

the optimisation model. The model is capable of accounting for different maintenance

duration of operating units instead of same maintenance duration of the units proposed

by conventional methods. The practical maintenance constraints of industrial plants

have also been modelled in the proposed optimisation model.

154

ChapTer 7 Total Site MainTenance Schedfllillg

Period I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18

PI

P2

P3

P4

BI 1-

B2

B3

Tl

T2

T3 I I f/d' I I T I J I 1 I I I I I I

T4

T5 I I I I I I [ r J J J r [ I I I I

GT

Periods 19 ::w 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 !-

36 .-

PI i-

P2

P3

P'+ Sh

Bl

B2

B3

TI

T2

T3 T I I I I I I 1 I I I [ J J I I I

T-+

TS T I I I [ I T I I I f J I I r T

GT

~ Idle Mai nlenance Shut down Slarl -up D Operation

Figure 7-3: Optimal maintenance and operation schedule of all units

155


_ 700

~ 600 ,..... -+-VHP st. "0 500

c: ___ HP st. co 400 E CI) 300

~ ;\0( MP st.

"0

E 200 a LP st. co 100 CI) -en 0 0 6 12 18 24 30 36

Time (10 days)

Figure 7-4: Optimal profile of steam consumed by processes

_ 300

~ 250 -"0 200 c: co 150 E CI)

100 "0 ...

/ \ 1 ~ ~ ~

CI) 50 ~ 0 a a..

o 6 12 18 24 30 36

Time (10 days)

Figure 7-5: Optimal power consumption profi Ie of processes

700 J? 600 I e. 500 ~.~ ..... ., '\0 I~

-+-B1 ell r. ...... ,.,~ ... io, ...... A .. ".:.~ ..... 1,J .. • ......... ,. ..... 1 ~ ___ B2 ~ 400 I i 0 -= 300 II" B3 ... .!! 200 HRSG '0 100 T In \ ~rv~ 0

0 6 12 18 24 30 36

Time (10 days)

Figure 7-6: Optimal boiler operation

156

Chapter 7

c 0 :;::

C'::S ... G) c G) C) ... G)

:: 0 Q.

Total Site Maintenance Schedulillg

120

100 O\)()()ooOOOOOOOOOOOv '.,. ~, )(tOE

I 80 r

60

I 40 ~ ...

20 I~ ~V /

0 ~~- . - ... .. .. - .. ....

0

120

~ 100 ~

~ 80

&. 60 >< 4) ... 40 ~ 20 o Il. 0

6 12 18 24 30 36

Time (10 days)

Figure 7-7: Optimal turbine operation

.... . ~ T\ J I \

t ~

o 6 12 18 24 30

Time (10 days)

Figure 7-8: Optimal power export profile

157

-+-T1

--T2

T3

T4

-.-T5

-+-GT

36

Chapter 8 Conclusions and Future Work

Chapter 8

Conclusions and Future Work

8. 1 Introduction

This chapter consists of two parts. The first part summarises the work presented in this

thesis. The second part gives some suggestions for future work.

8.2 Conclusions

An integrated approach has been proposed for the analysis and optimisation of total site

utility systems. The approach makes combined use of total site analysis, thermodynamic

analysis and mathematical optimisation techniques, in order to provide a comprehensive

solution to a multi-faced problem. A systematic methodology has been presented for the

design of total site utility systems, with particular emphasis on the anticipated

operational variations. In addition, the approach has proposed systematic optimisation

methods to address the debottlenecking and planning of site utility systems as well as

the maintenance scheduling of total sites.

8.2.1 Design of Total Site Utility Systems

A set of hardware models CTHM, BHM and GTHM are proposed. The use of the

models for the analysis and optimisation of site utility systems are explained in the

work. The models combine thermodynamic principles, engineering knowledge and

performance data for condensing turbines, boilers and gas turbines. They enable for an

158


accurate prediction of unit efficiencies and embody the efficiency trends of realistic

units in terms of their variation with capacity, load and operating conditions. These

effects are accounted for in a simple and linear fashion, the importance of which are

illustrated in the work.

The hardware models CTHM, BHM and GTHM provide results of good accuracy, by

considering the dependence of the efficiency on the capacity and operating conditions.

In view of operational variations, the effect of the part-load operation is well accounted

for all these models.

