Techno-economic optimisation methodology for HTGR balance of plant systems

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School of Mechanical Engineering North West University _i

TECHNO-ECONOMIC OPTIMISATION

METHODOLOGY FOR HTGR BALANCE

OF PLANT SYSTEMS

WILMA VAN ECK

Dissertation in partial fulfilment of the requirements for the degree

Master of Engineering

School of Mechanical Engineering

at

North West University

Potchefstroom Campus

Promoter: P Rousseau

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School of Mechanical Engineering North West University _ii

ABSTRACT

The nuclear industry lacks a well documented, systematic procedure defining the requirements for power plant cycle selection and optimisation. A generic techno-economic optimisation methodology is therefore proposed that can serve in the selection of balance-of-plant configurations and design conditions for High Temperature Gas-cooled Reactor (HTGR) power plants.

The example of a cogeneration steam plant coupled to a pebble bed reactor, with or without an intermediate buffer circuit, was used in search of a suitable methodology. The following analyses were performed:

• First order thermal hydraulic analysis

• Second order thermal hydraulic analysis including cost estimation • Third order steady state analysis to evaluate part-load operation • Third order transient analysis to test operability and controllability

The assumptions, level of detail required, modelling methodology and the type of decisions that can be made after each stage are discussed. The cycles under consideration are evaluated and compared based on cycle efficiency, capital cost, unit energy cost and operability.

The outcome of this study shows that it is worthwhile spending the effort of developing a second order costing model and a third order model capable of analysing off-design conditions. First order modelling could be omitted from the methodology.

The advantage of a second order model is that the cycle configuration can be optimised from a unit energy cost perspective, which incorporates the effects of both capital cost and cycle efficiency. The optimum cycle configuration differs from that predicted by first order modelling, which illustrates that first order modelling alone is insufficient. Third order part-load operation analysis showed operability issues that were not apparent after first or second order modelling. However, transient analysis does not appear justified in the very early design stages.

To conclude, the proposed methodology is summarised as follows: • Evaluate the user requirements and design constraints.

• Apply design principles from the Second Law of thermodynamics in selecting cycle configurations and base case operating conditions.

• Optimise the operating conditions by performing second order thermal hydraulic modelling which includes component design and cost estimation.

• Evaluate part-load operation with third order analysis.

• Select the cycle with the lowest Levelised Unit Energy Cost (LUEC) and simplest operating strategy.

Keywords: Cycle selection, optimisation methodology,

techno-economic analysis

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School of Mechanical Engineering North West University _iii

UITTREKSEL

Die kernindustrie beskik tans nie oor ’n goed gedokumenteerde, sistematiese prosedure wat die vereistes vir die keuse en optimering van aanlegte beskryf nie. ’n Generiese tegno-ekonomiese optimerings metodologie word dus voorgestel wat bruikbaar kan wees in die keuse van konfigurasies en ontwerpstoestande vir Hoё Temperatuur Gas Reaktor aanlegte.

In die soektog na ’n geskikte metodologie is die voorbeeld van ’n aanleg gebruik wat proses stoom sowel as elektristeit verskaf, direk of deur middel van ’n intermediere lus gekoppel aan ’n korrelbed reaktor, gebruik. Die volgende analises is uitgevoer: • Eerste orde termo-hidrouliese analise.

• Tweede orde termo-hidroulise analise met insluitend kosteberamings. • Derde orde gestadige toestand analise van bedryfstoestande by deelvrag. • Derde order dinamiese analise om aanleg bedryfbaarheid te toets.

Die aannames, vlak van detail wat vereis word, modelleringstegnieke en die besluite wat tipies na elke stadium geneem kan word, word bespreek. Die verskillende uitlegte onder oorweging is geёvalueer en vergelyk op grond van siklus effektiwiteit, kapitaalkoste, eenheids energie koste en bedryfbaarheid.

Die uitkoms van die studie dui daarop dat dit die moeite werd is om ’n tweede orde tegno-ekonomiese model te skep, sowel as ’n derde orde model wat afwykings van optimale ontwerpstoestande kan modelleer. Eerste orde modellering blyk nie broodnodig te wees nie.

Die voordeel van ’n tweede orde model is dat die aanleg geoptimeer kan word vanuit ’n eenheids energie koste perspektief, wat beide die effek van kapitaal koste en aanleg effektiwiteit insluit. Die optimale uitleg lyk anders as dit wat voorspel is deur eerste orde modellering, wat daarop dui dat eerste orde modellering aleen nie voldoende is nie. Derde orde analise van deelvrag bedryfstoestande dui op bedryfsbaarheid probleme wat nie voor die hand liggend was na eerste of selfs tweede orde analise nie. Let egter daarop dat derde orde dinamiese analise nie regtig geregverdig is in die vroeё ontwerpsstadia nie.

Die voorgestelde metodologie word hieronder opgesom:

• Evalueer die verbruiker se vereistes sowel as inherente ontwerpsbeperkinge. • Pas die beginsels toe van die Tweede Wet van Termodinamika in die keuse van

’n aanleg uitleg en basiese bedryfstoestande.

• Optimeer die bedryfstoestande deur tweede orde analise wat komponent ontwerp en kosteberamings insluit.

• Evalueer deelvrag bedryfstoestande met derde orde analise.

• Kies die uitleg met die laagste eenheids energiekoste en die eenvoudigste bedryfsstrategie.

Sleutelwoorde: Aanleg seleksie, optimeringsmetodologie,

tegno-ekonomiese analise

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School of Mechanical Engineering North West University _iv

ACKNOWLEDGEMENTS

I am especially grateful to my father, who passed away shortly before the completion of this work, for always believing in me and encouraging me to be the best in what I do. I also want to thank the other members of my family for their support and love. To my wonderful and supportive husband, Chris: thank you for your patience and understanding, and for keeping my motivated.

Furthermore, I want to thank my employer, PBMR (PTY) Ltd., for giving me the opportunity to conduct this research, and allowing me to perform work which is challenging and gratifying.

My promoter, Pieter Rousseau needs to receive a special thank you for guiding me and directing my work.

Lastly, a special thank you is due to my Heavenly Father. Although the past year has held many difficulties on a personal level for me, He has given me strength and endurance. “I can do everything through Him who gives me strength” (Philippians 4:13).

