Thermoeconomic and Optimization Analysis of Advanced

THERMOECONOMIC AND OPTIMIZATION ANALYSIS OF ADVANCED

SUPERCRITICAL CARBON DIOXIDE POWER CYCLES IN CONCENTRATED

SOLAR POWER APPLICATION

Dissertation Submitted to The School of Engineering of the UNIVERSITY OF DAYTON

In Partial Fulfillment of the Requirements for The Degree of Doctor of Philosophy in Engineering

By Ali Sulaiman H. Alsagri

UNIVERSITY OF DAYTON Dayton, Ohio

August, 2018

THERMOECONOMIC AND OPTIMIZATION ANALYSIS OF ADVANCED

SUPERCRITICAL CARBON DIOXIDE POWER CYCLES IN CONCENTRATED

SOLAR POWER APPLICATION

Name: Alsagri, Ali Sulaiman

APPROVED BY:

______Andrew D. Chiasson, Ph.D. Dave Myszka, Ph.D. Advisory Committee Chairman Committee Member Assistant Professor Associate Professor Department of Mechanical and Aerospace Department of Mechanical and Engineering Aerospace Engineering

______Muhammad Usman, Ph.D. Robert B. Gilbert, Ph.D. Committee Member Associate Committee Member Professor Professor Department of Mathematics Department of Mechanical and Aerospace Engineering

______Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Dean, School of Engineering Innovation Professor School of Engineering

©Copyright by

Ali Sulaiman Alsagri

2018

iii

ABSTRACT

THERMOECONOMIC AND OPTIMIZATION ANALYSIS OF ADVANCED

SUPERCRITICAL CARBON DIOXIDE POWER CYCLES IN CONCENTRATED

SOLAR POWER APPLICATION

Name: Alsagri, Ali Sulaiman University of Dayton

Advisor: Dr. Andrew D. Chiasson

Various supercritical CO2 Brayton cycles were subjected to energy and exergy analysis for the purpose of improving calculation accuracy; the feasibility of the cycles; and compare the cycles’ design points. With respect to improving the accuracy of the analytical model, a computationally efficient technique using constant conductance (UA) to represent heat exchanger performances. Three parametric analysis were conducted: total conductance, maximum and minimum operating temperature, and pressure ratio for appropriate optimization. Recompression sCO2 Brayton cycle based on three parametric analysis achieves the highest thermal efficiency and power output at different operating condition. Also, the findings show that the simple recuperated sCO2 Brayton cycle has the highest specific power output in spite of its simplicity.

Then a novel combined power cycle based on the recompression configuration were proposed for the purpose of improving overall thermal efficiency of power cycles by attempting to minimize thermodynamic irreversibilities and waste heat as a consequence

of the Second Law. The power cycle concept comprises an advanced recompression sCO2

Brayton configuration as a topping cycle and a split flow tCO2 Rankine configuration as a bottoming cycle. The topping sCO2 recompression Brayton cycle used a combustion chamber as a heat source, and waste heat from a topping cycle was recovered by the tCO2

Rankine cycle due to an added high efficiency recuperator for generating electricity. The combined cycle configurations were thermodynamically modeled and optimized using an

Engineering Equation Solver (EES) software. Single and multi-objective optimization techniques conducted in this research is developed using a genetic algorithm (GA). The findings show that the higher thermal efficiency was obtained with recompression sCO2

Brayton cycle – split flow tCO2 Rankine cycle. Also, the results show that the combined sCO2 cycles is practical and promising technology compared to conventional cycles.

To produce an ecologically justifiable energy along with cost-competitive, concentrated solar power tower plant model is conducted. The aim of concentrated solar power (CSP) system modeling was to assess the system viability in a location of moderate- to-high solar availability. A case study is presented of a city in Saudi Arabia. To achieve the highest energy production per unit cost, the heliostat geometry and thermal energy storage (TES) dispatch are optimized. Solar power tower (SPT) is one design of CSP technology that is of particular interest here because it can operate at relatively high temperatures. The present SPT-TES field comprises heliostat mirrors, a tower, a receiver, heat exchangers, and two molten-salt TES tanks. The main economic indicators are the capacity factor and the levelized cost of electricity (LCOE). The findings indicate that SPT-

TES with sCO2 power cycles is economically viable. The results also show that integrating

TES with an SPT has a strong positive impact on the capacity factor at the optimum LCOE.

DEDICATION

I dedicate this work to my beloved parents, Dr. Sulaiman and Mrs. Loloh, to my adorable

wife, Nora, to my breathtaking son, Sulaiman

ACKNOWLEDGEMENTS

First and foremost, I would like to thank my Almighty God (Allah) who turned this research to a success. As it always should be saying, “Alhamdulillah - All praise is due to

God alone - for the past, present, and future”.

I would like to express my huge thanks to my parents, Sulaiman and Loloh, for their unlimited love, and morally and emotionally support. All the success I am having because and for them.

I am deeply thankful and expressing my very profound gratitude to my wife Nora, for her endless amount of love, and unfailing support. I could not imagine how much more time this goal will be achieved without her. We went through both hard and happy time during this journey, and she was and is always with me. Also, I would like to thank my little son, Sulaiman, for his unstopped smiling when I looked at him after a long time of working. His similes are stress relief and happiness.

To my siblings, Dr. Mazen and Mrs Arwa, thank you so much for being a good supporter during the years I have been away from home.

Last but not least, I wish to present my warm special thanks to Dr. Andrew D.

Chiasson, my advisory committee chairman, for his encouragement, motivation, continuous support, and assistance to achieve the goal. Also, I would like to pay my warm

vii

regards to my committee members, Dr Dave Myszka, Dr Muhammad Usman, and Dr.

Robert B. Gilbert, for their recommendation, feedback and guidance that turned my research a success.

viii TABLE OF CONTENTS

ABSTRACT ...... iv DEDICATION ...... vi ACKNOWLEDGEMENTS ...... vii LIST OF FIGURES ...... xii LIST OF TABLES ...... xvi LIST OF ABBREVIATIONS AND NOTATIONS ...... xviii CHAPTER I INTRODUCTION ...... 1 1.1 Background/Motivation ...... 1

1.1.1 History of sCO2 as a Working Fluid ...... 2 1.2 Power Cycle ...... 6

1.2.1 Supercritical CO2 Brayton Cycle ...... 6

1.2.2 Supercritical CO2 Combined Cycle ...... 8 1.3 Concentrated Solar Tower ...... 13 1.4 Research Gaps ...... 15 1.5 Dissertation Organization ...... 15 CHAPTER II METHODOLOGY OF POWER CYCLES ...... 17 2.1 Research Objectives ...... 17 2.2 Problem Definition ...... 18

2.2.1 The Properties of Supercritical CO2 ...... 18 2.3 Turbomachinery Modelling...... 21 2.4 Heat Exchangers Modelling ...... 22 2.5 Exergy Modelling ...... 27 2.6 Power Block Model Validation ...... 29 CHAPTER III PERFORMANCE COMPARISON AND PARAMETRIC ANALYSIS OF S-CO2 POWER CYCLES CONFIGURATIONS ...... 32 3.1 Optimization Domain ...... 33 3.2 Power System Description ...... 34

3.2.1 The sCO2 Simple Recuperated Brayton Cycle Configurations ...... 36

3.2.2 The sCO2 Recompression Brayton Cycle Configurations ...... 38

3.2.3 The sCO2 Pre-compression Brayton Cycle Configurations ...... 41

3.2.4 The sCO2 Split Expansion Brayton Cycle Configurations ...... 44 3.3 Number of Sub-Heat Exchangers ...... 46 3.4 Cycle Compression ...... 47 3.4.1 Effect of Total Conductance ...... 47 3.4.2 Parametric Analysis of the Pressure Ratio ...... 51 3.4.3 Parametric Analysis of the Operating Temperature ...... 60 3.5 Summary and Results ...... 63 CHAPTER IV THERMODYNAMIC ANALYSIS AND MULTI-OBJECTIVE OPTIMIZATIONS OF A COMBINED RECOMPRESSION S-CO2 BRAYTON CYCLE T-CO2 RANKINE CYCLE FOR WASTE HEAT RECOVERY ...... 65 4.1 System Description ...... 66 4.2 Optimization and Objective Function ...... 69 4.2.1 Optimization Domain ...... 71 4.3 Modeling Approach...... 72 4.4 Results and Discussion ...... 73 4.5 Conclusion ...... 79 CHAPTER V VIABILITY ASSESSMENT OF A CONCENTRATED SOLAR POWER TOWER WITH A SUPERCRITICAL CO2 BRAYTON-CYCLE POWER PLANT ...... 80 5.1 Introduction ...... 81 5.2 Mathematical Modeling Approach...... 86 5.2.1 Solar Power Tower System ...... 86 5.2.2 Economic Approach ...... 93 5.3 Result and Discussion ...... 95 5.4 Conclusions ...... 107 CHAPTER VI CONCLUSIONS AND FUTURE RECOMMENDATIONS ...... 109 6.1 Conclusions ...... 109 6.2 Future Recommendations ...... 110 6.2.1 Pressure Drop ...... 110 6.2.2 Economic Calculating ...... 112

BIBLIOGRAPHY ...... 115

LIST OF FIGURES

Figure 1. Angelino’s condensation cycles ...... 4

Figure 2. Timeline of using CO2 as a working fluid ...... 5

Figure 3. Four advanced cycle efficiency comparison [41] ...... 7

Figure 4. Compressor inlet and outlet operate at high density at critical point ...... 18

Figure 5. Specific heat variation at different temperatures and pressures ...... 19

Figure 6. Density variation at different temperatures and pressures ...... 19

Figure 7. Heat exchangers location in the Cp-temperature diagram ...... 20

Figure 8. Sub-heat exchanger ...... 23

Figure 9. An explanation of heat exchanger nodalization ...... 23

Figure 10. Simple recuperated Brayton cycle efficiency at different maximum pressure and pressure ratio a) Dostal’s model b) predicted model ...... 30

Figure 11. Simple recuperated Brayton cycle efficiency at different maximum pressure and pressure ratio a) Bryant’s model b) predicted model ...... 30

Figure 12. Simple recuperated Brayton cycle ...... 36

Figure 13. Temperature - Entropy diagram of sCO2 simple recuperated Brayton cycle .. 37

Figure 14. Recompression Brayton cycle ...... 39

Figure 15. Temperature - Entropy diagram of sCO2 recompression Brayton cycle ...... 39

Figure 16. Pre-compression Brayton cycle ...... 41

Figure 17. Temperature - Entropy diagram of sCO2 pre-compression cycle ...... 42

Figure 18. Split expansion Brayton cycle ...... 44

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Figure 19. Temperature - Entropy diagram of sCO2 split expansion cycle ...... 44

Figure 20. Efficiency at different number of sub-heat exchangers ...... 46

Figure 21. The relationship between total conductance and efficiency (Pmax = 20 MPa) (simple recuperated cycle) ...... 48

Figure 22. The relationship between total conductance and efficiency (Pmax = 20 MPa) (pre-compression cycle) ...... 48

Figure 23. The influence of total conductance on the thermal efficiency ...... 49

Figure 24. Efficiency at different pressure ratio (simple recuperated cycle) ...... 51

Figure 25. Power output at different pressure (simple recuperated cycle) ...... 52

Figure 26. Efficiency at different pressure ratio (pre-compression cycle) ...... 53

Figure 27. Power output at different pressure ratio (pre-compression cycle) ...... 53

Figure 28. Efficiency at different pressure ratio (split expansion cycle) ...... 54

Figure 29. Power output at different pressure ratio (split expansion cycle) ...... 55

Figure 30. Efficiency at different pressure ratio (recompression cycle) ...... 56

Figure 31. Power output at different pressure ratio (recompression cycle) ...... 56

Figure 32. Efficiency compression of the four cycles at Pmax = 20 MPa...... 57

Figure 33. Power compression of the four cycles at Pmax = 20 MPa ...... 58

Figure 34. Efficiency at different TIT values for different UA values (pre-compression)60

Figure 35. Relates the efficiency of compression to different turbine inlet temperatures 61

Figure 36. Impact of compressor inlet temperature ...... 62

Figure 37. Transcritical CO2 simple bottom cycle T–S diagram ...... 66

Figure 38. Transcritical CO2 simple bottom cycle P–h diagram ...... 67

Figure 39. Recompression CO2 Brayton cycle with simple bottom Rankine cycle ...... 68

Figure 40. Recompression CO2 Brayton cycle with split flow bottom Rankine cycle ..... 69

Figure 41. Genetic algorithm flow chart ...... 70

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Figure 42. Thermal and exergy efficiency comparison as a function of maximum operating temperature for the simple and new combined cycles ...... 74

Figure 43. Power output comparison as a function of maximum operating temperature for the simple and new combined cycles ...... 74

Figure 44. Thermal efficiency improvement as a function of maximum operating temperature for the simple and new combined cycles ...... 76

Figure 45. Impact of compressor inlet temperature and turbine inlet temperature on the newly-conceived cycle efficiency ...... 77

Figure 46. Impact of compressor inlet temperature and turbine inlet temperature on the newly-conceived cycle power output...... 77

Figure 47. Exergy destructions rate and ratio in the sCO2 components ...... 78

Figure 48. Concentrated solar power tower system coupled with thermal energy storage ...... 84

Figure 49. Distance between heliostats ...... 88

Figure 50. Atmospheric attenuation losses at Daggett, USA [84], [85] ...... 89

Figure 51. Loss parameters in the heliostat field [22] ...... 90

Figure 52. Method for selecting direct normal irradiance ...... 91

Figure 53. Monthly solar irradiance in Riyadh, Saudi Arabia ...... 95

Figure 54. Levelized cost as a function of solar multiple and size of thermal energy storage ...... 96

Figure 55 Capacity factor as a function of solar multiple and size of thermal energy storage ...... 97

Figure 56. Heliostat-field layout with optical efficiency (colors)...... 98

Figure 57. Atmospheric attenuation efficiency of each heliostat ...... 99

Figure 58. Cosine efficiency of each heliostat ...... 100

Figure 59. Shading efficiency of each heliostat ...... 101

Figure 60. Blocking efficiency of each heliostat ...... 102

Figure 61. Intercept efficiency of each heliostat ...... 103

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Figure 62. Breakdowns of capital cost ...... 104

Figure 63. Breakdown of the solar power tower system cost for different thermal energy storage capacity ...... 106

Figure 64. Breakdown of the solar power tower system cost fraction for different thermal energy storage capacity...... 107

LIST OF TABLES

Table 1. Operating conditions of the validation studies ...... 29

Table 2. Variables lower and upper bounds...... 33

Table 3 Decision and design variables...... 35

Table 4. Literature input parameters and sCO2 cycle efficiency ...... 35

Table 5. Input and output data of a simple recuperated Brayton cycle...... 37

Table 6. Input and output data of a recompression Brayton cycle ...... 40

Table 7. Inputs and outputs data of a pre-compression Brayton cycle ...... 43

Table 8. Inputs and outputs data of a split expansion Brayton cycle ...... 45

Table 9. Summary of the effect of total conductance on the four cycles ...... 50

Table 10. Summary of the pressure effect on the four cycles ...... 59

Table 11. Optimum design points ...... 64

Table 12. Variables lower and upper bounds of the combined cycles ...... 71

Table 13. Literature input parameters and combined sCO2 cycle efficiency ...... 71

Table 14. Basic design and input parameters of the combined cycles ...... 72

Table 15. List of solar power tower projects ...... 85

Table 16. Meteorological data and basic design variables of the solar-tower field ...... 92

Table 17. Financing parameters and baseline component costs ...... 94

Table 18. Breakdown of yearly heliostat-field efficiency ...... 104

Table 19. Summary of the optimized model ...... 105

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Table 20. Economic and performance summary of different thermal energy storage (TES) options ...... 106

xvii

LIST OF ABBREVIATIONS AND NOTATIONS

sCO2 Supercritical Carbon Dioxide tCO2 Transcritical Carbon Dioxide

CSP Concentrated Solar Power

ST Solar Tower

TES Thermal Energy Storage

MSST Molten Salt Solar Tower

DNI Direct Normal Irradiance

DHI Diffuse Horizontal Irradiance

GHI Global Horizontal Irradiance

GHG Greenhouse Gas

ORC Organic Rankine Cycle

HTF Heat Transfer Fluid

PR Pressure Ratio

GT Gas Turbine

EES Engineering Equation Solver

SAM System Advisor Model

TRNSYS Transient Energy System Simulation Tool

UA Heat Exchanger Conductance

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Cp Specific Heat Capacity

HTR High Temperature Recuperator

LTR Low Temperature Recuperator

LMTD Log-Mean Temperature Difference

PCHE Printer Circuit Heat Exchangers

TIT Turbine Inlet Temperature

CIT Compressor Inlet Temperature

WHR Waste Heat Recovery

GA Genetic Algorithm

NREL National Renewable Energy Lab

CDF Cumulative Density Function

PDF Probability Density Function

LCOE Levelized Cost Of Energy

xix

CHAPTER I

INTRODUCTION

1.1 Background/Motivation

The unprecedented growth in the world population and economic activity, along with rising concerns about environmental issues, mean that energy efficiency plays a vital role in the development of future energy landscape. Conventional power plants, centered on a single prime mover, are highly inefficient (<39%), losing most of their energy as waste heat [1]. Motivated by limited energy resources, the accelerating growth of energy demand, cost, and growing environmental concerns, there has been a focus on improving such poor energy production efficiency. Currently, electric power is dominant: Half, if not more, of the projected growth in demand for energy into 2040 is anticipated to be in the form of electric power, and it has been the most rapidly increasing form of end-use energy in the world for several decades [2]. The world’s primary energy source, that supplies more than

80% of the demand is fossil fuels [3]. Burning fossil fuels is the main cause of human greenhouse emission. In 2013, total greenhouse gas emissions of CO2 reached 6,673 million metric tons (MMT), a 9% increase from 2005 [4]. A projection by the EIA (Energy

Information Administration) indicates that greenhouse gas emissions will increase another

2.7% from 2013 to 2040 [4].