With respect to the analysis and optimisation problem, the CTHM, BHM and the

GTHM models provide the basis for modelling the condensing turbines, boilers and gas

turbines respectively in a manner that the efficiency trade-offs of the various design

alternatives can be considered. The linear relations of the power output to the steam

load of condensing turbines, the steam load to the fuel requirement of boilers and the

power output to the fuel requirement of gas turbines are essential for simple

formulations for the optimisation of site utility systems.

A powerful optimisation methodology is proposed to address the needs of the

preliminary steam level selection for the total site system under operational variations.

By exploiting engineering knowledge, the BHM and THM models are capable of

predicting the real efficiency trends of units, by considering the dependency of the

efficiency on load and operating conditions. The application of the two models are

particularly important in the case of multiple operation scenarios, where the steam loads

and the respective efficiencies may vary significantly. By exploiting total site analysis

techniques, a new transhipment network is developed to represent the total site system.

It can be used to describe the interaction between the placement of steam levels and

steam loads of site processes. Based on the transhipment representation and combined

with the BHM and THM models, a multi-period MILP model is applied to minimise the

total utility cost for the total site under multiple operation scenarios. Major decision

variables include the overall fuel requirement, the cogeneration potential and the

cooling utility demand. The MILP model is a general model which can not only be used

159


for the Minimum Utility Cost (MUC) case but also for the Minimum Fuel Requirement

(MFR) case.

As regards configuration design of site utility systems under operational variations, a

systematic methodology has been developed. The methodology combines the benefits

of total site analysis, thermodynamic analysis and optimisation techniques. The

approach accounts for the interactions between the site utility systems and the site

processes. The design task is addressed in view of the anticipated variations in the

process demands and the effect of the unit capacities and varying loads on the

efficiencies of the selected units. These aspects normally give rise to highly complex

and large problems. The proposed methodology utilises total site analysis and

thermodynamic analysis to reduce the size and complexity of the design problem. The

total site analysis is employed to screen and identify all possible design options. A

thermodynamic curve is proposed in this approach. It is a useful tool to identify the

promising candidate design options to be included in the superstructure by screening

among all alternative design options. The size of the optimisation problem can be

reduced by screening out the uneconomic design options.

By using the engineering knowledge and analytical insight, a discrete scheme is

proposed to identify the sizes of the candidate steam turbines, condensing turbines and

gas turbines. The optimisation problem is formulated as a multi-period MILP model that

relies on the THM, CTHM, GTHM and the BHM to describe the performance of the BP

steam turbines, condensing turbines, gas turbines and boilers. The models account for

the efficiency variations with operating conditions and capacity. It should be

emphasised that, had conventional models for the units been applied, the use of an

MINLP formulation would be inevitable.

8.2.2 Debottlenecking and Planning Optimisation of the Existing Site

A systematic optimisation methodology has been presented for the optimal

debottlenecking and planning of site utility systems. Given forecasts for the demands

160


and prices of utilities, the approach determines investment schemes and schedules the

operation for maximum efficiencies.

A straightforward modelling effort results in a highly complex and large problem. A

new strategy is employed that combines advantages of total site analysis,

thermodynamics and mathematical optimisation. The total site analysis screens and

targets possible debonlenecking options. The thermodynamics excludes inefficient

options and the mathematical optimisation finalises the best structure and operation

options. The proposed methodology has been successfully used to solve an industrial

application.

8.2.3 Total Site Maintenance Scheduling

A multi-period MILP model is presented for the total site. The model can obtain a

minimum cost maintenance and operation schedule. The optimisation method

simultaneously considers the maintenance and the operation of the site processes and

the site utility systems. It is shown that interconnection mode of the utility system and

the process plant can lead to substantial changes in utility demand decisions and the

overall operating costs are reduced significantly. As the site processes start up and shut

down gradually, the start-up and shutdown models of site processes are incorporated in

the optimisation model. The model is capable of accounting for different maintenance

duration of operating units instead of same maintenance duration of the units proposed

by conventional methods. The practical maintenance constraints of industrial plants

have also been modelled in the proposed optimisation model.

8.3 Future Work

The following recommendations for future work are made:

In the design problem of this thesis, it is assumed that the design conditions of site

processes are fixed. However, the design of site processes without simultaneously

161

Chapler8 Conclusions and Future Work

considering the design of site utility systems may not be the optimal design in total site

context. There is a need for a methodology making simultaneous design of site

processes, heat exchanger network and site utility system under operational variations.

The debottlenecking and planning methodology presented has concentrated on site

utility systems. Apparently, the modifications in the design of site processes result in

changes in the utility demands, the debottlenecking and planning method can be

extended to account for the modifications in the design of site processes.