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School of Mechanical Engineering North West University _v

TABLE OF CONTENTS

ABSTRACT ... II UITTREKSEL ... III ACKNOWLEDGEMENTS ...IV ABBREVIATIONS ...X LIST OF VARIABLES ... XII

1. CHAPTER 1: INTRODUCTION ... 1

1.1 BACKGROUND ... 1

1.2 PROBLEM STATEMENT ... 1

1.3 OBJECTIVE AND PURPOSE OF STUDY ... 1

1.4 CONTRIBUTION ... 2

1.5 RESEARCH METHODOLOGY ... 2

2. CHAPTER 2: LITERATURE SURVEY ... 4

2.1 HTGR BACKGROUND... 4 2.2 DESIGN GUIDELINES ... 5 2.3 ORDERS OF ANALYSIS... 7 2.4 CYCLE EFFICIENCY ... 7 2.5 OPTIMISATION CRITERIA ... 8 2.6 ECONOMIC ANALYSIS ... 10

2.7 SECOND LAW ANALYSIS... 10

2.8 SUMMARY OF FINDINGS ... 11 3. CHAPTER 3: THEORY ... 13 3.1 CYCLE OPTIONS... 13 3.1.1 Rankine cycle ... 13 3.1.2 Brayton cycle ... 14 3.1.3 Combined cycle ... 15 3.1.4 Process heat... 16 3.1.5 Cogeneration ... 17

3.1.6 Direct versus indirect cycle... 17

3.2 LEVEL OF ANALYSIS ... 18

3.3 LEVELISED UNIT ENERGY COST ... 18

3.4 CONTROL SYSTEMS ... 19

3.5 GENERAL TERMINOLOGY AND DEFINITIONS ... 20

3.5.1 Cycle efficiency... 20

3.5.2 Heat exchanger performance ... 20

3.5.3 Turbo-machine efficiency ... 21

4. CHAPTER 4: MODEL DEVELOPMENT AND VERIFICATION ... 22

4.1 DESCRIPTION AND VERIFICATION OF MODELS... 22

4.1.1 Cycle naming convention ... 22

4.1.2 First order model... 23

4.1.3 Second order model ... 29

4.1.4 Third order model ... 38

5. CHAPTER 5: DEVELOPMENT OF CYCLE SELECTION METHODOLOGY... 45

5.1 CYCLE CONCEPT SELECTION... 45

5.1.1 Determination of high level requirements... 46

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5.2 SECOND LAW DESIGN PRINCIPLES ... 49

5.3 FIRST ORDER THERMAL HYDRAULIC MODELLING... 50

5.3.1 Base case results ... 50

5.3.2 Parametric study results ... 53

5.3.3 Optimised cycle results... 58

5.3.4 Discussion of results... 62

5.4 SECOND ORDER THERMAL HYDRAULIC MODELLING AND COSTING... 62

5.4.1 Base case results ... 62

5.4.2 Parametric study results ... 66

5.4.3 Optimised cycle results... 76

5.5 THIRD ORDER MODELLING ... 80

5.5.1 Steady state results ... 81

5.5.2 Definition of control philosophy... 84

5.5.3 Transient results ... 84

6. CHAPTER 6: RESULTS SUMMARY... 88

6.1 EVALUATION OF FIRST, SECOND AND THIRD ORDER MODELS... 88

6.2 SUMMARY OF METHODOLOGY... 89

7. CHAPTER 7: CONCLUSIONS ... 93

REFERENCES ... 94

A.1 PROGRAM STRUCTURE ... 98

A.2 NUMBERING CONVENTION ... 99

A.3 MODELLING METHODOLOGY... 100

A.3.1 Reactor... 100

A.3.2 Piping ... 101

A.3.3 Circulators (blowers) ... 101

A.3.4 IHX ... 101 A.3.5 SG ... 102 A.3.6 Turbines ... 102 A.3.7 Condenser... 102 A.3.8 Pumps ... 103 A.3.9 Generator ... 103

A.4 EES INPUT EQUATIONS ... 104

A.5 FIRST ORDER MODEL VERIFICATION (ALTERNATIVE CALCULATIONS)... 111

B.1 PROGRAM STRUCTURE ... 117 B.2 NUMBERING CONVENTION ... 119 B.3 MODELLING METHODOLOGY... 120 B.3.1 Assumptions... 120 B.3.2 Costing calculations ... 121 B.3.3 Material data... 121 B.3.4 Reactor... 121

B.3.5 Intermediate Heat Exchanger (IHX) ... 122

B.3.6 Steam Generator... 125

B.3.7 Circulators (blowers) ... 125

B.3.8 Piping ... 125

B.3.9 Isolation Valves ... 127

B.3.10 Helium inventory ... 127

B.3.11 Steam plant components ... 127

B.4 EES INPUT EQUATIONS ... 127

C.1 NUMBERING CONVENTION ... 156

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School of Mechanical Engineering North West University _vii

C.2.1 Flownex Model Inputs ... 156

C.2.1.1 Reactor... 156 C.2.1.2 IHX ... 157 C.2.1.3 Circulators (blowers) ... 158 C.2.1.4 SG ... 159 C.2.1.5 Piping ... 163 C.2.1.6 Helium Inventory ... 165 C.2.1.7 Control system ... 165 C.2.2 Simulink inputs ... 165

C.2.2.1 Reactor power ramp down ... 165

C.2.2.2 Primary blower controller ... 165

C.2.2.3 Secondary blower 1 controller ... 165

C.2.2.4 Steam temperature controller ... 165

C.3 SOLUTION METHODOLOGY ... 166

C.3.1 Steady state ... 166

C.3.1.1 Full power operation... 166

C.3.1.2 Reduced power operation (Case A)... 167

C.3.1.3 Reduced power operation (Case B)... 167

C.3.1.4 Reduced power operation (Case C) ... 168

C.3.1.5 Reduced power operation (Case D) ... 168

C.3.2 Transients ... 169

FIGURES Figure 2.1: Comparison of cycle efficiencies for steam turbine (ST), gas turbine (GT) and combined cycles ...9

Figure 3.1: A typical basic Rankine cycle...13

Figure 3.2: A recuperative, intercooled Brayton cycle with reheat ...14

Figure 3.3: Temperature-entropy diagram for a recuperative, intercooled Brayton cycle with reheat...15

Figure 3.4: A combined Brayton and Rankine cycle ...16

Figure 3.5: An example of a plant supplying process heat only...16

Figure 3.6: A schematic for a cogeneration plant...17

Figure 4.1: First order model for V&V (with IHX) ...26

Figure 4.2: Second order model for V&V (SG only) ...32

Figure 4.3: Adjusted first order model for V&V (SG only)...33

Figure 4.4: Second order model for V&V (with IHX)...34

Figure 4.5: Adjusted first order model for V&V (with IHX) ...35

Figure 4.6: Third order model representation as displayed on the Flownex Graphical User Interface ...40

Figure 4.7: Second order model without any design margin...43

Figure 4.8: Third order model base case result...44

Figure 5.1: Cogeneration plant with intermediate loop...47

Figure 5.2: Cogeneration plant without intermediate loop...48

Figure 5.3: Base case layout (with IHX) ...51

Figure 5.4: Base case layout (SG only)...52

Figure 5.5: Power and cycle efficiency vs. IHX approach temperature...53

Figure 5.6: Heat exchanger size indicators ...53

Figure 5.7: Power and cycle efficiency vs. ROT (with IHX)...54

Figure 5.8: Power and cycle efficiency vs. ROT (SG only) ...54

Figure 5.9: Heat exchanger size indicators (with IHX) ...55

Figure 5.10: Heat exchanger size indicators (SG only)...55

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Figure 5.12: Power and cycle efficiency vs. feed water temperature (SG only) ...56