In order to reduce emissions and the amount of waste in energy production, many researchers are examining ways to utilize waste heat with low-temperature cycles along with improving the system efficiency in order to increase overall power plant efficiency

[5]–[10].

The demand for renewable energy is also driving interest in high efficiency cycles, because these are necessary for achieving cost-parity between renewable and traditional energy production. Researchers developing solar driven heat engines are investigating

Carnot, Stirling, Ericsson, and Brayton cycles for this purpose [11]–[13]. For example, to increase the efficiency of the simple Brayton cycle, modifications including recuperator, isothermal heat addition, pre-compression, and reheat expansion have been studied [14]–

[16]. Researchers studying nuclear [16], [17], geothermal [18], and solar thermal [13], [19],

[20] energies are converging on the supercritical carbon dioxide (sCO2) Brayton cycle as superior for high-efficiency power production [21]. Among the variety of renewable power generation systems being examined, concentrated solar power (CSP) appears most promising and has costs which are projected to significantly decrease in the future [22].

1.1.1 History of sCO2 as a Working Fluid

As a working fluid, CO2 has the advantage of being nontoxic, abundant, low-cost, nonflammable, greenhouse gas (GHG) reduction, and thermal stablitly at temperatures of interest to CSP. At its critical point (T=31 °C, P=7.4 MPa), CO2 has a high density and is nearly incompressible, leading to considerable reduction in the compressor work, and therefore a higher thermal efficiency, for closed Brayton cycles relative to superheated or supercritical steam cycles [23]. Also, the low specific volume of CO2 near critical point

makes possible much smaller turbomachinery which, in turn, makes it more economic in both capital and life-cycle costs relative to other conventional cycles. In addition, for CO2 cycles that operate entirely above critical points, Blade erosion from droplet impingement becomes a nonissue with the use of carbon dioxide, as CO2 maintains its gaseous form throughout the supercritical Brayton cycle [24].

The use of CO2 as a working fluid for a partial condensation Brayton cycle dates to

1948 by Sulzer Bros [25]. Researchers understood the advantages of CO2, and further developments were made in several countries, including the Soviet Union [26], [27], Italy

[28]–[30], the United States [31], [32], and Switzerland [33]. In the late 1960’s, significant progress on the supercritical CO2 power cycle was made in the United States by Feher [31],

[32], and on the transcritical CO2 power cycle in Italy by Angelino [28]–[30]. Feher’s supercritical regenerative power cycle operated completely above the critical pressure of

CO2, where the pump was used for compression in the liquid phase. Feher explored several working fluids for operation in supercritical cycles. He focused on CO2 for his initial investigations because its lower critical pressure, allows lower operating pressures, and because its properties are well-studied. CO2 also has the advantages of being inert, stable, non-toxic, and abundant. Feher sought to improve upon conventional Rankine and Brayton cycles by developing a supercritical cycle using either steam or CO2 as a working fluid.

Rankine cycles have inconvenient restrictions on temperature and turbine exhaust conditions. Brayton cycles require significant compressive work and heat transfer area, and their performance is sensitive to pressure drops and compressor efficiency. Feher’s alternative supercritical cycle was partway between the Rankine and Brayton cycles, and addressed these problems.

Angelino first began working on condensation cycles [29], attempting to exceed the efficiency of the Rankine cycle (used with steam turbines) while maintaining the simplicity of the Brayton cycle (used with gas turbines). His first attempt was a simple transcritical condensing cycle, which had a large internal irreversibility in the recuperative heat exchanger (the pinch point problem). Later, Angelino [28] proposed four compound condensation cycles to correct this problem and improve cycle efficiency, each with their own advantages. The layouts for these four solutions are illustrated in Figure 1. He found that the CO2 cycle is better than the steam cycle with respect to efficiency and simplicity at high turbine inlet temperatures (650 °C – 800 °C), while it is inferior to the steam cycle at low temperatures (400 °C – 550 °C).

Figure 1. Angelino’s condensation cycles

Between the mid-1970s and late 1990s, the potential of these cycles has never been fully explored as achieving the high pressure and temperature required was prohibitively difficult. In 2004 [34], the dissertation of Vaclav Dostal sparked renewed interest in supercritical carbon dioxide power cycles. His doctoral work encompassed a slew of cycles, primarily focused on a simple recuperated sCO2 cycle with reheat and intercooling and a simple recompression sCO2 cycle. He delved into the effect of heat exchanger volumes and pressure drops in the simple and recompression cycles. Also Dostal researched application specifics as well as overarching factors such as control schemes the recompression cycle with nuclear reactors; a review of relevant economics; and the design of plants. A flow chart bellow summrizes the timeline of using CO2 as a working fluid in power cycles.

Figure 2. Timeline of using CO2 as a working fluid

1.2 Power Cycle

1.2.1 Supercritical CO2 Brayton Cycle

A full thermodynamic analysis of sCO2 cycles performed by several researchers in the early 2000’s [17], [19], [35]–[37], indicated that the sCO2 cycle can reach thermal efficiencies similar to those of helium Brayton cycles, which run at higher temperatures, thereby making it a comparatively better choice in an efficiency viewpoint, as shown in

Figure 3. At temperatures similar to CSP applications as well as coal-fired and nuclear ones, sCO2 Brayton cycle potentially offers greater efficiency than superheated or supercritical steam cycles. Additionally, systems based on the sCO2 Brayton cycle have reduced the power block weight, reduced thermal mass, and less complicated than those based on Rankine cycles [38]. These factors will most likely give the sCO2 Brayton cycle an advantage in terms of installation, maintenance, and operating costs. Working with CO2 in a simple regenerative Brayton cycle, Garg et al. compared supercritical, transcritical, and subcritical CO2 in terms of thermal efficiency, specific work output and entropy generation, and determined that supercritical CO2 is the most promising [13].

Of particular interest here, the use and performance of sCO2 in Brayton cycles were examined recently [13], [15], [23], [39], [40]. Al-Sulaiman and Atif [15] studied five sCO2

Brayton cycles (simple, regenerative, recompression, precompression, and split expansion) integrated with a solar power tower in Dhahran, Saudi Arabia. Maximum energetic efficiency was obrained with the recompression Brayton cycle at noon in the month of

June, with the integrated system thermal efficiency reaching 40%. The authors found similar performance for the regenerative cycle in spite of its configuration simplicity compared to the recompression cycle.

Figure 3. Four advanced cycle efficiency comparison [41]

Al-Sulaiman [42] reports a performance assessment of energy and exergy for a concentrated solar tower power and auxiliary boiler driven supercritical double- recompression carbon dioxide Brayton cycle. The focus was on the sizing of an auxiliary boiler for the system for the system run at three power output levels (41.5 MW, 60.0 MW, and 90.0 MW). The heat fractions from the solar field and auxiliary boiler are computed for each to maintain the turbine inlet temperature constant.

Sarkar and Bhattacharyya [16] used a supercritical CO2 recompression cycle with reheating to optimize the pressure ratio. The addition of a reheater and low pressure turbine served to increase efficiency by a peak of 3.5%. The authors provide a correlation for designers working with this type of cycle to determine optimal intermediate pressure.

In an effort to obtain the 50% efficiency goal set by the U.S. Department of

Energy’s Sunshot program for concentrated solar power, Turchi et al. [38] studied various configurations of supercritical CO2 Brayton cycles. The authors used results from nuclear power research to benchmark their models. They determined that intercooler added to the recompression configuration can hit the 50% target, even when dry-cooling is included in the configuration.

Garg, Kumar, and Srinivasan [13] compared the sCO2 power cycle performance versus subcritical and transcritical CO2 within a closed-loop Brayton cycle for CSP application. Among the configurations explored, sCO2 was shown to produce the highest efficiency (32%) with a source temperature of 873 °K and turbine exhaust pressure of 85 bar. The study demonstrated that sCO2 can operate with higher efficiency at lower source temperatures, with the trade-off that a high turbine inlet pressure (~300 bar) is required to achieve this. The authors also found much higher specific work output and lower total irreversibility for sCO2 than with subcritical or transcritical CO2.

1.2.2 Supercritical CO2 Combined Cycle

Researchers have experimentally and theoretically demonstrated that low temperature solar heat can power supercritical and transcritical CO2 Rankine cycles [10],

[43], [44]. Sarker [45] provides an organized review of sCO2 Rankine cycle configurations from the literature, focusing on low-grade heat supplies, and he provides a performance comparison with other working fluids. He finds that the sCO2 Rankine cycle has clear advantages to steam and organic Rankine cycles, and he discusses pathways to developing aspects of this cycle (parameter optimization, hardware components, control strategies, etc.).

Cheang, Hedderwick, and McGregor [46] compared three supercritical CO2 power cycle layouts to supercritical and superheated steam Rankine cycles, looking at cost and efficiency. For CSP applications, this study determined that the steam Rankine cycle is superior to the sCO2 cycles. Three reasons were identified for this conclusion: sCO2 turbomachinery requires gearboxes that reduce efficiency, the corrosiveness of CO2 requires expensive construction materials, and ambient temperatures that are far from the critical point for sCO2 tend to reduce net efficiency for this type of power cycle. It should be noted, however, that the authors of this study utilized a normalized cost measure to compare the cycles, whereas many other studies consider thermodynamic efficiency. In addition, the study considered molten salt as a sole medium that has been studied for thermal energy storage.

Dunham and Lipinski [7] performed a theoretical study of low power single and combined thermodynamic cycles appropriate for distributed concentrated solar power generation. A 150 kW nominal heat input was considered, as from a parabolic trough solar collector, along with parameters for a 50 kWe gas micro turbine. Many combinations of working fluids were compared for the single Brayton cycle and combined Brayton-Rankine cycles. CO2 led to the highest efficiency for a single Brayton cycle (15.31%), and the highest combined cycle efficiency (21.06%) was achieved with CO2 in the Brayton topping cycle and R-245fa in the Rankine bottoming cycle.

Some research has also been done on the Organic Rankine cycle (ORC) [47]. A bottoming cycle can be used to utilize waste heat from the topping cycle, usually using high-temperature gas turbines. Due to its simplicity, higher limited temperature, and higher efficiency, relative to conventional steam cycles, the ORC is frequently of interest as a

bottoming cycle [47]. The ORC has already been deployed for commercial applications as a way to recover energy from low grade heat (<350 °C) at temperatures below the gas turbine exhaust (>450 °C). Matching the ORC with a specific gas turbine is an essential technical problem for enhancing overall efficiency.

The use of sCO2 in a combined (Gas and ORC) cycle has been studied to evaluate and increase the potential of this configuration [5], [9], [43], [47]. Muñoz et al. [5] paired a topping gas turbine cycle with a bottoming ORC for low and medium temperature waste heat recovery as an alternative to more complicated steam cycles. Five commercial gas turbines were considered in this study, operating in load-following mode, and each was combined with an ORC bottoming cycle to improve overall efficiency during typical part- load conditions. The bottoming cycle was tested using various organic fluids and control strategies for maximizing heat recovery, and it was determined that maintaining constant live vapor conditions leads to the best power recovery for a range of operating conditions.

Akbari and Mahmoudi [8] modeled the exergoeconomic performance for a sCO2 recompression Brayton cycle whose waste heat is utilized by a bottoming ORC. Several working fluids for the ORC were compared, and the effects of system parameters on thermodynamic and economic performance were studied. Relative to the sCO2 recompression Brayton cycle alone, the combined cycle was shown to improve exergy efficiency by up to 11.7% and a lower total product unit cost when Isobutane was used as the ORC working fluid. However, using RC318 in the ORC served to optimize the economic performance for the combined cycle, leading to a 5.7% reduction in product unit cost.

Wang and Dai [10] compared the exergoeconomic performance for two bottoming cycles (transcritical CO2 and ORC) designed to optimize the waste heat recovery from a sCO2 recompression Brayton topping cycle. The parametric optimization analysis indicates that the tCO2 bottoming cycle has superior performance at lower PRc (off-design conditions), and that higher turbine inlet temperatures improve tCO2 exergoeconomic performance, unlike the ORC. Both combined cycles have similar second-law efficiency, and the ORC was shown to have a slightly lower total product unit cost.

Carcasci, Ferraro, and Miliotti [9] simulated an ORC for generating electrical energy from a gas turbine’s waste heat, and they compared its performance using four working fluids (toluene, benzene, cyclopentane, and cyclohexane). For plant safety, the authors utilized a diathermic oil circuit between the ORC and the gas turbine. Optimization of the ORC fluid pressure was conducted for different oil circuit temperatures, and a superheater for increasing electrical output is considered. The oil working temperature determined the choice of ORC fluid: cyclohexane was shown to be appropriate for low temperatures, benzene for intermediate temperatures, and toluene for high temperatures.

Sanchez et. al. [6] compared different organic fluids in a bottoming ORC for low- temperature heat recovery. Pure fluids were compared to mixtures of hydrocarbons, and a

7% improvement in global efficiency was found with the addition of a bottoming ORC, relative to a stand-alone CO2 cycle. The mixture composition was shown to affect performance.

Besarati and Goswami (2014) [48] studied the possibility of increasing the efficiency of the sCO2 Brayton cycle for CSP power generation by adding a bottoming

ORC Rankine cycle to the system. They performed a thermodynamic simulation for three

sCO2 configurations. The author found that recompression and partial cooling cycles are the most promising topping sCO2 configurations for CSP applications. For the combined cycle, the highest overall thermal efficiency was found with the recompression sCO2/ORC combined cycle.

The transcritical CO2 cycle has also been used and evaluated as a bottom cycle

[48]–[52]. Yari and Sirousazar [40] developed a tCO2 cycle for recovering waste heat from a topping sCO2 Brayton cycle, and they modeled the performance improvement for this new combined cycle relative to that of a simple sCO2 cycle. Optimization was performed with Engineering Equation Solver (EES) [50], and the comparison was made under identical operating conditions. The authors reported that their new system improved the first and second law efficiencies by 5.5%, to 26%, and that it reduced exergy destruction by 6.7%, to 28.8%.

Cao et al. [44] developed new optimization techniques, based on the genetic algorithm for thermodynamic cycles, and they applied these techniques to a system that coupled a sCO2 and tCO2 combined cycle with a gas turbine (GT). Simulations revealed that their new cascaded system had superior performance to a conventional GT with steam

Rankine combined cycle and a much higher performance (17.03%) than a GT alone.