The simple models of site processes are applied in the total site maintenance scheduling

approach. More rigorous models of site processes need to be developed.

Finally, due to growing environment concern on the fuel-related emissions, there is a

need to develop an efficient methodology for the design and operation of total site

utility systems under operational variations to reach emission limits at a minimum total

cost.

162

References

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167

Appendix A Correlations o/the THM

Appendix A

Correlations of the THM

A.I. Correlationfor Ml is

As suggested by Mavromatis and Kokossis (1998a), the isentropic enthalpy change,

Ml is of expansion can be correlated to the specific heat load, qin, entering the turbine

and the saturation temperature difference of expansion aT sa, as:

aT Sa/

Ml ------is - 1854-1931qill

(Ai)

where !l.T sa, is in °e, Mlis in MWhlt and qin in MWhlt.

A.2. Correlation for Ml is

Mavromatis and Kokossis (1998a) provided correlation equations for parameters A and

B. All these equations use the saturation temperature of steam at turbine inlet pressure

rat.

for wmax < 1.2MW

A = -0.0131 + 0.00117T sa' (A2)

B = 0.989 + 0.00152T sa' (A3)

168

Appendix A Correlations of the THM

for wmax > 1.2MW

A = -0.928 + O.00623T sat (A4)

B = 1.12 + O.OOO47T sa, (AS)

169

Appendix B Regression o/Condensing Turbine Efficiency Data

Appendix B

Regression of Condensing Turbine Efficiency Data

The regression parameters used in the condensing turbine hardware model are derived

from typical efficiency data as shown in Figure 3-6. By definition the maximum

efficiency is:

hence:

Emax

llis.max = b.H. M max ...

_ E max

MlisMmax =--

1]is.max

These curves are regressed by an expression of the form for each inlet pressure:

E max

Ml ;.,M max = --= AC + BC E

max

T/;s.max

(Bl)

(B2)

(B3)

Parameters A C and Be are extracted by regression for each inlet pressure. The plots of

parameters AC and BC against that saturation temperature corresponding to the inlet

pressure are given in Figure Bl and Figure B2 respectively. These parameters are in

tum approximated by the following expressions:

A C = -0.0896 + O.0013T sar (B4)

BC = 1.1752 + 0.OOO3T sQr (B5)

170

Appendix B Regression o/Condensing Turbine Efficiency Data

where the inlet saturation temperature is in DC. However, the above expressions don't

give accurate estimates of the maximum efficiency when the power output is below

1.5MW. More accurate estimates for the efficiency are obtained by conducting

regression below 1.5MW and above 1.5MW. The two segments' regression gives

efficiency estimates within 3% error. The corresponding expressions for the regression

parameters are:

for Emax < I.5MW

A C = -0.0981 +O.OOlT sat (B6)

BC = 1.2059 + 0.OOO6T sat (B7)

for Emax > 1.5MW

AC = -0.0376 +0.OOI4T sat (B8)

(B9)

0.35 0.3

0.25

AC 0.2 0.15 • 0.1 0.05

0 150 200 250 300 350

Figure 81: Regression parameter N as a function of inlet saturation temperature

171

Appendix B Regression a/Condensing Turbine Efficiency Data

1.35 -r-------------------,

1.3

1.25

1.2 +------r-------,----...,..-----I 150 200 300 350

Figure B2: Regression parameter Be as a function of inlet saturation temperature

172

Appendix C Regression olGas Turbine Efficiency Data

Appendix C

Regression of Gas Turbine Efficiency Data

The regression parameters used in the gas turbine hardware model are derived from

typical electrical efficiency data, such as the plot in Figure 3-8. The curve fitting of the

plot in Figure 3-8 yields the following expression:

wmax --=Ag + BgW max (Cl) lle,max

The parameters Ag and Bg are obtained by conducting regression for the curve in Figure

3-8. The resulting values of Ag and Bg are 6.7571 and 2.4381 respectively. But the

above expressions do not give accurate estimates of the maximum efficiency when the

power output is below 6.9MW by using the parameters. More accurate estimates for the

efficiency are obtained by conducting regression below 6.9MW and above 6.9MW. The

two segments' regression gives efficiency estimates within 2% error. The corresponding

regression parameters are:

for Wmax < 6.9MW

A g = 2.0836 (C2)

Bg = 3.1724 (C3)

for Wmax > 6.9MW

A''1 = 8.817 (C4)

B g = 2.3905 (C5)

173

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