Figure 5.15: Power and cycle efficiency vs. pressure (with IHX) ...57

Figure 5.16: Power and cycle efficiency vs. pressure (SG only) ...57

Figure 5.19: Optimised operating conditions (with IHX) ...60

Figure 5.20: Optimised operating conditions (SG only)...61

Figure 5.21: Base case (with IHX)...64

Figure 5.22: Base case (SG only) ...65

Figure 5.23: Grid power and cycle efficiency vs. IHX approach...66

Figure 5.24: Number of heat exchangers as a function of IHX approach temperature...67

Figure 5.25: Equipment cost vs. IHX approach temperature variation...67

Figure 5.26: Plant cost and LUEC vs. IHX approach ...68

Figure 5.27: Grid power and cycle efficiency vs. ROT (with IHX) ...68

Figure 5.28: Grid power and cycle efficiency vs. ROT (SG only) ...68

Figure 5.29: Equipment cost vs. ROT (with IHX) ...69

Figure 5.30: Equipment cost vs. ROT (SG only) ...69

Figure 5.31: Plant cost and LUEC vs. ROT (with IHX)...70

Figure 5.32: Plant cost and LUEC vs. ROT (SG only) ...70

Figure 5.33: Power and cycle efficiency vs. feed water temperature (with IHX) ...70

Figure 5.34: Power and cycle efficiency vs. feed water temperature (SG only)...71

Figure 5.35: SG pinch margin (without IHX)...71

Figure 5.36: SG pinch margin (with IHX)...71

Figure 5.37: Equipment cost vs. feed water temperature (SG only) ...72

Figure 5.38: Equipment cost vs. feed water temperature (with IHX)...72

Figure 5.39: Plant cost and LUEC vs. feed water temperature (with IHX) ...73

Figure 5.40: Plant cost and LUEC vs. feed water temperature (SG only)...73

Figure 5.41: Power and cycle efficiency vs. cycle pressure (with IHX) ...73

Figure 5.42: Power and cycle efficiency vs. feed water temperature (SG only) ...74

Figure 5.43: Equipment cost vs. cycle pressure (with IHX)...74

Figure 5.44: Equipment cost vs. cycle pressure (SG only) ...75

Figure 5.45: Plant cost and LUEC vs. cycle pressure (SG only)...75

Figure 5.46: Plant cost and LUEC vs. cycle pressure (with IHX) ...76

Figure 5.47: Second order model with IHX optimised for minimum LUEC ...78

Figure 5.48: Second order model with SG optimised for minimum LUEC ...79

Figure 5.49: Steady state result from third order model at 100 % power...81

Figure 5.50: Steady state result from third order model at 40 % power (case A) ...81

Figure 5.51: Steady state result from third order model at 40 % power (case B) ...82

Figure 5.52: Steady state result from third order model at 40 % power (case C) ...83

Figure 5.53: Steady state result from third order model at 40 % power (case D) ...84

Figure 5.54: Pressure vs. time using control strategy D...85

Figure 5.55: Reactor power vs. time (control strategy C)...85

Figure 5.56: Temperature vs. time (control strategy C)...86

Figure 5.57: Mass flow rate vs. time (control strategy C) ...86

Figure 5.58: Blower speed vs. time (control strategy C) ...86

Figure 5.59: Pressure vs. time (control strategy C)...87

Figure 6.1: Cycle selection and optimisation methodology ...90

Figure 6.2: First order model development ...91

Figure 6.3: Third order model development ...91

Figure 6.4: Second order model development ...92

Figure A.1: First order model numbering (with IHX)...99

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Figure B.1: Second order model numbering (with IHX)...119

Figure B.2: Second order model numbering (SG only) ...120

Figure B.3: Diagram showing the layout of one IHX core ...122

Figure B.4: Diagram showing the layout inside a typical IHX vessel ...123

Figure B.5: Hot Gas Duct ...126

Figure C.1: IHX Flownex representation ...157

Figure C.2: SG1 Flownex model ...159

Figure C.3: Upstream heat transfer coefficient calculation...162

Figure C.4: Downstream heat transfer coefficient calculation ...162

TABLES Table 2.1: HTGR plants operated...4

Table 4.1: First order model base case operating parameters ...23

Table 4.2: First order model (with IHX) verification results...27

Table 4.3: Comparison of power and efficiency calculations ...28

Table 4.4: Second order model base case operating conditions ...30

Table 4.5: MHTGR SG operating conditions ...37

Table 4.6: Comparison of SG design procedure and original MHTGR design ...38

Table 4.7: Third order model (with IHX) verification results ...41

Table 5.1: Base case operating parameters ...48

Table 5.2: Summary of base case first order results...50

Table 5.3: Summary of optimised first order results...58

Table 5.4: Summary of base case second order results ...62

Table 5.5: Summary of optimised second order results ...76

Table A.1: Alternative calculation (PHTS) ...112

Table A.2: Alternative calculation (SHTS) ...113

Table A.3: Alternative calculation (Steam plant) ...114

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School of Mechanical Engineering North West University _x

ABBREVIATIONS

This list contains the abbreviations or acronyms as used in this study.

Abbreviation or Acronym Definition

ASME American Society of Mechanical Engineers

AVR Arbeitsgemeinschaft Versuchsreaktor (German for

Jointly-operated Prototype Reactor)

CFD Computational Fluid Dynamics

CIP Core Inlet Pipe

COP Core Outlet Pipe

DPP Demonstration Power Plant

EES Engineering Equation Solver

FOAK First of a Kind

GBP Gas Cycle Bypass Valve

GT Gas Turbine

GT-MHR Gas Turbine Modular High-temperature Reactor

GUI Graphical User Interface

HGD Hot Gas Duct

HP High Pressure

HPT High Pressure Turbine

HTGR High Temperature Gas-cooled Reactor

HTR High Temperature Reactor

HTTR High Temperature Test Reactor

HX Heat Exchanger

IHX Intermediate Heat Exchanger

IP Intermediate Pressure

IPT Intermediate Pressure Turbine

KTA Kerntechnischer Ausschuss (German Nuclear SafetyStandards

Commission)

LMTD Log Mean Temperature Difference

LUEC Levelised Unit Energy Cost

LWR Light Water Reactor

MHTGR Modular High-temperature Gas-cooled Reactor

MWf Reactor fluidic power expressed in Megawatt

MWn Reactor neutronic power expressed in Megawatt

NGNP Next Generation Nuclear Plant

NHSS Nuclear Heat Supply System

O&M Operational and Maintenance

PBMR Pebble Bed Modular Reactor

PCS Power Conversion System

PCU Power Conversion Unit

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Abbreviation or Acronym Definition

PI Proportional-Integral

PR Pressure Ratio

RIT Reactor Inlet Temperature

ROT Reactor Outlet Temperature

SG Steam Generator

SHTS Secondary Heat Transport System

ST Steam Turbine

THTR Thorium High-temperature Reactor

UA Overall Area Heat Transfer Coefficient

UK United Kingdom of Great Britain and Northern Ireland

USA United States of America

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School of Mechanical Engineering North West University _xii

LIST OF VARIABLES

This list contains the variables or symbols as used in this study.