Chen et. al. [43] compared the performance of two cycles act as a bottoming cycle to extract useful work from low-grade waste heat. The ORC is most commonly used, but the authors found that the tCO2 power cycle showed better performance. Specifically, this cycle had a slightly higher power output than ORC, and it did not have a pinch limitation in the heat exchanger.

Chacartegui et al. [49] examined the application of novel supercritical and transcritical CO2 power cycles for CSP generation, including two stand-alone closed cycle gas turbines using CO2 and a third cycle that combined a CO2 gas turbine topping cycle with a bottoming ORC. These were shown to compare favorably with currently used CSP power cycles. For example, the work showed a 7-12% efficiency improvement for the simple sCO2 system, depending on turbine inlet temperature.

Wang et. al. [51] explored the feasibility of a simple and a recompression sCO2 configurations as topping cycles, combined with a bottoming tCO2 cycle for CSP generation. The behavior of the combined cycle was examined as a function of several thermodynamic parameters, and an efficiency optimization was performed. The authors found an efficiency increased by 10.12% and 19.34% for the simple sCO2/tCO2 and a recompression sCO2/tCO2, respectively.

1.3 Concentrated Solar Tower

One method for collecting solar power involves a tower surrounded by an array of mirrors (heliostats) on the ground that reflect the sunlight onto a large heat exchanger

(called: receiver) at the top of the tower. With two-axis computer controlled motion, the mirrors track the sun throughout the day. The concentrated solar energy heats a working fluid that, most recently, includes molten salts with high heat capacity that can store energy after the sun goes down. This hot working fluid (at temperatures around 565 °C) drives a thermal engine cycle to produce electric power.

To pass solar energy from the receiver to the power block in the CSP plant, heat transfer fluids (HTF), including synthetic oil or nitrate salts, are often used. However, these fluids limit plant performance due to upper temperature limits (400 °C for oil, 565 °C for

salts). Generally, higher operating temperatures improve thermal-electrical system efficiency. Some plants use direct steam generation, but this choice of fluid requires complicated controls, and it cannot store significant thermal energy. As both a working fluid and a HTF in a CSP plant, sCO2 allows for higher operating temperatures while providing greater thermal efficiency compared to a helium Brayton cycle at lower temperatures. This feature makes sCO2 attractive over a wide range of temperatures and powers.

Atif and Al-Sulaiman [52] developed optimization software for a heliostat field, for the purpose of minimizing annual losses caused by the collection of solar energy for a central tower. The evolutionary algorithm determines best field layout on an annual basis, optimizing either the weighted or un-weighted insolation efficiency. They determined a daily averaged annual efficiency for the heliostat field to be 0.5634.

Atif and Al-Sulaiman [53] created a complete model of a concentrating solar power plant consisting of a central tower and field of heliostats and tested its performance for six cities in Saudi Arabia. A sCO2 recompression Brayton cycle was used, and an auxiliary heat exchanger maintained constant turbine inlet temperature and a constant 40 MW plant output. Energy and exergy analyses for the full system, including the auxiliary combustion chamber.

Iverson et al. [21] examined the effect of a fluctuating solar energy input, as caused by intermittent cloud cover, on a sCO2 Brayton cycle. The authors used a laboratory-scale demonstration turbine as well as a benchmarked model. They determined that thermal mass in the system can overcome short-duration interruptions of input power. These results suggest that it is worthwhile to continue development of sCO2 Brayton cycles for solar

power generation, and that many of the remaining issues can be solved by moving to large- scale commercial systems.

1.4 Research Gaps

Firstly, according to the literature, most research in supercritical CO2 cycles used two ways to represent heat exchanger performance: using fixed heat exchanger effectiveness or pinch point temperature differences. However, due to sCO2 properties, assuming a constant recuperator effectiveness - minimum-temperature approach leads to markedly different conductance values in heat exchanger size and consequently cost. Thus this study seeks to develop a computationally efficient technique to design heat exchangers by using constant conductance (UA) to represent heat exchanger performance and thereby deliver improved accuracy in calculations.

Secondly, a newly-conceived combined power cycle is proposed in this study and it is generalized to be a novelty.

Thirdly, integrating power cycles with a CSP system has been studied recently in many papers; however, most of the studies assume a power cycle heat input that is similar to those of the CSP plants without modeling the CSP. In this research, the development of a comprehensive model and including the optimization of the dynamic behaviors of CSPs including the heliostat field will be pursued.

1.5 Dissertation Organization

After a brief background, motivation, and holistic view of prior studies of supercritical CO2 cycles that was presented, Chapter 2 presents the goals and methodologies that are employed to develop the off-design computational models that

calculate the performance of the entire system: the turbomachinery components, heat exchangers, exergy analysis, and the validation model.

Chapter 3 A compression of four supercritical CO2 Brayton cycles is presented for the purpose of choosing the suitable cycle for further analysis. A compression is made between the cycles for their efficiency, power output, and operating condition in order to couple the suitable cycle with the concentrated solar power. The results of the analysis will be classified and summarized in order to identify the optimum design points.

Chapter 4 presents an energy and exergy analysis and optimization of a newly- conceived combined power cycle in order to improve overall thermal efficiency of power cycles by attempting to minimize thermodynamic irreversibilities and waste heat as a consequence of the Second Law.

Chapter 5 describes the design of the concentrated solar power (CSP) system in detail. It also presents the computational model of the CSP dynamic behavior and TRNSYS simulations.

Chapter 6 presents the general conclusions; summarizes the most significant outcomes of the study; and discusses a future research and recommendations.

CHAPTER II

METHODOLOGY OF POWER CYCLES

2.1 Research Objectives

The main three goals of this dissertation are to improve the accuracy of sCO2 analysis by creating an efficient computational model, to enhance the performance of sCO2, and to viable with concentrated solar power in order to make it economically promising and versatile. The objectives that support the attainment of these goals are as follows:

1) Propose a new thermodynamic cycle configuration.

2) Develop a comprehensive thermodynamic model with which to study the feasibility

of sCO2 power cycles and to identify the optimum cycle and operating conditions.

3) Test the model comprehensively for supercritical carbon dioxide cycles and

examine the results against published data.

4) Develop a computationally efficient technique using constant conductance (UA) to

represent heat exchanger performance in order to improve calculation accuracy.

5) Develop a comprehensive model and optimize the dynamic behaviors of CSPs,

including the heliostat field. The integration of power cycles with a CSP system has

been studied recently by many researchers. However most of the studies assume

power cycle heat inputs that are similar to those of the CSP plants without modeling

the CSP.

2.2 Problem Definition

2.2.1 The Properties of Supercritical CO2

Under supercritical conditions, CO2 deviates from the ideal behavior of the gas and becomes an indistinct state between gas and liquid due to the fact that the critical point is

(T=31 °C & P=7.4 MPa). Figure 5 illustrates the instability of carbon dioxide’s specific heat (the amount of required thermal energy to increase the temperature of a system by 1

°C per unit of mass) near the critical point, presenting a variety of temperatures and pressures. Despite the advantages of reducing the compressor work due to high density near critical points, as is shown in Figure 4. Figure 6 show the thermodynamic characteristics fluctuate wildly, thereby influencing the CO2 properties.

Figure 4. Compressor inlet and outlet operate at high density at critical point

Figure 5. Specific heat variation at different temperatures and pressures

1200

P = 7.4 MPa P = 6.5 MPa 1000 P = 15 MPa P = 20 MPa P = 25 MPa

] P = 30 MPa 3 800

[

t 600

D 400

200

0 0 100 200 300 400 Temperature (°C)

Figure 6. Density variation at different temperatures and pressures

The sharp alteration in pressure and temperature near critical point makes specific heat capacity (Cp) an impractical measure. As fluid properties fluctuate near the critical

point, design difficulties with turbomachinery and heat exchangers arise [34]. The high variation in the specific heat and abrupt change in density near the critical point are particularly harmful to heat exchangers operating near the critical point, causing an internal pinch point, as is illustrated in Figure 7.

20 Precooler P = 7.4 MPa 18 P = 25 MPa

12 LTR

6 HTR Primary Heater Specific Heat (kJ/kg-°K) 4

0 -50 0 50 100 150 200 250 300 350 400 450 500 550 600 Temperature (°C)

Figure 7. Heat exchangers location in the Cp-temperature diagram

So, following the conventional method that assume a constant capacity to deal with a heat exchanger whose properties change arbitrarily near the critical point is invalid [54]. An adjustment needs to be made in order to reuse the convectional equations, which are described in detail in the heat exchanger model in the next section.

As it is shown in Figure 7, the primary heater is not a big issue with the working fluid since the heat capacity is almost the same, but it begins to be inconstant in the high temperature recuperator (HTR) and it gets worse in the low temperature recuperator (LTR) and precooler heat exchanger. In the HTR, LTR and the precooler heat exchangers the modeling needs to be designed carefully.

2.3 Turbomachinery Modelling

Turbomachinery analysis is modeled on the energy balance (energy conservation) of each components to study the performance of turbines, compressors, and the pump. In this research, the focus is on the off-design performance of the turbomachinery components. For turbomachinery modeling, some basic assumptions are considered: (i) the cycle functions in a steady state; (ii) the turbine expansion, compressors, and pump are adiabatic with given isentropic efficiencies; (iii) the effect of kinetic and potential energy are negligible; (iv) each component of the cycle is sufficiently insulated. The compressors

(휂푐) and turbine (휂푡) isentropic efficiencies are defined as

ℎ표푢푡 − ℎ푖푛 (1) 휂푐 = ℎ표푢푡𝑖푠푒 − ℎ푖푛

ℎ푖푛 − ℎ표푢푡 (2) 휂푡 = ℎ푖푛 − ℎ표푢푡𝑖푠푒

where ℎ푖푛 and ℎ표푢푡 are the actual inlet and outlet enthalpies, respectively, and ℎ표푢푡𝑖푠푒 is the isentropic outlet enthalpy. To calculate pressures at all states, a pressure ratio equation is employed for all cycles.

푃ℎ푖푔ℎ (3) 푃푅 = 푃푙표푤

Two properties at any state are sufficient to calculate the others properties in the same state. The inlet turbine and compressor temperature and pressure are assumed, while taking into consideration the pressure drop in the cycle. With known two-inlet turbomachinery properties and one-outlet turbomachinery properties, the model obtains the turbomachinery outlet properties using equations (4) and (5):

(4) 푠푖푛 = 푠표푢푡𝑖푠푒

(5) ℎ표푢푡𝑖푠푒 = 푓 (푃표푢푡 , 푠표푢푡𝑖푠푒)

Where 푠푖푛 and 푠표푢푡𝑖푠푒 are the inlet actual specific entropy and outlet isotropic specific entropy respectively. After specific isentropic outlet enthalpy is calculated in equation (5), the actual enthalpy can be obtained using the isentropic turbomachinery efficiencies.

Finally, after determining the actual inlet and outlet properties, the specific actual work is calculated as

푤 = ℎ푖푛 − ℎ표푢푡 (6)

2.4 Heat Exchangers Modelling

Conventional techniques for analyzing heat exchangers (log-mean temperature difference (LMTD) and effectiveness-number of transfer units (NTU)) rely on assumptions to set up the equations, such as constant specific heat capacity. Therefore, these techniques are not valid for recuperators operating under inconstant capacitances, such as CO2 near its critical point. To overcome this impediment, two approaches will be explored: either develop a complicated numerical model or divide the heat exchanger into numerous sub heat exchangers (an approach known as Nodalization).

The appropriate design of heat exchangers is extremely important because they are the largest part in the cycle. In the analysis of heat exchangers, compact heat exchangers are necessary as they reduce the total volume of the heat exchanger. Thus, counter-flow printer circuit heat exchangers (PCHEs) will be considered for all heat exchangers as they are considered the ideal equipment for sCO2 applications [34], [55]. Dry cooled heat exchangers will be selected for the coolers and heater.

In the model presented below, the printed-circuit heat exchangers (PCHEs) are divided into sub-heat exchangers (nodalization) as shown in Figure 8. Nodalization is a heat exchanger modeling strategy that is necessary when a CO2 working fluid is used due to its significant properties change at or near the critical point. Each sub-heat exchanger is then modeled independently (each component is evaluated as a separate control volume).

At each sub-heat exchanger, the capacitance is almost the same and therefore the conventional techniques (LMTD and effectiveness-NTU) can be used after the adjusting of heat exchanger as shown in Figure 9 compared to Figure 7.

Figure 8. Sub-heat exchanger

Figure 9. An explanation of heat exchanger nodalization

The small orange rectangle in Figure 9 represents a sub-heat exchanger in the low temperature recuperator. With enough numbers of sub-heat exchangers, the model accurately characterizes the significant properties’ changing through the heat exchanger and therefore improves the accuracy of the model. The number of nodes has to be chosen correctly because too many nodes will yield a long computation time, while too few nodes will reduce the accuracy of capturing the effect of a changing property. For the simple recuperated Brayton cycle validation model, 10 nodes were seen to be adequate enough for all heat exchangers to increase the model accuracy. In the comprehensive model described in chapter 3, the number of sub-heat exchangers are optimized for each heat exchanger.

In further work analysis, the effectiveness-NTU is chosen over LMTD to evaluate the heat exchangers performances as they are algebraically equivalent and effectiveness-

NTU seems more suitable in the model design. The counter-flow effectiveness and number of transfer units (NTU) are given by equations (7) and (8), respectively.

1 − exp[−푁푇푈 ∗ (1 − 퐶 )] (7) 휀 = 푅 1 − CR ∗ exp[−푁푇푈 ∗ (1 − 퐶푅)]

1 − 퐶 ln[ 푅] (8) 푁푇푈 = 1 − 휀 1 − 퐶푅 where CR is the dimensionless capacity ratio describing the heat exchanger balanced. It is defined as:

퐶푚푖푛 (9) 퐶푅 = 퐶푚푎푥

With the nodalization method, the total heat transfer rate is calculated first using either equations (10) or (11) based on energy balance, and is then divided equally between the sub-heat exchangers using equation (13).

̇ (10) 푞퐻̇ = 퐶퐻 ∗ (푇ℎ𝑖푛 − 푇ℎ표푢푡) = 푚̇ 퐻 ∗ (ℎℎ𝑖푛 − ℎℎ표푢푡 )

̇ (11) 푞퐶̇ = 퐶퐶 ∗ (푇퐶𝑖푛 − 푇퐶표푢푡) = 푚̇ 퐶 ∗ (ℎ퐶𝑖푛 − ℎ퐶표푢푡)

푞퐻̇ = 푞퐶̇ (12)

푞̇ (13) 푞 = 푡표푡푎푙 푖 푁 where 퐶퐻̇ , 퐶퐶̇ and 푚̇ 퐻, 푚̇ 퐶 are the capacitance rates and mass flow rates of the hot and cold

streams, respectively, 푇ℎ𝑖푛, 푇퐶𝑖푛 and ℎℎ𝑖푛, ℎ퐶𝑖푛 are the inlet temperatures and enthalpies of

the hot and cold streams, respectively, 푇퐻표푢푡 , 푇퐶표푢푡 and ℎℎ표푢푡 , ℎ퐶표푢푡 are the out temperatures and enthalpies of the hot and cold streams, respectively, and N is the number of sub-heat exchangers.

Then enthalpies for each sub-heat exchangers is calculated using equation (14) and (15)

푞̇푖 (14) ℎℎ표푢푡 = ℎℎ𝑖푛 − 푚̇ 퐻

푞̇푖 (15) ℎ푐표푢푡 = ℎ푐𝑖푛 − 푚̇ 퐶 where 푞̇ is the heat transfer rate of the sub-heat exchanger.