Variable Unit Definition

A - Annual equivalent of capital cost

A m2 Area

Cp kJ/kg Constant pressure heat capacity

Cv kJ/kg Constant volume heat capacity

D m Diameter

f - Friction factor

L M Flow path length

H kJ/[kg.K] Enthalpy

i - Discount rate

K - Loss factor

m& kg/s Mass flow rate

n Years Plant lifetime

MWn MW Reactor neutronic power

MWf MW Reactor fluidic power

P kPa Present value of capital cost

P kPa Pressure

P0 kPa or MPa Ambient pressure

Q kW or MW Rate of heat transfer

Re - Reynolds number

S kJ/[kg.K] Entropy

T0 K or °C Ambient temperature

Tha K or °C Average temperature of the hot stream

Tca K or °C Average temperature of the cold stream

V m/s Linear velocity

v m3/kg Specific volume

Greek symbols

∆ - Differential change

ε - Pebble bed porosity

γ - Ratio between Cp and Cv

η - Efficiency

µ kg/[m.s] Viscosity

Π - Pi

ρ kg/m3 Density

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School of Mechanical Engineering North West University Page 1

1. CHAPTER 1: INTRODUCTION

1.1 BACKGROUND

High Temperature Gas-cooled Reactors (HTGR’s) are a new generation technology that shows promise in the electricity as well as high temperature process heat markets. For this technology to become a commercial success, the configuration of the balance of plant systems needs to be optimised, as it can contribute 30 % of the total plant cost (Dostal et al., 2004:1). To obtain a technically viable and cost-effective cycle design that will fulfil the requirements of the customer is a challenge for the rapidly developing HTGR industry. There exists a need for a proper design procedure which will lead to at least a near-optimal cycle layout.

Power plant design has progressed over the years and many advanced designs are in operation today. The assumptions and methodology used for fossil-fired power plants are not necessarily applicable to nuclear cogeneration plants. For coal power plants, the capital cost is relatively low compared to the plant life cycle costs (Lawrence et al., 1995:71-72), which created a culture of optimising for efficiency only. In nuclear power plants this approach is not sufficient as the capital cost forms a significant part of the total plant cost (Abu-Khader, 2009:226). Therefore significant effort must be spent to minimise capital cost as well.

A literature survey has shown that the industry practice for cycle comparison and selection is first order modelling. It is not custom to perform detailed second to third order thermal hydraulic modelling and cost estimates to aid in the concept design process.

The literature study also revealed that in most cases where optimisation of the balance of plant systems has been attempted, cycles were optimised for maximum efficiency only. This can cause suboptimal design and operating parameters which are only discovered later on in the design process. This could lead to significant additional costs in terms of engineering rework and procurement. The assumptions used in first order analysis are usually optimistic in nature since many simplifications have to be made. By taking the analysis one or two steps further before the final selection of cycle configuration and design conditions, a more realistic representation of the cycle’s performance and cost might be achieved.

Further background on the type of modelling and cycle selection often applied in the nuclear industry, is supplied in Chapter 2.

1.2 PROBLEM STATEMENT

The design and optimisation methodology for HTGR balance of plant configurations is not clearly defined. Only limited, and sometimes conflicting, guidelines are available in literature to aid engineers with cycle selection. It is not clear to how much detail cycle analysis should be performed to obtain a near-optimal techno-economic design.

1.3 OBJECTIVE AND PURPOSE OF STUDY

A need has been identified for a systematic methodology that will assist design engineers in selecting a nuclear power plant configuration that fulfils its design requirements in terms of performance, cost and operability. The purpose of this study is to provide generic guidelines for the pre-conceptual design of such plants, rather than to arrive at the ultimate cycle design for all applications.

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School of Mechanical Engineering North West University Page 2 • Develop relevant calculation models.

• Use these models to perform cycle analysis, evaluation and optimisation in increasing levels of detail.

• Propose a well defined and step-by-step guideline to aid in the selection of optimal plant configurations.

1.4 CONTRIBUTION

The potential impact of this work is that by following the systematic methodology proposed, engineers will be able to select suitable plant configurations and operating parameters quicker and more effectively than before. This will prevent major engineering rework at later stages in the design. The methodology will serve as a guideline to develop a feasible and close to optimal cycle layout in a structured and concise way.

This methodology will also be beneficial to the larger nuclear and conventional power industry as the principles can be extended beyond HTGR design.

1.5 RESEARCH METHODOLOGY

During the course of the selection, different analysis tools and models will be developed by the author of this document as part of an engineering analysis team. The development of all the models will not be claimed as being the sole work of the author. The models will only serve as a tool to demonstrate the cycle selection and optimisation methodology. The model development will be documented, however, to serve as an example of the procedure that is proposed. A Pebble Bed Modular Reactor (PBMR) specific cogeneration case study will be used as demonstration of the modelling required at each stage of the process.

As a starting point for the investigation, a number of cycles will be analysed at first order level using the software Engineering Equation Solver (EES). These models will be optimised in terms of cycle efficiency. Thereafter, these cycles will be remodelled in EES using second order analysis. This will consist of more detailed thermal hydraulic analysis as well as cost estimation of the major components. Optimisation will be performed in terms of a combination of capital cost and energy produced. The results will then be compared with those from the first order model. An assessment will be made on whether the second order modelling added value to the process by judging whether the increased level of detail brought forward new insights. If the optimum operating conditions changed significantly, it will be an indication that first order modelling alone is not sufficient. However, if the same conclusions can be made than after the first order modelling, the necessity of second order modelling may be questioned.

A detailed third order model will then be developed capable of doing off-design and transient analyses. This model will be used to test the operability of the cycles before confirming the selection. If unanticipated control problems arise during this stage, it is an indication that third order modelling ought to be considered as part of the methodology.

The necessity for exergy analysis will also be investigated. This second law analysis method is sometimes used to minimise the lost work in the cycle, thereby optimising the plant configuration.

At the end of this evaluation, judgment will be made on whether the selected cycle is technically and economically feasible. The impact of the increased level of modelling detail on the results will be assessed. The analysis of each stage will be revisited to evaluate the

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School of Mechanical Engineering North West University Page 3 important findings. Finally, based on the results from this study, a methodology will be proposed that could be used for cycle selection and optimisation.

Therefore, the deliverables of this study will be:

• First, second and third order techno-economic models of selected cogeneration cycles.

• Results comparing the various stages and evaluating the necessity of each stage. • A step-by-step methodology that would lead to the selection of an optimal or

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2. CHAPTER 2: LITERATURE SURVEY

2.1 HTGR BACKGROUND

In recent years the interest in nuclear energy has increased as an almost non-exhaustible, carbon free energy source. The public’s main concerns have always been the possibility of accidents, radio-active waste disposal and the possibility of terrorist activities based on the nuclear fuel cycle (Marcus, 2008:91). However, the inception of Generation IV reactors will create nuclear reactors that are safer, more economical and have less waste than previous reactors (Elder & Allen, 2009:501). Increasing pressure from environmental lobbyists to limit CO2 emissions are driving the energy industry away from fossil fuels and toward nuclear and

hydrogen applications. HTGR’s have the potential to replace gas-fired boilers and natural gas as heat source (Kuhr et al., 2008:4).

A HTGR or High Temperature Reactor (HTR) is a gas cooled graphite moderated nuclear reactor. The fuel can be block type (prismatic) or pebble bed. Helium is usually used as the reactor coolant. Table 2.1 (Elder & Allen, 2003:511) summarises the HTGR’s that has been built and operated to date.

Table 2.1: HTGR plants operated

Reactor Location Power Core outlet

temperature

Years in operation

Dragon UK 20 750 1965-1975

Peach Bottom USA 115 750 1967-1974

AVR Germany 46 950 1968-1988

Fort St Vrain USA 842 775 1976-1989

THTR Germany 750 750 1985-1989

HTTR Japan 30 950 1998 -

HTR-10 China 10 700-950 2000 -

According to Marcus (2008) a market opportunity exists for small reactors that can produce heat and electricity in remote locations. Hydrogen production is a niche market for HTGR’s as conventional Light Water Reactors (LWR’s) do not provide the high temperature process heat (>800 °C) required (Kuhr, 2007:3013). Some further advantages HTGR’s hold over conventional light water nuclear reactors are smaller reactor sizes, higher reliability, improved economics, higher availability due to online refuelling (in the case of a PBMR) and the possibility to situate the nuclear heat source closer to the chemical process plant because of inherent safety features (Kuhr et al., 2008:1-2). HTGR plants are also economically competitive with conventional LWR’s in small to medium sized power plants according to Ide et al. (1996:357). In work performed by Nisan et al. (2003:311) it can be seen that HTR plants have the same order of magnitude costs as LWR’s per MW electricity.

This leads to the conclusion that the possible applications and opportunities for nuclear power plants, especially process heat plants, are increasing. Therefore the need arises to design new and innovative HTGR plants for specific customer requirements instead of only producing electricity. A methodology to aid in the design and selection of these plants will therefore be useful to the HTGR industry.

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School of Mechanical Engineering North West University Page 5 2.2 DESIGN GUIDELINES

Limited and conflicting guidelines on power plant design and cycle optimisation are available in open literature. In general the work in this field varies significantly in the complexity of analysis undertaken and the grounds on which evaluation of various cycles were performed. The work performed can be divided roughly into the following categories:

• The qualitative evaluation of cycles as performed by Johnson (2008), Minatsuki et al. (2008) and Baxi et al. (2007).

• First order cycle analysis claiming very high efficiencies because of idealistic assumptions, such as Herranz et al. (2009).

• Optimisation of cycles based on: o_{Efficiency (Oh et al., 2007a).} o_{Exergy (Gomez et al., 2007).}

o First order cost indicators such as heat exchanger area (Barner, 2006). • Second order costing based on more detailed design such as Oh et al. (2007b) • Testing the dynamic response of a proposed plant layout, such as Mizokami et al.

(2008), Rousseau & Van Ravenswaay (2003), Kumar et al. (2001) and Kikstra (2000). • Detailed economic analysis of a given plant layout, such as the work done by the Economic Modelling Work Group (2005). This analysis includes not only the major equipment but also additional costs such as the site and facilities, construction, labour, lifetime operating cost, and also takes factors into account for first of a kind engineering and technology maturity.

In recent years a lot of work has been performed and published with regards to selecting a suitable cycle for the advancement of HTGR technology. Brayton, Rankine and combined cycles have been compared by numerous authors. Idaho National Laboratory in particular has made good progress in this regard (Oh et al., 2005, 2006a, 2006b, 2006c, 2007a and 2007b). However, none of these studies offered a complete procedure combining the methods above.

The lack of a proper selection procedure is demonstrated by the fact that conflicting views exist in industry with regards to the cycle, the working fluid and the operating parameters that hold the most promise for Generation IV applications. General Atomics previously recommended a direct gas turbine cycle and a combined steam / gas turbine cycle using helium as working fluid as their HTGR offering for NGNP (the United States Department of Energy Next Generation Nuclear Plant project). Areva and Westinghouse both recommended indirect steam turbine cycles with a primary helium loop, with Areva proposing a mixture of helium and nitrogen in the intermediate loop (Idaho National Laboratory, 2007). Rolls Royce proposed a combined gas turbine cycle with a nitrogen/helium working fluid in the intermediate loop (Persson & Donaldson, 2009). Recently, however, General Atomics (Shenoy, 2008), Areva (Lommers, 2008) and Westinghouse have all indicated that their design proposal will change to direct steam cycles (although at different operating conditions), which indicates some form of convergence with regards to cycle selection procedures.

PBMR previously recommended a direct Brayton cycle because of its superior potential for very high cycle efficiencies. However, this decision was based on optimistic assumptions for turbo-machine operation with regards to efficiency and controllability. In the earliest work a three shaft design was selected because of freedom of operability and the possibility of small

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School of Mechanical Engineering North West University Page 6 turbo-machines. However, once the design progressed to the detailed stage, transient analysis showed problems with instable fourth-quadrant turbine operation and unacceptable heat-up of the power turbine system during certain plant events (Matzner, 2004:8). This type of operating problems cannot be shown through first or even second order analysis.

First order analysis often results in unrealistically high cycle efficiencies. This is due to simplified plant models which does not account for cooling, bleed or bypass flows, and model little or no pressure drop and heat losses. Herranz et al. (2009) claims cycle efficiencies higher than 50 % for direct recuperative Brayton cycles with inter-cooling, based on first order analysis. The GT-MHR design claims cycle efficiencies higher than 46 % (General Atomics, 1995:1-2) for a direct Brayton cycle. These claims have been refuted by Muller’s third order cycle analysis (2009:22) which showed overall cycle efficiencies of 38 % for the PBMR direct Brayton cycle. It seems therefore that first order analysis is not sufficient in predicting plant performance.

Process design is typically performed at steady state operating conditions, assuming that a control system can be designed that would maintain the process at the desired operating conditions and within design constraints. This is not necessarily the case. Off-design performance may influence the selection of a cycle, and this can only be investigated by third order analyses. In an in-depth study, El-Genk and Tournier (2009) developed detail component designs and models for axial turbines and compressors, and included details such as turbine and vessel cooling bleed flows into an integrated plant model. This enabled them to investigate the effect of different fluids and operating conditions on turbo-machine efficiencies, giving an indication of part-load performance instead of only nominal plant conditions as is most commonly done. Off-design conditions are important as many power plants are required to operate at base load conditions as opposed to nominal load for long periods. Furthermore, cycle comparisons based on dynamic analysis (Rousseau and Van Ravenswaay, 2003) showed that there are important differences between three and single shaft gas turbine systems when analysing their transient response. This is another indication that important operability issues can only be investigated by this level of analysis.