The average specific heat 퐶푝 and heat capacity rate (Ċ) of each sideof the sub-heat exchanger are calculated as follows:

(16) (ℎℎ𝑖푛 − ℎℎ표푢푡) 퐶푃ℎ = (푇ℎ𝑖푛 − 푇ℎ표푢푡)

(17) (ℎ퐶표푢푡 − ℎ퐶𝑖푛) 퐶푃퐶 = (푇퐶표푢푡 − 푇퐶𝑖푛)

(18) 퐶ℎ = 푚̇ 퐻 ∗ 퐶푃ℎ

(19) 퐶푐 = 푚̇ 푐 ∗ 퐶푃푐

To calculate the performance of a sub-heat exchanger, the dimensionless effectiveness (휀) is defined as:

푞̇ 푞̇ (20) 휀 = 푖 = 푖 푞̇ 푖푚푎푥 퐶푚푖푛 ∗ (푇ℎ𝑖푛 − 푇푐표푢푡 ) where 푞푖̇ 푚푎푥 is the maximum possible heat transfer rate through the sub-heat exchanger, and 퐶푚푖푛 is minimum capacitance of either hot or cold side and defined as:

퐶푚푖푛 = min (퐶ℎ, 퐶퐶) (21)

Three methods exist for modeling the heat exchangers when nodalization techniques apply: calculating necessary conductance (UA) from a specified fixed effectiveness; calculating effectiveness with a specified UA value; or choosing two inlet temperatures and one outlet temperature [39]. Most of the researchers in the literature defined the heat exchanger performance by using either an effectiveness approach, how well a recuperator is capable to transfer heat, and a pinch point approach, specifying a temperature differences between two stream sides. However, assuming a constant recuperator effectiveness – the minimum-temperature approach is not only computationally difficult, but also it may lead to markedly different conductance values in the heat exchanger size and consequently cost values too. This can result in conclusions which are deceiving regarding the relative economic benefit of these cycles [24].

In the case of CO2 as working fluid, with properties variations in the vicinity of the critical point, and for more accurate compression calculation, using a UA method is believed to be a better measure of recuperator performance. The constant conductance approach, as opposed to the constant effectiveness approach is preferred since it not only characterizes cycle performance but also has a more direct relation to the size and therefore to the cost. During the detailed models of Brayton configurations, a counter-flow configuration having constant conductance (UA) will be used.

Finally, calculating the conductance for each sub-heat exchanger as it shown in equation (22):

푈퐴푖 = 퐶푚푖푛 ∗ 푁푇푈푖 (22) where NTU is the dimensionless number of transfer units that defined in equation (8).

2.5 Exergy Modelling

Exergy is the highest possible useful work that can be extracted from reversible system processes. Exergy analysis is essential as it provides a detailed thermodynamics analysis in each of the cycles’ components. In order to evaluate each cycles’ components, a comprehensive exergy model is conducted to locate the critical component that causes thermodynamics losses due to irreversible processes.

The total exergy rate of the system is the total physical exergy rate, and chemical exergy rate:

Etotal = 퐸푝ℎ푦 + 퐸푐ℎ (23)

Where 퐸푝ℎ푦, by definition, the exergy of each state point is defined as:

퐸푝ℎ푦 = 푚̇ ∗ [(ℎ − ℎ0) − 푇0 ∗ (푠 − 푠0)] (24)

Where 푚̇ is the mass flow of the stream, h and s are the enthalpy and s entropy, and ℎ0 and

푠0 are the enthalpy and s entropy at the dead state. The kinetic and potential exergies rates are neglected in this work.

The chemical exergy rate is defined as: (25) 퐸푐ℎ = 푛̇ ∗ [∑ 푋푘 ∗ 푒푘̅ + 푅̅푇 ∑ 푋푘 퐿푛 푥푘] 푘 푘

The exergy transfer associated with heat transfer can be expressed as:

2 푇0 (26) 퐸퐻푇 = ∫ (1 − ) 훿푄 1 푇푗

Where 푇푗 represent the temperature on the boundary

The exergy transfer associated with work can be expressed as:

퐸푊 = [푊 − 푃0(푉2 − 푉1)] (27)

The maximum possible exergy of the heat transfer rate (exergy input) associated with the rate of heat transfer (푄̇푗) across the boundary of 푇푗 is defined as: 푇0 (28) 퐸푗̇ = 푄̇푗 ∗ (1 − ) 푇푗

The total irreversibility of the system (destruction of exergy) can be defined as:

푇0 (29) 퐸퐷 = ∑ 푄푗 ∗ (1 − ) − 푊푐푣 + ∑ 퐸푥 − ∑ 퐸푥 = 푇0 ∗ 𝜎 푇푗 푖푛 푖푛 표푢푡

The overall exergy efficiency is expressed as:

푊푛푒푡 ∑(퐸푙표푠푠,푐표푚푝 + 퐸푑,푐표푚푝) (30) 휂푒푥푔 = = 1 − 퐸푗 퐸푗

2.6 Power Block Model Validation

As no experimental data are currently available for validating the model, the basic

Brayton cycle model proposed in this chapter is validated against two independent numerical studies of Dostal et. al. [56] and Bryant et. al. [57] and shows a good agreement.

The main objective of modeling a simple Brayton cycle is to validate it with a reliable available study to give sufficient confidences in the results of advanced configurations that cannot be validated analytically. Table 1 presents the operating condition used for the validation of the simple recuperated Brayton cycle using a heat exchanger effectiveness approach that assumed by Dostal et. al. and Bryan et. al.

Table 1. Operating conditions of the validation studies

Simple Recuperated Brayton Cycle Dostal et. al. [56] Bryant et. al. [57] Compressor inlet temperature [°C] 32 32 Compressor inlet pressure [MPa] 7.4 Vary Maximum pressure [MPa] 10 - 25 MPa 10 - 25 MPa Pressure ratio Vary Vary Turbine inlet temperature [°C] 550 550 Turbine efficiency [-] 90% 90% Compressor efficiency [-] 89% 89% Recuperator effectiveness [-] 95% 95% Pressure drop [-] Neglected Neglected

The turbine inlet pressure and pressure ratio was varied from 10 MPa to 25 MPa, from 2 to 4 with a 0.05 increment respectively. Then the thermal efficiency is calculated at different maximum pressures and pressure ratios. The results obtained by the preliminary predicated validation model is presented in Figure 10 and Figure 11 against the result of

Dostal and Bryant models.

0.5 Predicted model Dostal model 0.48 Pmax = 10 MPa Pmax = 10 MPa

]

[ P = 15 MPa Pmax = 15 MPa

max

y 0.46

c Pmax = 20 MPa Pmax = 20 MPa

e i 0.44 P = 25 MPa Pmax = 25 MPa c max

0.42

m r 0.4

T 0.38

0.36 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8 4

Pressure Ratio [-]

Figure 10. Simple recuperated Brayton cycle efficiency at different maximum pressure and pressure ratio a) Dostal’s model b) predicted model

0.48 Pridected model Bryant Model

Pmax = 10 MPa Pmax = 10 MPa

Pmax = 12.5 MPa Pmax = 12.5 MPa

] 0.44 Pmax = 15 MPa Pmax = 15 MPa

[

Pmax = 17.5 MPa Pmax = 17.5 MPa y P = 20 MPa c Pmax = 20 MPa max n Pmax = 22.5 MPa Pmax = 22.5 MPa

i Pmax = 25 MPa Pmax = 25 MPa f 0.4

h 0.36

0.32 2 4 6 8 10 12 Compressor Inlet Pressure (MPa) Figure 11. Simple recuperated Brayton cycle efficiency at different maximum pressure and pressure ratio a) Bryant’s model b) predicted model

The result comparison in Figure 10 and Figure 11 shows a perfect consistency between the models. A detailed study of the simple recuperated Brayton is covered in chapter 3. The comprehensive model optimizes the number of sub heat exchangers for each heat exchanger in the cycle, using different approaches to define the heat exchanger performance and size. The model appears to be more accurate than the approach used by the literature, and better at identifying the optimum operating conditions.

CHAPTER III

PERFORMANCE COMPARISON AND PARAMETRIC ANALYSIS OF S-CO2

POWER CYCLES CONFIGURATIONS

In this chapter, four supercritical CO2 Brayton cycles will be subjected to thermodynamic analysis and optimization in order to improve calculation accuracy; the feasibility of the cycles; and compare the cycles’ design points. In particular, the overall thermal efficiency and the power output are the main targets in the optimization study.

With respect to improving the accuracy of the analytical model, a computationally efficient technique using constant conductance (UA) to represent heat exchanger performances is executed. In order to determine the most suitable cycle for further analysis, a comparative analysis that seeks optimum operating conditions of four cycles will be performed. The cycles so involved will be 1) the simple recaptured Brayton cycle; 2) recompression

Brayton cycle; 3) pre-compression Brayton cycle; 4) and split expansion Brayton cycle was all performed under different conditions. The most suitable cycle will be used in a detailed thermodynamic model creating a newly-conceived combined power cycle in

Chapter 4, and integrated with concentrated solar power in Chapter 5.

Measurement of the working fluid properties is the initial step in the thermodynamic modeling of sCO2 cycles. To calculate the CO2 thermodynamics and transport properties,

REFPROP database (version 9), developed by The National Institute of Standards and

Technology (NIST), is used through a built-in library in Engineering Equation Solver

(EES). The REFPROP program provides accurate thermophysical properties of CO2 as well as other properties of CO2, and other fluids by using the most accurate equations and coefficients to calculate the state point of a fluid [34], [58].

3.1 Optimization Domain

For an appropriate optimization, the variables bounds have to be predetermined to govern the optimization process and provide more reliable solutions. Based on the literature review at

Table 4, the upper and lower bounds are specified. The lower and upper bounds set at the acceptable values to allow the model to test as mush variables as it could be. The optimization domain of the lower and upper variables is shown is the Table 2

Table 2. Variables lower and upper bounds

Lower Bound ≤ Variables ≤ Upper Bound 15 Maximum pressure [MPa] 25 1 Pressure ratio 6 10 Total conductance [kW/°K] 17 500 Turbine Inlet Temperature [K] 900 280 Compressor Inlet Temperature [°K] 350 350 Recompressor Inlet Temperature [°K] 700 500 Reheat turbine Inlet Temperature [°K] 900 12 Reheat turbine Inlet Pressure [MPa] 25 1 Total mass flow rate [kg/s] 100 0 Split ratio [-] 1 0 Temperature factor [-] 1 0 Ratio of the pressure ratio [-] 1 0 Recompression fraction [-] 1

3.2 Power System Description

As noted above, several cycle configurations will be thermodynamically modeled and optimized for thermal efficiency and power output using Engineering Equation Solver

Software (EES). Variables not to be considered in this Chapter include cost, weight, volume, reduced thermal mass and power block complications. Ultimately the goal is to optimize the energy efficiency of a power plant in order to couple the most suitable cycle with a CPS. In this Chapter, four model will be considered: 1) the simple recuperated

Brayton cycle; 2) a recompression Brayton cycle; 3) a pre-compression Brayton cycle; 4) and a split expansion Brayton cycle to identify each configuration features. The detailed analysis and multi-objective optimization of the design point model are presented in chapter 4 for the most suitable cycle.

The input variables are divided into two categories, decision variables and design variables. The main difference is that the decision variables are assumed to be constant for all runs, while the design variables are the optimizer which is varied for each run. The initial parameter assumptions of the heat exchangers and turbomachinery are presented in

Table 3. These are chosen based on several studies in the literature Table 4.

Table 3 Decision and design variables

Input Pre- Split Recompression Decision variables Simple compression expansion compressor inlet temperature (°C) 32 32 32 32 Turbine inlet temperature (°C) 600 600 600 600 Turbine Isentropic efficiency [%] 93% 93% 93% 93% Compressor Isentropic efficiency [%] 89% 89% 89% 89% Inlet cooling air temperature [°C] 22 22 22 22 Inlet heating air temperature [°C] 900 900 900 900 Recompressor efficiency [-] - - 89% 89% Design variables Main compressor inlet pressure vary vary vary vary Mass Flow rate vary vary vary vary Pressure Ratio vary vary vary vary Total fixed UA vary vary vary vary Recompression fraction [-] - - vary vary Pressure Ratio for second turbine - - vary - split expansion pressure factor - - vary - ratio of pressure ratios - vary - - Temperature factor - vary - -

Table 4. Literature input parameters and sCO2 cycle efficiency

- Dostal - Dostal CoRERE NREL Sarkar Pichel MIT [59] [60] [15] [38] IIT [16] [61] Compressor inlet 31 32 31.09 45-60 32 30 temperature [°C] Compressor inlet pressure 7.4 7.35 7.4 9.25 - 8.0 7.4 [MPa] 10 Maximum pressure [MPa] 20 25 19.98 25 20 25 Turbine inlet temperature 550 500-850 826.85 700 550 500 [°C] HTR effectiveness [-] 98.0% 95.0% 85% 97% 86.0% 95% LTR effectiveness [-] 92.0% 95.0% 70% 88% 86.0% 95% Turbine efficiency [-] 87% * 93.0% 90% 93.0% 90.0% 93% Compressor efficiency [-] 85% * 89.0% 80% 89.0% 85.0% 89% Pressure drop [-] 1% 0% 0.0% 0.0% 0.0% 50 kPA/HX Cycle efficiency [%] 0.43 0.40- 0.52 0.52- 0.4118 0.435 0.55 0.497

3.2.1 The sCO2 Simple Recuperated Brayton Cycle Configurations

The simple recuperative sCO2 Brayton cycle as it illustrated in Figure 12 is the typical power cycle that other advanced cycles are derived from. The simple recuperative cycle consists of a turbine, a compressor, a recuperator, a cooler, and a heater. In this configuration, CO2 is compressed at or near the critical point in the compressor (state 1 – state 2). Then, the compressed CO2 is preheated in the recuperator (state 2 – state 3) by extracting energy from the turbine’s exiting hot stream (state 5) that enters the recuperator as a hot stream (state5). The compressed preheated CO2 passes through the primary heater

(state 3 – state 4), where the heated CO2 reaches the target turbine inlet temperature at constant pressure. Then the maximum cycle CO2 temperature and pressure (state 4 – state

5) expands to the lower pressure based on the given pressure ratio in the turbine (state 5) while generating power at the generator. Next the hot CO2 stream (state 6) is cooled in the cooler prior to entering the compressor at the compressor inlet temperature. The (T-s) diagram of the simple recuperated Brayton cycle is illustrated in Figure 13. The input output data of the (of the aforementioned) simple recuperated Baryon cycle are presented in the Table 5 below:

Figure 12. Simple recuperated Brayton cycle

900 4

Compressor process 800 recuperatore process Heating in the primary heater Turbine Process 5 700 3

]

[ 600

T 20 MPa

500 7.4 MPa

400 2 6 300 1 -1200 -900 -600 -300 0 s [J/kg-°K]

Figure 13. Temperature - Entropy diagram of sCO2 simple recuperated Brayton cycle

Table 5. Input and output data of a simple recuperated Brayton cycle

Input Outputs Decision Variables Air Mass Flow rate Cycle thermal efficiency [%] CO2 Mass Flow rate Power Output [MW] Turbine Isentropic efficiency Cycle temperature and pressure Compressor Isentropic efficiency Heat Exchangers Area [m2] Generator efficiency Inlet cooling air temperature Inlet heating air temperature Design Variables Turbine inlet temperature Pressure Ratio Total fixed UA Main compressor inlet temperature Main compressor inlet pressure

3.2.2 The sCO2 Recompression Brayton Cycle Configurations

The simple recuperative sCO2 Brayton cycle has been found to have a large internal irreversibility in the single recuperative heat exchanger (the pinch-point problem) due to a drastic change in the heat capacity at or near the critical point of CO2 [62]. The existence of pinch point is the main disadvantage of sCO2 cycles, which affecting heat exchanger design; reduces heat exchanger efficiency; and possibly increase heat exchanger size. The pinch point problem manifests with sCO2 as a cycle medium more than with any other such medium due to its properties that significantly changing near critical point. The main cause of the pinch point problem in the simple recuperative sCO2 Brayton cycle is the mismatch

(large difference) in the specific heat capacities between the cold and hot streams at different pressures resulting in poor recuperator effectiveness and lower cycle efficiency

[63]. This problem can be overcome by using a small amount of an admixture between pure CO2 and another substance, such as Argon, Nitrogen or Helium [64]. Also, another way to lessen the pinch point problem, used in this research, is to make a change in the cycle design or use different mass flows on either side of the exchangers. Thus, a recompression Brayton cycle is proposed that is designed with two recuperators and two compressors as shown in Figure 14. In recompression cycles, the single recuperator is divided into two recuperators, a low temperature recuperator (LTR) and a high temperature recuperator (HTR). The flow leaving LTR (state 10) splits into two streams. The first stream is directed to the primary compressor through the precooler. The second stream is diverted to the recompressing compressor and exits on the high pressure side between the two recuperators (state 4). This configuration reduces the capacitance rate of the high pressure side in LTR by varying the mass flow rate through the cold side and thereby

moderates the pinch point. The (T-s) diagram of the recompression Brayton cycle is illustrated in Figure 15.