Economic evaluations are typically done without taking plant controllability and robustness into account, which could lead to the elimination of easily controlled but slightly more expensive designs. Controllability is the ease at which a dynamic process can be kept at the desired equilibrium state, while robustness is a measure of the resilience and stability of a system in the presence of external disturbances (Seider et al., 1998:439). In order to ensure a design that is easy to control as well as robust, process design and control must be integrated from the conceptual phase. It is becoming more and more evident that cycle selection based on steady state economics alone is risky, because operational difficulties, translating into profit loss and higher operational and maintenance cost, are not considered A suggestion is made by Terpenny (1998) with regards to a procedure for the early stages of plant design and technology selection. A blending of the top-down and bottom-up approaches of system engineering is proposed. The top-down approach implies that the requirement is defined and then a solution (in this case a cycle) that will fulfil the need is attempted; however in first-of-a-kind (FOAK) systems there are no guarantee that this process is feasible. In contrast, the bottoms-up approach will add together and modify existing component designs in the hope that it will fulfil some need. This approach focuses on the details before ensuring that the concept is feasible or that there is an existing need. She concludes that a blend of the two methodologies would give a better solution.

Kikstra (2001:9) observed that a systematic approach to conceptual power plant design and analysis is not available in literature, and therefore proposed his own. It is mentioned that

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School of Mechanical Engineering North West University Page 7 an economic assessment step should have been included but was omitted due to lack of input data.

Kikstra’s proposed design procedure consists of the following steps: • Define the design specifications or goals and customer requirements • Choose a cycle based on information from existing designs

• Model a thermodynamic design using typical component efficiencies

• Optimise the design parameters with the basic steady state thermodynamic model • Design the dimensions of the main components and perform sensitivity analysis • Choose off-design conditions

• Test the system’s transient behaviour with a dynamic model • Design a control system

Kikstra’s approach corresponds to the top-down approach. Instead of taking a number of cycles through the complete selection procedure in order to arrive at an optimal design, one is chosen and evaluated. If this cycle proves to be satisfactory, although not optimal, the design will proceed. This methodology may, however, lead to unsatisfactory results at a later stage which then calls for repeating the procedure using a different cycle design.

2.3 ORDERS OF ANALYSIS

The distinction between the different analysis stages and the terminology used in literature varies widely. Furthermore, it is unclear at which stage in the design what type of analysis should be used.

Oh et al. distinguish between thermal hydraulic cycle analysis (2006a; 2006b & 2007a) and engineering analysis (2006c & 2007b). Their definition of cycle analysis is a high level thermal hydraulic analysis while engineering analysis tends towards detailed component design. Greyvenstein, R (2005) considered cycle analysis to be high level thermal hydraulic modelling with limited component sizing.

Both Mizokami et al. (2008) and Shimakawa et al. (2006) performed dynamic analysis to investigate control methods for a HTGR steam cycle. El-Genk and Tournier (2009) modelled various cycles in comprehensive detail in what they called “plant performance analysis”, carrying the design up to almost basic design level.

Greyvenstein, G.P. (2006) gives a clear indication of the orders or analysis. These definitions are given below:

• First order cycle analysis is a high level thermal hydraulic analysis to determine system performance based on the cycle layout.

• Second order engineering analysis offers details such as piping losses, turbo-machine efficiencies and leak or bleed flows which improves the accuracy of the model.

• Third order analysis can entail steady state or transient models with enough detail to represent the dynamic behaviour of systems.

2.4 CYCLE EFFICIENCY

A literature search was performed to investigate the definitions used in industry for cycle efficiency. The definition of cycle efficiency is important when a claim is made about the value obtained with a specific layout. In most cases cycle efficiency is defined as turbine output from which compressor power is subtracted. However, no mechanical efficiency, generator or switching efficiency to calculate the true power supplied to the grid is mentioned

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School of Mechanical Engineering North West University Page 8 in most cases. For comparative purposes this can be ignored, but when calculating the total power generated for economic purposes it becomes important.

Distinction should also be made between thermal efficiency and overall cycle or electrical efficiency. Thermal efficiency is usually the gross turbine power, or net power, divided by the power of the heat source. The heat source is not always clearly defined as whether it is the original heat source, e.g. the reactor, or the intermediate heat source, which is important for indirect cycles.

Oh et al. (2006c:10) as well as Dostal et al. (2004:64) defines overall cycle efficiency as the electrical power supplied to the grid divided by the reactor thermal power. In an indirect cycle they define the Power Conversion Unit (PCU) efficiency as the electrical power divided by the thermal power of the intermediate heat exchanger (IHX). (Note that the terms PCU and PCS are used interchangeably in literature.)

Herranz et al. defines thermal efficiency as the net power divided by the heat source, which corresponds to the definition of PCU efficiency from Oh et al. (2006c:10). The definition of plant efficiency per Minatsuki et al. (2008) corresponds to overall cycle efficiency from Oh et al. as given above.

Zhu et al. (2008: 4) distinguishes between gross and net efficiency where gross is meant to imply that the total turbine power output is used divided by heat input, while net indicates that the house load (the electricity usage by all plant components) is subtracted from the turbine power before dividing by the heat input.

To summarise, two main types of efficiency are defined in literature, regardless of the terminology used:

• The gross overall cycle efficiency indicating the power supplied to the national grid expressed as a percentage of the reactor power.

• The total turbine power produced before any subtractions, expressed as a percentage of either reactor power or IHX heat input.

2.5 OPTIMISATION CRITERIA

The term “optimal design” could have contradicting meanings. It is sometimes used to indicate a design that will obtain the highest possible cycle efficiency without regards to cost, but it could also imply the lowest cost design that will satisfy the requirements. Furthermore, a technically optimal design is often selected which turns out not to be the optimal configuration from another perspective, such as plant availability or lifecycle cost. For example, the Fort St Vrain plant was offline most of the time due to water ingress from its water-cooled bearings on the circulator (Oh et al., 2005). Even if it was an optimal design in terms of cycle efficiency, the operability issues prevented it from fulfilling its design requirements.

In coal fired power plants, the capital cost is a fairly small part of the plant lifetime cost because of high operating costs (Lawrence et al., 1995:71-72). This resulted in a culture of mostly optimising cycles in terms of cycle efficiency and not cost. For example, Schleicher et al. (2001:824) states that it is better to optimise for efficiency than component cost. They claim that the power conversion system (PCS) contributes only to 10 – 20 % of the total plant cost and therefore it is not worth minimising capital cost at the expense of life time cycle efficiency. However, Dostal et al. (2004:1) states that the balance of plant contributes to as much as 30 % of the total plant cost. Furthermore, in nuclear plants the operating cost is expected to be low but the capital expenditure to build such a plant is enormous (Abu-Khader, 2009:226). Equipment for nuclear plants is three times as expensive as exactly the

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School of Mechanical Engineering North West University Page 9 same equipment for non-nuclear applications, due to licensing and safety aspects, according to Van Heek (1996:29). Therefore some effort must be spend to minimise capital cost as well.

In the early stages of PBMR design the cycle was designed to optimise cycle efficiency. It was also stated that component simplicity was an objective, but this was not quantified (Liebenberg, 1996). The combination of hardware configuration and operating conditions determines the electrical power produced and therefore the cycle efficiency. Some options might improve the cycle efficiency marginally, but the impact it has on the cost of the hardware levels out the gain. For example, Ballinger et al. (2003:110) found that the complexity and cost introduced by inter-cooling in a Brayton cycle, offsets the increase in cycle efficiency except at very large pressure ratios. The importance of trade-off studies between capital cost and cycle efficiency is hereby stressed.