Figure 14. Recompression Brayton cycle

800 4 Compressor process LTR Process 700 HTR process Heating in the primary heater

]

K Turbine Process

[ 600 e 5

a 3

e 6 p 500

400 2 7

300 1 -1200 -1000 -800 -600 -400 -200 0

Entropy [J/kg-°K]

Figure 15. Temperature - Entropy diagram of sCO2 recompression Brayton cycle

The inputs and outputs of the aforementioned system are presented in Table 6. The sCO2 recompression Brayton power cycle and its models are then discussed in detail in

Chapter 4, with an exploration of how the various operating conditions affect the thermodynamic cycle and overall cycle performance.

Table 6. Input and output data of a recompression Brayton cycle

Input Outputs Decision Variables Air Mass Flow rate Cycle thermal efficiency [%] CO2 Mass Flow rate Power Output [MW] Turbine Isentropic efficiency Cycle temperature and pressure Compressor Isentropic efficiency Heat Exchangers Area [m2] Recompressor Isentropic efficiency Generator efficiency Inlet cooling air temperature Inlet heating air temperature Design Variables Turbine inlet temperature Pressure Ratio Recompressor fraction Total fixed UA Main compressor inlet temperature Main compressor inlet pressure

3.2.3 The sCO2 Pre-compression Brayton Cycle Configurations

The pre-compression Brayton cycle is similar to the recompression Brayton cycle.

The only difference is that the configuration arrangement, where the second compressor is staged between the two recuperators, for which there is not split flow after the low temperature recuperator. When the flow exits the high temperature recuperatore, instead of passing to the low temperature recuperatore on the low pressure side, it goes to the boost compressor (PC). Then the fluid is compressed to a higher pressure before entering the

LTR associated with a temperature increase. The increase in temperature, before entering the LTR (T8), helps alleviate the pinch point problem. An example of a pre-compression

Brayton cycle configuration is shown in Figure 16. The temperature and entropy diagram of the pre-compression cycle is illustrated in Figure 17

Figure 16. Pre-compression Brayton cycle

Compressor process 5 800 LTR Process HTR process Heating in the primary heater

]

K Turbine Process

[ Pre-compressor Process

u t 4 6

r 600

T 8 3 7 400 2 9

1 -1200 -1000 -800 -600 -400 -200 0 Entropy [J/kg-°K]

Figure 17. Temperature - Entropy diagram of sCO2 pre-compression cycle

In the pre-compression cycle, a ratio of the pressure ratio needs to be defined [38].

푃ℎ푖푔ℎ (31) 푃 − 1 푅푃푅 = 푖푛푡푒푟푚푒푑푖푎푡푒 푟푐 − 1

Where 푟푐 represent the compressor pressure ratio.

The inputs and outputs of the pre-compression Brayton cycle are presented in the

Table 7.

Table 7. Inputs and outputs data of a pre-compression Brayton cycle

Input Outputs Decision Variables Air Mass Flow rate Cycle thermal efficiency [%] CO2 Mass Flow rate Power Output [MW] Turbine Isentropic efficiency Cycle temperature and pressure Compressor Isentropic efficiency Heat Exchangers Area [m2] Pre-compressor Isentropic efficiency Generator efficiency Inlet cooling air temperature Inlet heating air temperature Design Variables Turbine inlet temperature Pressure Ratio Pre-compressor pressure ratio Total fixed UA Main compressor inlet temperature Main compressor inlet pressure

3.2.4 The sCO2 Split Expansion Brayton Cycle Configurations

The split-expansion Brayton configuration in Figure 18 is resemblance to the recompression Brayton cycle with a two stage expansion instead of a single stage, and where the primary heater is staged between the two turbines. On the high pressure side, when the working fluid exits the high temperature recuperator, the fluid enters the second turbine where it benefits from the increasing power output constrained to maximum temperature. The temperature and entropy diagram of the split-expansion cycle is illustrated in Figure 19.

Figure 18. Split expansion Brayton cycle

900

Compressor process 6 LTR Process HTR process 750 split expansion process 7 ] Heating in the primary heater

K 4

[ Turbine Process

r 600

u 5 t 8

r 3

e 450

T 9 2 300 1

-1400 -1200 -1000 -800 -600 -400 -200 0 200 Entropy [J/kg-°K]

Figure 19. Temperature - Entropy diagram of sCO2 split expansion cycle

The inputs and outputs of the split expansion Brayton cycle are presented in the

Table 8.

Table 8. Inputs and outputs data of a split expansion Brayton cycle

Input Outputs Decision Variables Air Mass Flow rate Cycle thermal efficiency [%] CO2 Mass Flow rate Power Output [MW] Turbine Isentropic efficiency Cycle temperature and pressure Compressor Isentropic efficiency Heat Exchangers Area [m2] recompressor Isentropic efficiency Generator efficiency Inlet cooling air temperature Inlet heating air temperature Design Variables Turbine inlet temperature Pressure Ratio Recompression fraction Total fixed UA Main compressor inlet temperature Main compressor inlet pressure Pressure ratio for the second turbine

A split ratio (SR) in the second turbine is expressed as [38]:

푚̇ (32) 푆푅 = 1 푚̇ 7

3.3 Number of Sub-Heat Exchangers

First, the appropriate number of sub-heat exchangers were studied to characterize the high variation of properties near the critical point. As it is explained in Chapter 2, too many nodes slow down the computational analysis, while too few nodes reduce the calculation accuracy. Deciding how many sub-heat exchangers are needed is crucial. The system is first modeled with 20 sub-heat exchangers for each heat exchanger in the cycle, then dropped to 15, where there was not a big difference in the system efficiency. Then it reduces to 10 sub-heat exchangers, the efficiency still looks identical. Then, when the system is modeled with 8 sub-heat exchangers, a slight difference occurs. Finally, the system is tested with 6 sub-heat exchangers, there is a noticeable difference. Figure 20 shows different number of sub-heat exchangers versus cycle efficiency. Starting with ten sub-heat exchangers, the efficiency starts to converge. From 10 to 20 nodes, the efficiency seems identical, and therefore, 10 sub-heat exchangers seems to be enough for further analysis.

Figure 20. Efficiency at different number of sub-heat exchangers

3.4 Cycle Compression

3.4.1 Effect of Total Conductance

For an appropriate comparative analysis, conductance (UA) has to be fixed for all cycle optimizations in order to compare them on an equivalent basis. It has been observed that there is a strong relationship between UA and cycle thermal efficiency. To illustrate the phenomenon, the total heat exchanger conductance of a sample recuperated cycle and a pre-compression cycle are plotted in Figure 21 and Figure 22 respectively against cycle performance at different pressure ratios. With the increase of heat exchanger conductance, the efficiency increases as well until it converges to its ideal value, and therefore system costs increases as well. It has been found that it is not an ideal method to compare two cycles’ efficiencies with different total conductance, because simply larger recuperators result in higher efficiency. For example, a pre-compression cycle has one more heat exchanger than a simple recuperated cycle, thus a pre-compression cycle requires more heat exchanger conductance than a simple cycle by a factor of 2 to 4.5 [57]. If the total

UA is different for each cycle, then it is difficult to exactly know whether the higher efficiency of the advanced cycles are due to the improvement of the cycle or to the larger total conductance.

0.45

0.42

]

[ 0.39

i 0.36 f UA = 11 W/°K

E UA = 14 W/°K UA = 17 W/°K 0.33 UA = 20 W/°K

0.3

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

Pressure Ratio [-]

Figure 21. The relationship between total conductance and efficiency (Pmax = 20 MPa) (simple recuperated cycle)

0.45

0.42

]

[ 0.39

c 0.36

f UA = 11 W/K

E UA = 14 W/K UA = 17 W/K 0.33 UA = 19 W/K

0.3

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

Pressure Ratio [-] Figure 22. The relationship between total conductance and efficiency (Pmax = 20 MPa) (pre-compression cycle)

As it can be observed from the figure above, the efficiency rate increases with the increasing of total conductance. From the heat transfer principle, a larger UA decreases the temperature drop in the heat exchanger resulting in a higher efficiency. But a larger UA is relate directly with a physically larger heat exchanger and therefore a higher price. More investigation of the impacts of total conductance on the cycles’ efficiencies will be conducted. Figure 23 compares the influence of total conductance on the thermal efficiency of the four cycles. The importance of the Figure 23 comparison comes from the economic optimization consideration.

0.48

0.46

]

[

0.44

e i 0.42

l 0.4

r e 0.38 Simple recuperated

T Pre-cpmpression Split expansion 0.36 recompression

0.34 10 15 20 25 30 35 40 45 50 55 60 Total UA (kW/°K)

Figure 23. The influence of total conductance on the thermal efficiency

As can be seen in Figure 23, the four cycles’ efficiencies increase asymptotically with the increase of total conductance until they reach their ideal value, where the efficiency remains constant with increasing total conductance. In the beginning, the efficiencies of the four cycles appear similar at some certain low total conductance values.

However, a slight advantage of the simple recuperated cycle over other cycles emerges at

total conductance bellow 13 kW/°K. At low total conductance (~ 14 kW/°K), the figure shows an overlap between the simple recuperated cycle and the recompression cycle which is have been proved by other researches [60], [71-72]. However, starting from 15 kW/°K, the recompression surpasses the other cycles until it reaches its maximum efficiency 47.6% at 40 kW/°K. Pre-compression and split expansion cycle efficiencies take advantage of the simple recuperated cycle efficiency at total conductance of 18 kW/°K and 15 kW/°K respectively. Finally, it can be apparently seen that the recompression Brayton cycle has the highest thermal efficiency over the range of total conductance. The total conductance comparison is the most important comparative factor as it directly relates the system economy. Table 9 summarizes the effect of total conductance on the four cycles.

Table 9. Summary of the effect of total conductance on the four cycles

Simple Pre- Split Recompression Recaptured compression Expansion Highest efficiency [%] 42.1 47.6 43.8 45.9 Maximum power output [kW] 117 138 119 109 Maximum pressure [MPa] 20 20 20 20 Optimized UA [kW/°K] 55 40 60 35 Fixed UA [kW/K] Thermal efficiency [%] 13 37.4 37.3 37.1 35.2 15 38.2 42 38.1 38.2 25 40.8 64.4 41 44.4 35 41.7 47.5 43 45.9 45 42.05 47.6 43.2 45.9 55 42.2 47.6 43.8 45.9

Thus, in the analytical model, for the purpose of compression, the conductance is fixed at 17,000 W/°K for all cycles for an appropriate compression. The reason behind fixing the total conductance of all the cycles is to facilitate the appropriate comparative study between the four cycles.

3.4.2 Parametric Analysis of the Pressure Ratio

As a way of optimization, each cycle runs at different design points, in order to identify the optimum operating conditions to be used for further analysis. The maximum operating pressure is studied at 18 MPa, 20 MPa, 22 MPa, and 25 MPa, while the lowest operating pressure is obtained by varying pressure ratios. Pressure ratio plays a vital role on both cycles’ efficiencies and power outputs. To appropriately investigate the effect of the pressure ratio, the total heat exchangers conductance is fixed at 17,000 W/°K for all cycles. Each heat exchanger’s conductance in the system is modeled separately, but the total heat exchanger conductance is fixed. The aim of this analysis is to compare the four cycles at different fixed operating condition. The optimization target in this section is efficiency and power output. Figure 24 and Figure 25 show the effect of pressure ratio and maximum operating pressure on the simple recuperated cycle’s efficiency and power outputs respectively.

0.42

0.4

]

[

c 0.38

E 0.36

Pmax = 18 MPa

Pmax = 20 MPa 0.34 Pmax = 22 MPa Pmax = 25 MPa

0.32 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25

Pressure Ratio [-] Figure 24. Efficiency at different pressure ratio (simple recuperated cycle)

140

Pmax = 18 MPa

130 Pmax = 20 MPa

Pmax = 22 MPa

] Pmax = 25 MPa

[ 120

u 110

o 100

80 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25

Pressure Ratio [-] Figure 25. Power output at different pressure (simple recuperated cycle)

It can be observed from the two figures above that the highest efficiency and power output occur at the highest maximum operating pressure (25 MPa) at pressure ratio of 3.25.

Also, it is worth noting that the highest efficiency for each maximum operating pressure occurs at the critical point. Thermal efficiency and power output are linearly increase with the increase of the pressure ratio until they reach their highest values. When thermal efficiency reaches its maximum value, it decreases smoothly. In comparison the power out decreased sharply when it reached its maximum value then increased slowly. Thus, designing the system with an appropriate pressure ratio is highly positively affect the outcomes.

Figure 26 and Figure 27 show the effect of pressure ratio and maximum pressure on the pre-compression cycle’s efficiency and power outputs.

0.42 Pmax = 18 MPa Pmax = 20 MPa Pmax = 22 MPa Pmax = 25 MPa 0.4

]

[

n 0.38

f E 0.36

0.34

0.32 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25

Pressure Ratio [-] Figure 26. Efficiency at different pressure ratio (pre-compression cycle)

130

Pmax = 18 MPa P = 20 MPa 120 max Pmax = 22 MPa Pmax = 25 MPa

]

W 110

[

p 100

r 90

P 80

60 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25

Pressure Ratio [-] Figure 27. Power output at different pressure ratio (pre-compression cycle)

The pre-compression cycle efficiency and power output increase with the increase of the pressure ratio until they reached their maximum value at or near the critical points.

Then it starts to decrease. Thus, considering possible outcomes allows the designer to choose the appropriate operating condition that meet their needs. The two figures above are shown the importance of keeping the cycle runs at or near the critical point.

Figure 28 and Figure 29 show how the pressure ratio and maximum pressure relate on the split expansion cycle’s efficiency and power outputs.

0.45

0.42

]

[ 0.39

f 0.36

E Pmax = 18 MPa Pmax = 20 MPa Pmax = 22 MPa 0.33 Pmax = 25 MPa

0.3 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 Pressure Ratio [-] Figure 28. Efficiency at different pressure ratio (split expansion cycle)

110

100

]

[

t 90

r 80

P Pmax = 18 MPa 70 Pmax = 20 MPa Pmax = 22 MPa Pmax = 25 MPa

60 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25

Pressure Ratio [-] Figure 29. Power output at different pressure ratio (split expansion cycle)

Figure 28 and Figure 29 show how important it is to run the system at or near the critical point to take full advantages of CO2 as a sole system medium. The highest efficiency and power output of the split expansion cycle occurs near the critical points, because the high density of CO2 near critical points that reduces compressor work. It is interesting to note that running the cycle in the supercritical region, at higher maximum pressure, leads to less dependence on the pressure ratio. Also, increasing the pressure ratio does not always increase the thermal efficiency because increasing the pressure ratio results in an increase in the compressor outlet temperature. However, a drawback of increasing the maximum operating pressure is that the system components need to have thicker walls in order to withstand the high pressure, thereby increasing the system cost.

Figure 30 and Figure 31 show the effect of pressure ratio and maximum pressure on the recompression cycle’s efficiency and power outputs.

0.46

0.44

0.42

]

[

y 0.4

i 0.38

E Pmax = 18 MPa P = 20 MPa 0.36 max Pmax = 22 MPa Pmax = 25 MPa 0.34

0.32 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 Pressure Ratio [-] Figure 30. Efficiency at different pressure ratio (recompression cycle)

140

Pmax = 18 MPa Pmax = 20 MPa Pmax = 22 MPa Pmax = 25 MPa

] 120

[

u 100

o P 80

60 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 Pressure Ratio [-] Figure 31. Power output at different pressure ratio (recompression cycle)

The highest efficiency and power output of the recompression cycle with respect to four maximum pressures (18 MPa, 20 MPa, 22 MPa, and 25 MPa) occurs near the critical point. At different pressure ratios, while fixing all other variables, the recompression cycle

achieves the maximum efficacy (43%) and power output (118 kW) compared with the other cycles. The two graphs above indicate that the optimum pressure ratio varies between the four cycles studies. An interesting finding from Figure 31 is that the power output at the lowest maximum pressure (18 MPa) increases with the increasing of pressure ratio. This that might be because the pressure drop is neglected in this chapter. Another interesting finding is that, in the recompression configuration, efficiency and power output move in opposition to each other. Thus in order to properly choose the optimum pressure ratio, a multi-objective optimization is needed.