Another problem with current optimisation procedures is that various cycles are often compared without optimising each, for example Minatsuki et al. (2008). Cycles are compared thermodynamically or economically at the same reference points, which takes away the inherent advantage one type of cycle may have over another. By comparing a Brayton and a Rankine cycle at the same core outlet temperature, instead of at each cycle’s optimum operating conditions, an unfair advantage is given to one of the cycles.

For example, Brayton cycles have high cycle efficiencies at very high temperatures, while Rankine cycles could have better cycle efficiencies than Brayton or combined cycles at lower temperatures. This is illustrated in Figure 2.1 (Frohling et al., 2002):

Figure 2.1: Comparison of cycle efficiencies for steam turbine (ST), gas turbine (GT) and combined cycles

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School of Mechanical Engineering North West University Page 10 2.6 ECONOMIC ANALYSIS

Financial analysis is an important part of nuclear plant design. Before the availability of high-speed desktop computers and data base systems, nuclear plant designs were nearly always fixed and completed before the detailed cost estimation process was initiated. With new computational and data management tools, it is now possible to integrate cost estimation directly into the design process. This allows the possibility of Levelised Unit Energy Cost (LUEC) and baseline capital cost optimisation during design. (Economic Modelling Working Group, 2005:34-35).

In the energy industry the LUEC is used to express the relative cost to produce a unit of energy and is often used to compare different types of energy (coal, wind, nuclear etc). The terminology “unit energy cost” refers to the cost to design, procure, construct and operate a plant to produce one unit of energy. This is generally expressed in a monetary unit per lifetime energy produced, such as $/MWh. The term “levelised” implies that the expenditure is spread evenly over the lifetime of the plant.

The LUEC consists of the following cost components:

• Capital cost (includes equipment hardware cost and installation).

• Operational & Maintenance (O&M) costs, such as electricity if it is not self-supplied, water, and the labour, spares and special tools needed for maintenance.

• Fuel cost over the plant lifetime.

• Decommissioning cost (labour cost and special tools required for dismantling).

All of the above is converted to an annual cost, and divided by the annual energy produced, which is dependent on the power output and the plant load factor (Economic Modelling Working Group, 2005:99).

Until now not many plant designs were performed with the objective to minimise the LUEC. However, with better cost estimation methods and improved computational power, the potential exists to integrate economic modelling and plant design such that the lowest LUEC can be realised.

2.7 SECOND LAW ANALYSIS

The effective use of a system is determined not only by the first law of thermodynamics (conservation of energy), but also by the second law. It states that the entropy of a system will either stay the same or increase due to irreversibilities. The first law can determine the energy transfer requirements of a process, but the second law gives an indication of the efficiency of a system (Seider et al., 1998:207). Second law analysis is also described by the terms exergy or lost work analysis.

Exergy is defined as the difference of the state of the system from that of the environment and is also called the available work. Exergy can be destroyed and is generally not conserved. The change in exergy of a system is given as

0 0, 0 , 0 ) ( ) (H T S _T_P H T S _T _P Exergy= − − − [2-1]

Where H is the enthalpy and S the entropy of the system (Seider et al., 1998:215). The subscript 0 denotes the conditions of the surrounding environment. Increasing the enthalpy change or decreasing the entropy change will increase the available work.

Lost work (i.e. work performed that is not available as useful to the system) is a measure of the irreversibility of a system. When the lost work is zero, the process is completely reversible. The more efficient a process, the smaller the lost work. By eliminating or reducing

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School of Mechanical Engineering North West University Page 11 the causes of irreversibilities in a system, entropy generation as well as exergy destruction can be minimised. This will result in a thermodynamically more efficient system.

Some causes of irreversibilities are (Seider et al., 1998:223-224): • The mixing of streams that differ in enthalpy and / or composition. • Large differences in approach temperatures in heat exchangers. • Fluid friction, typically as a result of high flow velocities.

• Transferring heat to a heat sink instead of recuperating. • Mechanical friction in turbo-machines.

For a counter flow heat exchanger, the exergy destruction due to heat transfer is given by:

ca ha ca ha T T T T Q T n Destructio Exergy = ₀ − [2-2]

Where ED is the exergy destruction, Q the rate of heat transfer, Tha the hot steam average

temperature and Tca the cold stream average temperature (Bejan et al.,1996:146). The term

Tha – Tca is the temperature difference between the streams. It can be seen that the lower

the average temperature, the higher the exergy destruction and the more important to reduce the temperature difference between the hot and cold streams.

The exergy loss for a system due to friction is defined as follows:

ha T f V D L m T n Destructio Exergy (4 / )( /2) 2 0& = [2-3]

Where m is the mass flow rate, L the flow path length, D the flow path diameter, V the linear velocity and f the friction factor (Bejan et al.,1996:147). At low temperatures it is important to minimise the frictional losses to limit the exergy destruction.

Exergy analysis can be performed to investigate the lost work in the cycle, as was done by Gomez et al. (2007). This approach will favour the plant with the highest quality of heat, i.e. at the highest temperature. This would indicate the most efficient plant thermodynamically, but not necessarily at the lowest cost. Therefore it is important, once again, to use this method in combination with cost optimisation and not in isolation.

The general design principle of minimising known causes of irreversibilities will be beneficial to the plant design, even without performing detailed calculations of the exergy losses in the cycle.

2.8 SUMMARY OF FINDINGS

The findings from the literature survey are summarised below.

• The level of analysis required for cycle selection and optimisation has not been determined explicitly before.

• Cycle evaluation and selection is often performed based on high level first order analysis.

• First order analysis often gives an unrealistic estimate of plant performance.

• Second order analysis can be used to obtain detailed component design information and cost estimates.

• Plant controllability and operability must be evaluated early on to prevent an unattainable design. This can be done through third order analysis.

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School of Mechanical Engineering North West University Page 12 • Cycles are usually optimised for maximum cycle efficiency but not for minimum capital cost. However, research has shown that the cost of the HTGR balance of plant configuration is significant and a concerted effort should therefore be make to minimise this.

• The term cycle efficiency is broadly used but not always defined in the same way. This could be misleading when directly comparing cycles. Efficiency numbers are quoted without distinguishing exactly whether overall plant efficiency, thermal or PCS efficiency is meant and how it was calculated.

• When comparing different cycles it must be carefully noted whether optimum solutions are to be compared, or whether the analysis must compare a given baseline operating point. When making comparisons at fixed parameters, such as the same reactor outlet temperature for various cycles, the relative advantage to each technology that is due to it might not be apparent.

• Financial analysis can be used to compare designs in terms of capital or lifecycle plant costs. The LUEC is used in the energy industry to compare different technologies using the same basis. It would be very beneficial to optimise cycles in terms of the unit energy cost as it would incorporate factors such as capital and operating costs as well as cycle efficiency.

• Second law analysis can be used to provide sound general design principles. Known causes of irreversibilities can be minimised without having to go into the effort of setting up a detailed model which can quantify exergy destruction.