Figure 32 and Figure 33 shows the comparison of the four cycles’ efficiencies and net power output at different pressure ration at the maximum operating pressure of 20 MPa

0.44

0.42

]

[

y 0.4

f 0.38

0.36 Simple cycle Pre-cpmpression cycle 0.34 Split expansion recompression

0.32 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 Pressure Ratio [-] Figure 32. Efficiency compression of the four cycles at Pmax = 20 MPa

120

110

] 100

[

p 90

e 80 w Simple cycle

P Pre-cpmpression cycle 70 Split expansion recompression

60 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4 4.25 Pressure Ratio [-] Figure 33. Power compression of the four cycles at Pmax = 20 MPa As can be observed from pressure ratio study, the highest overall cycles’ efficiencies are 43% and 42%. These are achieved by the recompression cycle and split expansion respectively at the pressure ratio of 2.75, where the total conductance is fixed at

17,000 W/°K for all cycles. On the other hand, the simple recuperated cycle achieved the highest power output over the other cycles despite its comparative simplicity.

An interesting finding from the Figure 32 and Figure 33 is that the increase and decrease of pressure ratio beyond the critical point results on a reduction on the thermal efficiency and power output as a result of the reduction on the recuperator effectiveness.

The recuperator effectiveness decline with the increase of pressure ratio dues to the turbine and compressor outlet temperatures that being closer together which reduce the heat exchanger temperature difference. While the recuperator effectiveness decline with the decrease of pressure ratio dues to the great increase in the specific heat of the CO2 close to the critical point, thereby increase the parasitic losses [34].

Another interesting finding is that the efficiency of the recompression and split expansion cycles are appreciably dependent on the pressure ratio, while the simple recuperated and pre-compression cycles have a lesser dependence. All cycles demonstrate their highest efficiency at or very near the critical points, although each responds differently to increasing pressure ratio.

Figure 32 and Figure 33 indicate that the efficiency and power output growth and decline rates are different for all cycles; the optimum design and decision variables are different, and need to be chosen carefully for each configuration. Also it is worth noting that there is significant drop of the thermal efficiency on the recompression and split expansion cycles around the critical points. Table 10 summarizes the outcomes of the effect of the pressure ratio in the four cycles.

Table 10. Summary of the pressure effect on the four cycles

Simple Re- Pre- Split

Recaptured compression compression Expansion Highest efficiency [%] 39.5 43.3 41.2 42.1 Maximum power output [kW] 128 118 127.8 105 Maximum pressure [MPa] 25 25 25 25 Pressure ratio 3.32 3.35 3.5 3.3 Total conductance [W/°K] 17000 17000 17000 17000 Temperature factor [-] - - 0.3 - Ratio of the pressure ratio [-] - - 0.8 - Maximum Temperature [K] 873 873 873 873 Compressor Inlet Temperature [K] 305 305 305 305 Split ratio [-] - - - 0.9 Recompression fraction [-] - 0.21 - 0.2

3.4.3 Parametric Analysis of the Operating Temperature

In this section, the impacts of cycle temperatures is presented. The model runs at a variety of turbine inlet temperatures (TIT) and compressor inlet temperatures (CIT). To accurately study the effect of operating temperature on the cycle, the model decisions and design parameters are fixed while varying turbine inlet temperatures. Two plots are presented to demonstrate the concept of operating temperature impacts. Figure 34 illustrates the impact of TIT at different total heat exchanger conductance values in the pre- compression cycle.

0.44

0.43

0.42

]

[ 0.41

n 0.4

f 0.39

E UA = 11 W/K 0.38 UA = 14 W/K UA = 17 W/K 0.37 UA = 19 W/K

0.36

0.35 780 800 820 840 860 880 900 920

Maximum Temperature [°C] Figure 34. Efficiency at different TIT values for different UA values (pre-compression)

Figure 34 shows the relationship between the conductance and efficiency over a range of turbine inlet temperatures. As expected, the increased TIT results in a linear increase in thermal efficiency due simply to the Carnot principle. Another finding from

Figure 34 that increasing the total conductance (UA) increases the thermal efficiency with different growth rate.

Figure 35 compares the relative efficiency of the four cycles under study over a range of turbine inlet temperatures while fixing the total conductance at 17000 W/°K.

0.48 Simple cycle Pre-cpmpression cycle 0.46 Split expansion

] recompression

[ 0.44

e i 0.42

l 0.4

h 0.38

0.36

0.34 450 500 550 600 650 700 750

Turbine Inlet Temperature [°C]

Figure 35. Relates the efficiency of compression to different turbine inlet temperatures

Figure 35 shows the strong impact of turbine inlet temperature variations on the overall efficiency. Specifically, it shown a nearly steady rate of efficiency increase relates to an increase of TIT for all cycles. This is consistent with Carnot’s principle when the control parameters are constant. Also, it should be noted that the efficiency growth rate is different between the cycles. At the lowest turbine inlet temperature (450 °C) in the plot, the recompression cycle has the highest efficiency among other cycles. At (480 °C), an

overlap between the pre-compression and split flow cycles. Also, at (603 °C), an efficiency intersection occurs between recompression cycle and the pre-compression cycle due to the higher rate of efficiency increase in the pre-compression cycle with increasing TIT.

Starting from 603 °C (TIT), the pre-compression cycle efficiency exceeds the recompression cycle efficiency and maintains the overall thermal efficiency advantage over other cycles. In contrast, the simple recuperated cycle has the lowest thermal efficiency over the range of turbine inlet temperatures compared to other cycles.

Also, as a way to investigate the impact of operating temperature on the cycle performance, the recompression cycle were simulated at different compressor and turbine inlet temperatures, as shown in Figure 36.

0.55

Tmax = 720 [°C] Tmax = 680 [°C] Tmax = 620 [°C]

) 0.5 Tmax = 550 [°C]

(

f 0.45

C 0.4

0.35 27 29 31 33 35 37 39 41 43

Compressor inlet temperature (°C)

Figure 36. Impact of compressor inlet temperature

Figure 36 illustrates how compressor and turbine inlet temperatures affect the cycle efficiency. Higher thermal efficiency occur with higher turbine inlet temperature and lower compressor inlet temperature, which is coincide with Carnot principle.

3.5 Summary and Results

Four supercritical carbon dioxide (sCO2) Brayton cycles have been thermodynamically studied under different operating conditions: simple recaptured; recompression; pre-compression; and split expansion. Three parametric analysis are used: effect of total conductance (UA), effect of maximum and minimum operating temperatures, and effect of pressure ratio.

For all cycles, increasing the total conductance (UA), increasing the turbine inlet temperature, and being operated near or at the critical point, have a significant positive impact on thermal efficiency and power output.

To summarize the conducted work in this chapter, the optimized design parameters, assumed variables, and outputs are shown in Table 11. The assumed variables remain constant for each configuration, while the design variable vary depend on each cycle for the purpose of maximizing both efficiency and specific power output.

Table 11. Optimum design points

Simple Re- Pre- Split

Recaptured compression compression Expansion Highest efficiency [%] 48.32 54.8 50.1 52.3 Maximum specific power output [kJ/kg] 174.6 165.1 149.3 162.9 Maximum pressure [MPa] 25 25 25 25 Pressure ratio 3.4 3.36 3.44 3.38 Total conductance [W/°K] 17000 17000 17000 17000 Temperature factor [-] - - 0.33 - Ratio of the pressure ratio [-] - - 0.78 - Maximum Temperature [°K] 873 873 873 873 Compressor Inlet Temperature [°K] 305 305 305 305 Split ratio [-] - - - 0.87 Total mass flow rate [kg/s] 60 68 65 64 Recompression fraction [-] 0.24 0.22 Turbine efficiency [-] 0.91 0.91 0.91 0.91 Compressor efficiency [-] 0.88 0.88 0.88 0.88

After the complete thermodynamics analysis and comparative study of the four sCO2 Brayton cycles, it appears the most suitable cycle for further analysis in Chapter 4 is the recompression cycle because it demonstrated the highest efficiency and power output at the desired parameters. Also, using the recompression cycle reduces the internal irreversibility (pinch point problem) due to the drastic change in the specific heat capacity near the critical point of CO2.

CHAPTER IV

THERMODYNAMIC ANALYSIS AND MULTI-OBJECTIVE OPTIMIZATIONS OF

A COMBINED RECOMPRESSION S-CO2 BRAYTON CYCLE T-CO2 RANKINE

CYCLE FOR WASTE HEAT RECOVERY

A thermodynamic (Energy and Exergy) analysis and optimization of a newly- conceived combined power cycle were conducted in this chapter for the purpose of improving overall thermal efficiency of power cycles by attempting to minimize thermodynamic irreversibilities and waste heat as a consequence of the Second Law. The power cycle concept comprises a topping advanced recompression sCO2 Brayton cycle and a bottoming tCO2 Rankine cycle. The bottoming cycle configurations included a simple tCO2 Rankine cycle and a split tCO2 Rankine cycle. The topping supercritical CO2 recompression Brayton cycle used a combustion chamber as a heat source, and waste heat from a topping cycle was recovered by the tCO2 Rankine cycle due to an added high efficiency recuperator for generating electricity. The combined cycle configurations were thermodynamically modeled and optimized using an Engineering Equation Solver (EES) software. Simple bottoming tCO2 Rankine cycle cannot fully recover the waste heat due to the high exhaust temperature from the top cycle, and therefore an advance split tCO2

Rankine cycle was employed in order to recover most of the waste heat. Result show that

the highest thermal efficiency was obtained with recompression sCO2 Brayton cycle – split flow tCO2 Brayton cycle. Also, the results show that the combined CO2 cycles is a promising technology compared to conventional cycles.

4.1 System Description

Two configurations are considered in this chapter: a topping recompression sCO2

Brayton cycle and a bottoming cycle configurations included 1) a simple tCO2 simple

Rankine cycle and 2) a split flow tCO2 Rankine cycle. The two bottom cycles studied are operating at both subcritical and supercritical states, which called transcritical cycle. The temperature – entropy and pressure - enthalpy diagrams of the simple bottom tCO2 cycle, as an example of transcritical cycle, is illustrated in Figure 37 and Figure 38.

440 420 6 400

380 0.0057 0.0017

0.01

5 0.019 0.034 360 4 0.063 m3/kg 3 340 7 320 T [K] 2 300 7.00E6 Pa 8 280 1 3.00E6 Pa 260 2.00E6 Pa 240 900000 Pa 220 0.2 0.4 0.6 0.8 200 -2250 -2000 -1750 -1500 -1250 -1000 -750 -500 -250 0 s [J/kg-K]

Figure 37. Transcritical CO2 simple bottom cycle T–S diagram

108

-1731 -1521 -1310 -1099 -888.4 -677.7 J/kg-K

4 5 2 3 6

]

a 7 P 10

[

r 1

u 8 7

s 400 K

r 270 K 360 K

330 K 300 K 240 K 106

0.2 0.4 0.6 0.8 5x105 -5.0x105 -3.0x105 -1.0x105 1.0x105 3.0x105 Enthalpy [J/kg]

Figure 38. Transcritical CO2 simple bottom cycle P–h diagram

The first combined system as is shown in Figure 39 is comprehensively studied in this Chapter. It is constructed from a top recompression cycle and a bottom simple Rankine cycle. Four components are added to the original recompression cycle: waste heat recovery, turbine, condenser, and pump. When the flow leaving LTR (state 10), it divided into two stream. The first stream goes to the primary compressor through the precooler and the waste heat recovery (WHR). The second stream is directed to the recompressing compressor and exits on the high pressure side between the two recuperators (state 4).

Then, the stream temperature reduces while it leaves the WHR (state 11) to the precooler before entering the main compressor. At state 16 another stream preheated in the WHR before entering the bottom cycle’s turbine (state 17). Then the flow expands in through the turbine while it generates power at the generator. Finally, the low pressure stream is precooled in the condenser before entering the pump (state 19).

Figure 39. Recompression CO2 Brayton cycle with simple bottom Rankine cycle

The second combined system is comprehensively studied in this Chapter is a toping recompression cycle with a bottoming split flow Rankine cycle as it shown in Figure 40.

Six components are added to the original recompression cycle: waste heat recovery, turbine, two recupertors, condenser, and pump. When the flow leaving LTR (state 10), it divided into two flows. The first fluid flow goes to the recompression compressor, while the second stream directed to the waste heat recovery (WHR) heat exchanger. Then, the stream temperature reduces while it leaves the WHR (state 11) to another heat exchanger that reduces the temperature even more before entering the precooler. At state 16 another stream preheated in the WHR before entering the bottom cycle’s turbine (state 17). Then the flow expands in the turbine while it generates power at the generator. Then, the exist turbine stream is precooled in the recuperator before cooled again in the condenser. Then, the low temperature and pressure stream compressed in the pump (state 20). The flow then split into two streams. The first streams directed to the recuperator to be preheated, while

the second stream diverted to the new added heat exchanger. The two preheated streams are intersected at state 16 before entering the waste heat recovery heat exchanger.

Figure 40. Recompression CO2 Brayton cycle with split flow bottom Rankine cycle

4.2 Optimization and Objective Function

The Multi-objective optimization technique conducted in this chapter is developed based on a genetic algorithm (GA) using Engineering Equation Solver (EES). Using the

GA method allows the model to handle non-linear and non-differentiable optimization tasks. It simply works by having initial individual points (1st generation) that are evaluated against an objective function to create a quantity fitness function for each individual point.

Then the first iteration finds the fittest possible solution from the 1st generation to create a subsequent other possible solutions while retaining the initial fitness value to be calculated and used again. Then the second iteration evaluates the subsequent possible solutions and creates other subsequent individual points. The iteration of creating new generations is repeated until the algorithm converges, which occur when the best objective (fitness)

function changes a really small amount or is no longer changing. The computationally expensive process is the main drawback of the Genetic Algorithm due to the fact that the algorithm repeats using the fitness values. The flow chart of the Genetic Algorithm used in the study is exhibited in Figure 41.

Figure 41. Genetic algorithm flow chart

4.2.1 Optimization Domain

The importance of govern the optimization process by realistic lower and upper bounds is described in chapter 3. According to the literature review at Table 13, the upper and lower bounds are set. The lower and upper bounds set at the acceptable values to allow the model to test as mush variables as it could be. The optimization domain of the lower and upper variables is shown is the Table 12.

Table 12. Variables lower and upper bounds of the combined cycles

Lower Upper ≤ Variables ≤ Bound Bound 12 Maximum pressure [MPa] 30 1 Pressure ratio 6 15 Total conductance [kW/°K] 35 400 Turbine Inlet Temperature [°K] 900 280 Compressor Inlet Temperature [°K] 340 350 Recompressor Inlet Temperature [°K] 650 1 Total mass flow rate [kg/s] 600 0 Recompression fraction [-] 1 0 Split flow fraction 1

Table 13. Literature input parameters and combined sCO2 cycle efficiency

Wang Besarati Pichel Wang [10] Akbari [8] Yari [40] [51] [22] [61]

Top cycle sCO2 sCO2 sCO2 sCO2 sCO2 sCO2 sCO2 ORC ORC ORC ORC ORC Bottom cycle tCO2 tCO2 Isopentane Isopentane Isopentane R245ca R134a Minimum temperature [C] 32 35 35 32 55 30 Minimum pressure [MPa] 7.4 7.4 7.4 8 - 7.4 Maximum pressure [MPa] 20.72 22.2 24.3386 20 25 25 Turbine inlet temperature [°C] 550 550 650 550 800 500 HTR effectiveness [-] 86% 86% 86% 95% 95% 95% LTR effectiveness [-] 86% 86% 86% 95% 95% 95% Turbine efficiency [-] 90%/70% 90%/87% 90%/80% 90%/85% 90%/87% 93%/85% Compressor/Pump efficiency 85%/80% 85%/80% 85%/80% 89%/85% 89%/85% 89%/80% 50 Pressure drop [-] negligible negligible negligible negligible negligible kPA/HX Combined Cycle efficiency 0.449 0.4523 0.4422 0.49 0.4672 0.5433 0.435

4.3 Modeling Approach

Table 14 presents the operating condition, based on the literature at Table 13, used for the two cycles studied in this Chapter (i.e., a topping recompression sCO2 Brayton cycle and a bottoming cycle configurations included 1) a simple tCO2 simple Rankine cycle and

2) a split flow tCO2 Rankine cycle).