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3. CHAPTER 3: THEORY

This chapter presents general theory and definitions as used throughout the document.

3.1 CYCLE OPTIONS

In this section a summary of the thermodynamic systems currently in use to generate power will be given. Some of the anticipated problems with regards to each cycle design will be discussed.

3.1.1 Rankine cycle

Rankine cycles, also referred to as steam turbine cycles, are applied in the vast majority of coal fossil and nuclear power stations. Steam is generated either in a nuclear heated steam generator (SG) or a coal-fired boiler. The steam passes through a turbine, after which it is condensed and then pumped back to the SG / boiler. A typical basic Rankine cycle and its corresponding temperature-entropy diagram are displayed in Figure 3.1 (Botha, 2008:29).

Figure 3.1: A typical basic Rankine cycle

There are various methods of improving cycle efficiency such as reheating of the steam or preheating the feed water in a regenerator (mixing steam extracted from the turbine with the feed water in an open heat exchanger) (Elder & Allen, 2009:507). Supercritical Rankine cycles are the newest improvement which could improve the cycle efficiency even further. Zhu et al. (2008:9) claims an improvement of 3 % over sub-critical cycles.

Rankine cycles have the advantage of an extensive experience base in both nuclear and fossil fuel power stations. Furthermore, all of the major components can be bought off-the-shelve, and no development work is needed for a standard cycle. One disadvantage is that because of the gas in the primary loop of a HTGR, the Rankine cycle can only be an indirect cycle. It can at best be coupled to a main loop SG, but if contamination issues or reactor water ingress requirements demand, it needs to have an additional buffer loop which decreases cycle efficiency. The coupling between the primary loop and the buffer loop then requires an IHX, which still remains to be demonstrated in a nuclear environment at the temperatures required (Kuhr, 2008:3016).

In the intermediate temperature range Rankine cycles could have higher cycle efficiencies than Brayton or combined cycles, especially if the gas cycles are of the indirect type (Frohling et al., 2002).

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School of Mechanical Engineering North West University Page 14 3.1.2 Brayton cycle

In a Brayton cycle, also referred to as a gas turbine cycle, the fluid is in a gaseous state for the entire cycle. Brayton cycles utilise the diverging shape of the temperature–entropy diagram to extract useful work from the gas. In a simple Brayton cycle, a compressor and a turbine is mounted on the same shaft. Gas is compressed to a high pressure and heated by the nuclear or other heat source before entering the turbine. In the turbine work is performed by the gas and it is expanded to low pressures. The exit gas is cooled before re-entering the compressor. Various methods of improving cycle efficiency can be applied, such as intercooling, recuperating and reheating. A diagram of a recuperative, intercooled Brayton cycle with reheat is shown in Figure 3.2, with its corresponding temperature-entropy diagram shown in Figure 3.3 (Botha, 2008:55).

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School of Mechanical Engineering North West University Page 15 Figure 3.3: Temperature-entropy diagram for a recuperative, intercooled Brayton

cycle with reheat

At very high temperatures (> 800 °C), Brayton cycles can obtain much higher theoretical efficiencies than Rankine cycles (Frohling et al., 2002). Furthermore, single or multiple shafts can be considered, each with its own set of problems and advantages. (Botha, 2008:37) One advantage of the Brayton cycle is that it can be operated directly coupled to a nuclear reactor which could further improve efficiencies. However, there are other disadvantages associated with this, such as possible fission product plate-out on the turbine blades (Botha, 2008:31), and the fact that all the Brayton cycle components have to be designed to nuclear licensing codes.

Gas turbine technology holds some risk for near term deployment as it needs development; it has not been demonstrated in a commercial nuclear power plant as yet (Elder & Allen, 2009).

3.1.3 Combined cycle

A combined gas turbine / steam cycle is a combination of a Brayton cycle, utilising the high temperature heat, and a bottoming Rankine cycle. This implies that the cooled turbine exit gas enters the SG before entering the recuperator (if present). The steam is then used in a traditional Rankine steam turbine cycle. An example of a combined cycle is shown in Figure 3.4 (Botha, 2008:29).

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School of Mechanical Engineering North West University Page 16 Figure 3.4: A combined Brayton and Rankine cycle

It is generally thought that this cycle has the most long term potential as it can theoretically achieve superior cycle efficiencies (Frohling et al., 2002). However, Johnson (2008:1) mentions that it is the most costly of all the cycles and provided little performance advantage over supercritical Rankine cycles.

3.1.4 Process heat

In a process heat plant, the heat from the reactor is transferred to a process plant either directly or indirectly, with no electricity being generated, as is shown in Figure 3.5 (taken from Kuhr et al., 2008:3):

Figure 3.5: An example of a plant supplying process heat only

In such a plant it is not easy to define what an optimised cycle should be, since there is no electricity produced which can serve as a measure of cycle efficiency. If the amount of heat transferred or mass flow rate of process fluid at the desired condition is used as ultimate objective, then the optimum cycle would be the largest one. This does not account for any factors such as the feasibility of manufacturing and transporting large components or its associated operating cost. In this case the amount of process heat required by the client

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School of Mechanical Engineering North West University Page 17 must be clearly specified, and then the plant with the lowest life cycle cost that can provide this must be designed. To optimise the operating conditions, other methods such as exergy analysis can be followed.

3.1.5 Cogeneration

The term cogeneration is used to describe a plant where some of the heat is utilised to heat a process stream, and the remainder to produce electricity as is shown in Figure 3.6 (taken from Kuhr et al., 2008:3):

Figure 3.6: A schematic for a cogeneration plant

In some cases the electricity production only needs to be sufficient to provide the house load of the plant, while in other cases it may be exported to the national grid. Either the process or the electricity part may be required to go off-line at times without disturbing the operation of the other part. These varying requirements put different constraints on the design.

Similar to the purely process heat plant, as was mentioned in section 3.1.4, the optimisation of such a cycle is not a straight forward concept. There would be some optimal plant configuration that determines the split between process heat and electricity production, and whether the two processes must be in series or parallel. If one optimises for cycle efficiency, the optimal plant would always be one that provides no process heat due to the definition of cycle efficiency. In this case the client requirements clearly become very important as it will determine the layout.

3.1.6 Direct versus indirect cycle

A direct cycle has the advantage of potentially higher cycle efficiencies and a higher temperature of the available heat, but it also has its disadvantages. In case of gas turbines being coupled directly to the reactor, it introduces constraints on the design because of possible radio-active contamination of the turbine blades (Botha, 2008:30-31). Furthermore, all components in the primary loop have to be designed to nuclear design codes, which results in more expensive components and a more complicated licensing process. In the case of a Rankine cycle, water ingress into the primary loop and contamination of the water system is possible.

To avoid these problems an intermediate buffer loop can be used, but this implies the use of a heat exchanger to transfer the heat from the reactor. Such a heat exchanger has not yet been demonstrated at the temperatures required (Elder & Allen, 2009:519). Therefore a significant challenge to the design of an indirect nuclear cycle is the development of this Intermediate Heat Exchanger (IHX).