Table 14. Basic design and input parameters of the combined cycles

Operating Condition Value Compressor inlet temperature [°C] 32 Compressor inlet pressure [MPa] 6.8 Pump inlet temperature [°C] 25 Maximum pressure [MPa] 25 Pressure ratio 3.6 Turbine inlet temperature [°C] 720 Isentropic turbine efficiency [-] 93.0% Isentropic Efficiency of Compressors 89.0% Pump efficiency [-] 85.0%

The two objective targets in the optimization processes are: 1) the overall thermal efficiency and 2) the power output. Both objective targets need to be maximized simultaneously, while at some points they are conflicted to each other. Thus, the weighted sum method is employed in this study for the purpose of properly solving the conflicted of the multi-objective functions. The general multi objective optimization can be expressed as:

푇 푛 푀푎푥푖푚푖푧푒: 퐹(푥) = [퐹1(푥) , 퐹2(푥) , 퐹3(푥), … , 퐹푍(푥)] , 푥 ∈ 푅 , (33)

Subjected to 푔(푥) = [푔1(푥) , 푔2(푥) , 푔3(푥) , … , 푔퐽(푥)] ≥ 0

퐻(푥) = [ℎ1(푥) , ℎ2(푥) , ℎ3(푥) , … , ℎ퐾(푥)] = 0 퐿 푈 푥푖 ≤ 푥푖 ≤ 푥푖 , 퐼 = 1,2, … , 푁 where F(x) is the objective function, Z represents the number of objective functions, g(x) and H(x) are the inequality and equality constraints respectively, J and K respectively are

퐿 푈 the number of inequality and equality constraints, and 푥푖 and 푥푖 represent the lower and upper bound of each design variable respectively.

So, using the weighted sum method based on the general form of the multi objective optimization in equation (33) yields to:

푀 푀푎푥푖푚푖푧푒: 퐹(푥) = ∑푚=1 푤푚푓푚(푥) , (34)

Subjected to 푔푗(푥) ≥ 0, 푗 = 1,2, … , 퐽

ℎ푘(푥) = 0, 푘 = 1,2, … , 퐾

퐿 푈 푥푖 ≤ 푥푖 ≤ 푥푖 , 퐼 = 1,2, … , 푁 Simply, the weighted sum method is converting the multi-objectives function into a single objective function using a proper weighs and summation.

4.4 Results and Discussion

Two combined cycles are studied in this chapter. The top cycle, recompression sCO2 Brayton cycle, is used for both cycles as has been proven in chapter to be the most suitable cycle for the further analysis. While two simple bottoming sCO2 Rankine cycle configurations are study. The parametric analysis of the maximum cycle operating temperature show that the simple bottom Rankine cycle cannot fully recover the waste heat from the top recompression sCO2 Brayton cycle. Thus, a newly-conceived bottom cycle is proposed to utilize the remaining waste heat from the top cycle. Figure 42 and Figure 43 shows thermal efficiency, exergy efficiency, and power output of the two combined cycles at different maximum operating temperature.

0.8

0.76

]

[ 0.72

c 0.68 Split-flow exergy efficiency

e simple bottom exergy efficiency

c 0.64 i Split flow thermal efficiency

f Simple bottom thermal efficinecy

E 0.6

m 0.56

h 0.52

0.48

0.44

0.4 600 650 700 750 800 850 900 950 1000

Turbine Inlet Temperature (Top Cycle] [°C] Figure 42. Thermal and exergy efficiency comparison as a function of maximum operating temperature for the simple and new combined cycles

4750

4500

] Split-flow 4250 simple bottom

[

t 4000

u 3750

r 3500

o 3250

P 3000

2750

2500 600 650 700 750 800 850 900 950 1000 Turbine Inlet Temperature (Top Cycle] [°C] Figure 43. Power output comparison as a function of maximum operating temperature for the simple and new combined cycles

Figure 42 indicates that the energetic and exergetic efficiency increase with the increase of the maximum cycle operating temperature of both combined cycles. While increasing ambient temperature increases the external irreversibilities (exergy losses) and therefore reducing the system performance. Another interesting finding is that, exergy and energy efficiency follow the same pattern, which they are linearly increasing as the turbine inlet temperature increases. Figure 42 shows how higher energetic and exergetic of the newly-conceived cycle at all different maximum cycle operating temperatures can be achieved by adding two recuperators to unitize the remaining waste heat that the simple bottom Rankine cycle cannot recover. The newly-conceived cycle, using two more recuperators, increase the cycle efficiency by about 2% to 2.5% compared to the simple bottom cycle.

Figure 43 demonstrates the higher power output of the newly-conceived cycle compared to the simple bottom cycle when they operate at same maximum turbine inlet temperature. An interesting finding from the simple bottom tCO2 Rankine cycle results is that, increasing the maximum operating temperature, above 390 °C, leads to two conflicts results. The first result is increasing the cycle efficiency, and the second result is lowering the waste heat recovery effectiveness, and thereby having a lower system efficiency. So, system thermal efficiency is optimized by balancing the cycle efficacy against the waste heat recovery effectiveness to have a higher system efficiency. Thus, the simple bottom cycle turbine inlet temperature has to be less than 390 °C in order to maintain a high waste heat recovery effectiveness. Otherwise, a drop in the waste heat recovery effectiveness occur which lower the system efficiency. To overcome this issue, a newly-conceived cycle is proposed. It allows higher bottom cycle turbine inlet temperature without adverse

effecting the waste hear recovery effectiveness by adding two recuperators to the system.

Increasing the maximum cycle operating temperature lead to an increase of enthalpy difference across the turbine and therefore an increase of power output.

0.6 Top Cycle (recompression) 0.58 Combined Cycle (Split flow bottom) Combined Cycle (simple bottom) ] 0.56

[

c 0.54

i 0.52

l 0.5

r 0.48

h T 0.46

0.44

0.42 600 650 700 750 800 850 900 950 1000

Turbine Inlet Temperature (Top Cycle] [°C]

Figure 44. Thermal efficiency improvement as a function of maximum operating temperature for the simple and new combined cycles According to Figure 44 results, the combined cycles improve the overall cycle thermal efficiency by about 2% - 2.5% (simple bottom cycle), and 4% - 4.5% (split-flow bottom cycle) compared to the stand-alone recompression sCO2 Brayton cycle. The optimum turbine inlet temperature is determined based on the concentrated solar power

(CSP) heat source availability, which will be describe in Chapter 5. Also, economic analysis are important to be combined with the power cycle analysis to find out whether that higher efficiency, due to the higher operating temperature, is associated with the higher cost, due to larger heat exchanger and higher temperature material, worth or not.

The impact of the main compressor inlet temperature on the first law efficiency, second law efficiency, power output has been studied, as it shown in Figure 45 and Figure 46.

0.8

0.75 n

e 0.7

]

E [ 0.65

y T = 720 [°C]

c max

n Tmax = 650 [°C]

e 0.6 i Tmax = 600 [°C]

y f Tmax = 550 [°C]

0.55 n

e 0.5

0.45 E

0.4 27 30 33 36 39 42 45 Compressor inlet temperature [°C]

Figure 45. Impact of compressor inlet temperature and turbine inlet temperature on the newly-conceived cycle efficiency

3800 Tmax = 720 [°C] T = 650 [°C] 3600 max Tmax = 600 [°C] Tmax = 550 [°C] 3400

]

[

3200

t 3000

e 2800

P 2600

2400

2200 27 30 33 36 39 42 45 Compressor inlet temperature [°C]

Figure 46. Impact of compressor inlet temperature and turbine inlet temperature on the newly-conceived cycle power output

Figure 45 and Figure 46 show how the minimum operating inlet temperature and maximum operating inlet temperature affect the cycle efficiency and power output.

Increasing the turbine inlet temperature has a direct positive effect to the power output and efficacy. Also, it is important to note that, a high-temperature-resistant material may be needed with the increasing of maximum operating temperature, thereby increasing the system cost.

Exergy analysis of the newly-conceived combined power cycle is conducted in order to identify thermodynamic losses in each cycle component for the purpose of improving overall thermal efficiency by attempting to minimize thermodynamic irreversibilities. External irreversibilities (exergy loss) and internal irreversibilities (exergy destruction) have been determined through the exergy analysis, as they shown in Figure

47.

500 0.4

Exergy Distrcution ratio ]

% ] Exergy Distrcution rate

[ 400 0.32

[

300 0.24 i

200 0.16 D

E e 100 0.08

0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0 Main Recompressor Turbine Primary Primary HTR LTR compressor cooler heater

Figure 47. Exergy destructions rate and ratio in the sCO2 components

Figure 47 shows the exergy destruction in the top recompression sCO2 cycle components. Primary heater, which transfer heat from the primary source to the cycle, accounts for 35% of the thermodynamic losses, follow by the low temperature recuperator, which has an internal cycle heat transfer, accounts for 18% of the total thermodynamic losses. One way to minimize the thermodynamic losses on the primary heat exchanger and low temperature recuperator is to minimize heat exchanger temperature difference between the two streams (cold – hot).

4.5 Conclusion

The energy and exergy analysis of the two advanced combined cycles were conducted in this chapter. The internal irreversibilities (exergy destruction) and external irreversibilities (exergy losses) for each component were investigated in order to provide appropriate guiding improvements. The top sCO2 recompression Brayton cycle’s waste heat is utilized by a bottom tCO2 Rankine cycle for the purpose of improving both efficiency and power output. The two cycles comparison is based on the parametric analysis of the maximum cycle operating temperature. The result demonstrate that the new- conceived cycle, sCO2 recompression Brayton coupled with a tCO2 split-flow Rankine cycle, surpasses the simple combined cycle, sCO2 recompression Brayton coupled with a tCO2 simple Rankine cycle, in respect to energy and exergy efficiencies and power output.

Based on the exergy analysis, primary heater has the highest thermodynamic losses, follow by the low temperature recuperator (LTR). On the other hand, the turbine and compressors have the lowest thermodynamic losses. The high potential improvements of the cycle should be focused on the heat exchangers and especially primary heater and low temperature recuperator.

CHAPTER V

VIABILITY ASSESSMENT OF A CONCENTRATED SOLAR POWER TOWER

WITH A SUPERCRITICAL CO2 BRAYTON-CYCLE POWER PLANT

The aim of this chapter was to conduct thermodynamic and economic analyses of a concentrated solar power (CSP) plant utilizing a supercritical CO2 recompression Brayton cycle. The objective was to assess the system viability in a location of moderate-to-high solar availability. A case study is presented of a city in Saudi Arabia. To achieve the highest energy production per unit cost, the heliostat geometry and thermal energy storage (TES) dispatch are optimized. Solar power tower (SPT) is a type of CSP technology that is of particular interest here because it can operate at relatively high temperatures. The present

SPT-TES field comprises heliostat mirrors, a tower, a receiver, heat exchangers, and two molten-salt TES tanks. The main economic indicators are the capacity factor and the levelized cost of electricity (LCOE). The findings indicate that SPT-TES with supercritical

CO2 power cycles is economically viable. The results also show that integrating TES with an SPT has a strong positive impact on the capacity factor at the optimum LCOE.

5.1 Introduction

The demands for improved energy performance and alternative sources of energy are being driven by unprecedented growth in global population, energy demand, and environmental concerns. As clean and sustainable energy, renewable energy is currently of great interest in this regard.

Concentrated solar power (CSP) technology uses a large reflective surface to concentrate solar radiation onto a receiver (in the form of a line or a point), whereupon working fluid flowing through tubes is heated to high temperatures to drive a heat engine that produces electricity. There are a number of different CSP designs: SPTs, sometimes referred to as receiver power towers), parabolic-dish concentrators, parabolic-trough concentrators, and linear Fresnel reflectors are all represented strongly in the power industry. The SPT approach is considered superior to the others because it operates at higher temperatures and therefore has higher thermal efficiency.

There have been several economic and thermodynamic studies of CSP systems in various locations [71-77]. However, the findings of such studies vary because CSP performance depends strongly on location. James et al [73] analyzed the costs of parabolic- trough and SPT CSP in Australia and found that SPT technology had more potential to reduce the levelized cost of electricity (LCOE). Turchi et al. [74] assessed the current and future costs of two molten-salt CSP technologies (parabolic-trough and SPT) in the US market. Their predictions were based on current technology and expected future improvements in aspects such as field temperature, heliostat cost, the heat-transfer fluid

(HTF) system, and the power block. Turchi et al. assessed the two CSP technologies as promising and viable, with high capacity factors; the LCOE of each is expected to be less

than $0.11/kWh by 2025. Turchi et al. concluded that an SPT plant would have cost and performance advantages over a parabolic-trough plant. They also estimated that the capacity factor of an SPT plant would be two to three times greater than that of a utility- scale photovoltaic system. Antonio et. al. [75] evaluated the potential of medium and large

SPT plants in Spain, USA, and South Africa. They conducted a parametric analysis of two

HTF technologies: direct steam generation (DSG) and molten nitrate salts. TES was not taken into account during the analysis to compare the two technologies on an equivalent basis. The results showed that DSG was practical and had the lower LCOE.

Eddhibi et. al. [76] created a mathematical model to predict the optical efficiency of an SPT plant in Seville, Spain. They proposed a new way of calculating the blocking and shadowing efficiency. The results showed that blocking and shadowing are the most significant factors affecting the optical efficiency. Iverson et al. [21] examined the effect of fluctuating solar-energy input (e.g., due to intermittent cloud cover) on a supercritical

CO2 (sCO2) Brayton cycle. They used a laboratory-scale demonstration turbine as well as a benchmarked model and determined that the thermal mass of the system could overcome short interruptions in input power. These results suggest that (i) it is worthwhile to continue developing sCO2 Brayton cycles for solar power generation and (ii) several of the remaining issues could be solved by moving to large-scale commercial systems.

Molten-salt solar power tower (MSSPT) –as shown schematically in Figure 48- technology is a type of CSP technology that is of particular interest in the present research.

TES is used in the system to overcome the hourly intermittency of solar irradiation and thereby increase the energy output from the CSP plant. TES stores the auxiliary thermal energy from the CSP plant for later use. The main advantages of molten-salt TES are the

higher operating temperatures (resulting in higher efficiency) and potentially lower capital costs compared with those of mechanical or chemical storage. Various recent studies have considered integrating molten-salt TES with an SPT system to drive a heat engine [82-85].

Daniele Cocco and Fabio Serra [81] compared the performances of two TES technologies

(two-tank direct and thermocline) for a linear Fresnel CSP plant utilizing organic Rankine- cycle power generation. They found that the two-tank TES had the slightly higher specific energy production. Wang and He [77] used a genetic algorithm to conduct energy and exergy analyses of an MSSPT that derived an sCO2 recompression/reheating Brayton cycle. They found that the optimum outlet temperature of the salt (a mixture of 60% NaNO3 and 40% KNO3) was 565°C, which is the maximum allowable temperature. They explained the temperature limitation of the existing molten-salt as an HTF and suggested a new salt- based HTF that would allow higher outlet temperatures, thereby increasing the energy and exergy efficiencies. To the best of our knowledge, no SPT system has ever been built in

Saudi Arabia. Therefore, there are no available data on cost or performance to compare with the model results presented herein. The cost data used in this study are for plants deployed internationally. SPT plants have been deployed worldwide; a list of ground projects is given in Table 15 in chronological order.

Furthermore, a review of the current literature found a scarcity of studies involving sCO2 Brayton cycles incorporated in SPT systems. The few studies that were found were based on the assumption of a heat source with outputs similar to those of the SPT; they did not evaluate the performance of the sCO2 Brayton cycles after modeling the SPT. The present study developed a model of the dynamic behavior of a CSP system, including optimizing the heliostat layout, receiver, tower height, and TES dispatch. Then, enter the

the performance curve of the advanced sCO2 Brayton cycle into the System Advisor Model

(SAM) [82]. The main aim of this chapter is to model a MSSPT that has a high capacity factor and an optimum LCOE.

Figure 48. Concentrated solar power tower system coupled with thermal energy storage

Table 15. List of solar power tower projects

Turbine Receiver Tower net Heat Transfer Project Name: Location: Start Year Inlet/outlet Height Capacity Fluid Temp (°C) (m) (MW) Planta Solar 10 Spain 11 2007 NA/285 Water 120 Jülich Solar Tower Germany 1.5 2008 NA/680 Air 60 Planta Solar 20 (PS20) Spain 20 2009 NA/301 Water 165 Sierra USA 5 2009 218/440 Water 55 Lake Cargelligo Australia 3 2011 200/500 Water/steam 0 ACME Solar Tower India 2.5 2011 218/440 Water/steam 46 Gemasolar Spain 19 2011 290/565 Molten salt 140 Greenway Turkey 1 2012 NA/550 Molten salt 60 Dahan Power Plant China 1 2012 104/400 Water/Steam 118 ISEGS USA 377 2014 284/565 Water 140 Crescent Dunes (Tonopah) USA 110 2015 287/565 Molten salt 195 Golden Tower China 100 2016 - Molten salt 263 Khi Solar One South Africa 50 2016 - Water/steam 200 SunCan Dunhuang II China 10 2016 - Molten Salt 138 Sundrop Australia 1.5 2016 - Water/Steam 127 Huanghe Qinghai Delingha China 135 2017 - Molten salt - Emalong Australia 1.1 2017 270/560 Liquid sodium 30 NOOR III Morocco 134 2017 - Molten salt - Ashalim Plot B (Megalim) Israel 121 2017 - Water/steam 250 Golmud China 200 2018 - Molten salt - Redstone South Africa 100 2018 288/566 Molten salt - Atacama-1 Chile 110 2018 300/550 Molten salt 243 Yumen II China 50 2018 - Molten salt - Copiapó Chile 260 2019 - Molten salt - DEWA UAE 100 2020 - Molten salt 260 Aurora Australia 135 2020 - Molten salt - MINOS Greece 52 2020 - - - Tamarugal Chile 450 2021 - Molten salt - Likana Chile 390 2021 - Molten salt - Hami China 50 UD - Molten salt - Qinghai Gonghe China 50 UD - Molten salt - DSG China 50 UD - Water/steam SunCan Dunhuang I China 100 UD - Molten salt - Supcon China 50 UD - Molten salt 80 Yumen I China 100 UD - Molten salt - UD: under development

5.2 Mathematical Modeling Approach

5.2.1 Solar Power Tower System

Modeling the CSP system is crucial for rationalizing energy production and increasing plant efficiency. The cost of a CSP plant is roughly 50% of the total capital cost of the CSP-sCO2 Brayton cycle plant, and 40% of the total loss [83]. Therefore, appropriate

CSP optimization is clearly a way of making the technology more effective.

Solar radiation and other weather aspects were derived from the EnergyPlus weather database and imported them into SAM software. Weather data for the city of

Riyadh in Saudi Arabia was used.

The first step in CSP modeling is to calculate the solar position and time. The former is calculated as

푠푖푛 훽 = 푐표푠 (퐿) 푐표푠 (훿) 푐표푠 (퐻) + 푠푖푛 (퐿) 푠푖푛 (훿) (35)

퐻 = (Solar time – 12: 00) × 15/ℎ푟 (36) where 훽 is the solar altitude angle L is the latitude angle, H is the hour angle, and 훿 is the declination angle defined as

360 ( 284 + 푁) (37) 훿 = 23.45 푠푖푛 [ ] 365 where N is the day of the year.

The relationship between solar time (longitude dependent) and standard time is expressed as

푆푇 (푚푖푛) = standard time + ET + 4 ∗ (L푠푡 − Lloc ) (38)

where ST is the standard time, the factor of 4 refers to the four minutes per degree of earth rotation, L푠푡 and Lloc are standard meridian for time zone (in degrees west) and meridian of location (in degrees west), respectively, and ET is the equation of time that determined by the following equation

ET (in minutes) = 9.87 sin(2B°) – 7.73 cos(B°) – 1.5 sin(B°) (39) where B° is defined as

360 ∗ (퐷푎푦 표푓 푡ℎ푒 푦푒푎푟 − 81) B° = (40) 퐵° = 364

Finally, the solar azimuth angle (휙) is determined by

푐표푠 훿 푠푖푛 퐻 (41) 푠푖푛 휙 = 푐표푠 훽

A negative value of the solar azimuth angle means that sun is located east of south, and a positive value meanss that sun is located west of south.

The second step is to design the radial staggered distribution of the heliostats. It is important to design and distribute the heliostats carefully to avoid design losses such as shading and blocking. Shading causes a deficiency in the direct normal irradiance (DNI), whether by a building, tree, or another nearby heliostat. The distance between heliostats is designed to alleviate the heliostats losses and is expressed using a characteristic heliostat diameter DM (see Figure 49):

퐷푀 = DH + desp (42) where DH is the heliostat diagonal as defined in equation (43), and “desp” is any safety separation distance that is necessary for any reason (it is assumed to be zero):

2 2 2 2 (43) 퐷퐻 = √퐻ℎ + 퐻푤 ∗ 푓ℎ = Hh ∗ √1 + 푓ℎ

where 퐻ℎ is the height of the heliostat, and 푓ℎ is the width and height ratio of the heliostat

Figure 49. Distance between heliostats The third step is to calculate the annual performance of the heliostat system. This depends on the losses that adversely affect the optical efficiency of the heliostat field. The optical heliostat-field efficiency can be expressed as

휂표푝푡 = 휂푐표푠 × 휂푖푛푡 × 휂푎푡푡 × 휂푠&푏 × 휂푟푒푓 (44) where 휂푐표푠 is the cosine-effect efficiency, 휂푖푛푡 is the intersection efficiency, 휂푎푡푡 is the atmospheric attenuation efficiency, 휂푠&푏 is the shading and blocking efficiency, and 휂푟푒푓 is the spillage of the heliostat field. These loss parameters are calculated separately; some depend on the design whereas others depend on geographical location. The cosine losses due to the sun and heliostat locations, and can be defined as [22]

(45) 휂푐표푠 = cos(휃푖) = 푃⃗⃗⃗푛 푃⃗⃗⃗푠

where P⃗⃗⃗n is point of sun vector and P⃗⃗⃗s represents the point receiver surface. Another significant factor affecting the optical efficiency is the atmospheric attenuation loss, which is related to the field geographical location, visibility, ambient humidity, and the distance between the receiver and the heliostat. Figure 50 shows the atmospheric attenuation losses at Daggett, USA for two different visibilities.

Figure 50. Atmospheric attenuation losses at Daggett, USA [84], [85]

The atmospheric attenuation efficiency ηatt is calculated as [84], [85][86]:

Loss (%) = 0.6739 + 10.46푅 − 1.70푅2 + 0.2845푅3, 푉푖푠푖푏푖푙푖푡푦 = 23 푘푚 (46) Loss (%) = 1.293 + 27.48푅 − 3.394푅2 + 0.0 푅3, 푉푖푠푖푏푖푙푖푡푦 = 5 푘푚 Loss (%) = 0.99321 − 0.0001176푅 + 1.79퐸 − 8푅2 푉푖푠푖푏푖푙푖푡푦 = 40 푘푚 "푅 ≤ 1000푚"

Loss (%) = exp(−0.0001106푅) 푉푖푠푖푏푖푙푖푡푦 = 40 푘푚 "푅 > 1000푚" { where R is the distance (in kilometers) between the heliostat and the receiver. Another performance loss is that due to the intersection efficiency (휂푖푛푡), which is defined as [86]

. . 1 푥2 + 푦2 (47) 휂푖푛푡 = 2 ∫ ∫ exp (− 2 ) 푑푦 푑푥 2 ∗ π ∗ σtot 2 ∗ 𝜎푡표푡 푥 푦

where σtot is total standard deviation that can be calculated as defined by [52].

2 2 2 2 (48) σtot = 푑퐻푅√𝜎푠푢푛 + 𝜎푏푞 + 𝜎푎푠푡 + 𝜎푡푟푎푐푘

where 𝜎푠푢푛, 𝜎푏푞, 𝜎푎푠푡, and 𝜎푡푟푎푐푘 are the standard deviations due to sun-shape error, beam- quality error, astigmatic error, and tracking error, respectively.

Figure 51. Loss parameters in the heliostat field [22]

The fourth step is to calculate the solar optical receiver efficiency as:

Q̇ net (49) 휂푠푡 = Q̇ st,in where Q̇ st,in is the intercepted solar flux, and Q̇ net is the net useful energy that can be as defined by [52]:

̇ 푄̇푛푒푡 = αR × 푄̇푠표푙푎푟 − (푄푟푎푑 + 푄̇푐표푛푣 + 푄̇푐표푛푑) (50) where αR is coating absorptance, 푄̇푟푎푑, 푄̇푐표푛푣, and 푄̇푐표푛푑 are radiation, convection, and conduction heat losses, respectively.

̇ 4 4 푄푟푎푑 = Fview × A × 휀 × σ × ( 푇푅 − 푇푆 ) (51)

푄̇푐표푛푣 = hconv × A × (TR − 푇푎푚푏) (52) where 휀 is the heliostat emissivity, and σ is the Stefan–Boltzmann constant

The solar useful energy (Q̇ st,in) is defined as:

Qst,in = 휂표푝푡 × DNI × Nhel × Ahel (53) where DNI is the direct normal irradiance, Ahel is the heliostat area, and Nhel is the number of heliostats. The design point of the DNI, which is based on the local weather, is significant because it has a strong effect on both the heliostat field and the receiver. The approach to selecting the DNI as shown in Figure 52 is based on the National Renewable

Energy Laboratory (NREL) method using SAM software [82].

Figure 52. Method for selecting direct normal irradiance

Figure 52 represents the beam irradiance of solar time. The black curve represents the cumulative density function (CDF) of how often the DNI can be observed, and the brown bars represent the probability density function (PDF) of the beam irradiance. An arbitrary DNI value is chosen at 95% CDF, which is recommended by NREL.

The thermal energy storage (TES) capacity is expressed as:

QTES = hrs × Qth푖푛 (54) where “hrs” is the number of hours for which the TES can supply energy to the cycle and

Qth푖푛 is the thermal input of the power cycle.

The concentrated SPT plant and the TES presented in this chapter are modeled and optimized using SAM and SolarPILOT™ [87] developed by NREL.

The basic design parameters of the solar-tower field are based on various studies

[49], [52], [83], [88]; the optimized parameters are listed in Table 16. A detailed analysis of the CSP system optimization is presented below.

Table 16. Meteorological data and basic design variables of the solar-tower field

Decision variables Location (city) Riyadh, Saudi Arabia Location (latitude/ longitude) 24.5°N / 46.5°E Design point day Equinox Heat transfer fluid (HTF) Molten salt Design turbine gross output [MW] 50 Heliostat width [m] 12.84 Heliostat height [m] 9.45 Image error [mrad] 1.3 Direct normal irradiance [W/m2] 960 Fraction of mirror area of heliostat [-] 95.83% Field availability [-] 99% Storage type Two-Tank Design variables Tower height [m] Optimized Receiver height [m] Optimized Receiver diameter [m] Optimized Tank height [m] Optimized Heliostat number [-] Optimized

Heliostat layout (-) Optimized Solar multiple Optimized Thermal Energy storage full-load hours Optimized

5.2.2 Economic Approach

An economic model was developed of MSSPT plant using SAM. System component costs derived from several recent reports on plant data [74], [89]. Table 17 lists the financing parameters and the MSSPT component costs. The LCOE economic metric that is used is based on an advanced method proposed by Stanford [90]. The parameters involved in Stanford’s LCOE calculation are assumed lifetime, depreciation tax shield, system price, system operating and maintenance cost (O&M), capacity factor, investment and production tax credits, discount rate, CO2 emission charge, carbon intensity and fuel cost. Combining these parameters gives the LCOE as:

퐼 + 푂 &푀 + 퐹 ∑푛 푡 푡 푡 푡 (55) 푡−1 (1 + 푟)푡 퐿퐶푂퐸 = 퐸 ∑푛 푡 푡−1 (1 + 푟)푡 where r is the discount rate, n is the assumed lifetime, 퐼푡 is the investment expenditure in year t, 푂푡 is the operating expenditure in year t, 푀푡 is the maintenance expenditure in year t, 퐹푡 is the fuel cost in year t, and 퐸푡 is the energy production in year t.

Table 17. Financing parameters and baseline component costs

Financing parameters Comment Analysis period 25 years - Inflation rate 2.5% - Real discount rate 8% - Salvage value 0 - Loan term 20 years - Loan rate 8% - Contingency 7% of component capital cost Taxes 0% No tax in Saudi Arabia Component Cost [82] Land cost $10,000/acre EPC & Owner Costs 11% of direct cost Tower / receiver - Calculated in equations (56) and (57) Tower cost fixed $3,000,000 Tower cost scaling exponent 0.0113 Receiver reference cost $103,000,000 Receiver reference area 1,571 m Receiver cost scaling exponent 0.7 Thermal energy Storage $24/kWht Power block 1,140 kWe Balance of plant 350/kWe Solar field $150/m2 Site improvements $16/m2 Variable O&M cost $3.5/MWh Fixed O&M costs $65/kW-yr

The total tower and receiver costs are obtained using equations (56) and (57) as defined by the NREL’ SAM software [82]:

푅 퐻 푇퐶푆퐸∗(푇 − ℎ+ ℎ) (56) 푇표푡푎푙 푡표푤푒푟 푐표푠푡 ($) = 퐹푇퐶 x 푒 ℎ 2 2

퐴 푅퐶푆퐸 (57) 푇표푡푎푙 푟푒푐푒푖푣푒푟 푐표푠푡 ($) = 푅푅퐶 x ( 푅 ) 퐴푅푅 where 퐹푇퐶 represents the fixed tower costs, TCSE is the tower-cost scaling exponent, 푇ℎ is the tower height, 푅ℎ is the receiver height, 퐻ℎ is the heliostat height, RRC is the receiver reference cost, 퐴푅 is the receiver area, 퐴퐴푅 is the receiver reference area, and RCSE is the receiver-cost scaling exponent.

5.3 Result and Discussion

The monthly DNI, diffuse horizontal irradiance (DHI), and global horizontal irradiance (GHI) are shown in Figure 53.

Figure 53. Monthly solar irradiance in Riyadh, Saudi Arabia

It is important to optimize the heliostat positions appropriately because they relate directly to the efficiency of the solar plant and constitute the largest fraction of the system cost. The solar multiple is important to specify the size of the heliostat field as a function of the sCO2 power cycle rated capacity and TES. A smaller solar multiple than necessary yields insufficient thermal energy to the sCO2 plant, thereby reducing the capacity factor.

By contrast, a higher solar multiple than necessary means more wasted thermal energy due to the excess energy at certain times, thereby increasing the LCOE. Therefore, a parametric analysis is conducted to choose the most significant design variables (solar multiple and storage capacity) effectively with regard to the capacity factor and LCOE. Figure 54 and

Figure 55 show the effects of full-load storage hours and solar multiple on the LCOE and capacity factor, respectively, with all the other decision variables held constant.

0.22 SM = 1.5

] SM = 2.0 h 0.2 SM = 2.5

W SM = 3.0

k SM = 3.5

$ SM =4.0

[ 0.18

i 0.16

l 0.14

0.12

C 0.1

e Design point

i 0.08

e 0.06

4 6 8 10 12 14 16 18 20 22 24 26 28 30

Thermal Energy Storage [hrs] Figure 54. Levelized cost as a function of solar multiple and size of thermal energy storage

80 SM = 1.5 SM = 2.0 SM = 2.5 70 SM = 3.0 SM = 3.5 SM =4.0

60 Design point

Capacity Factor [%] Capacity Factor

20 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Thermal Energy Storage [hrs] Figure 55 Capacity factor as a function of solar multiple and size of thermal energy storage The design point for the full-load hours of storage and the solar multiple is shown in Figure 55. The optimal design values for TES and solar multiple are 13 hrs and 3, respectively. The solar multiple refers to the ratio between the solar thermal energy collected at the design point and the installed power-cycle capacity. The capacity factor refers to the ratio between the average solar thermal energy actually generated and the rated peak power.

The radially staggered method is used to distribute the heliostats appropriately using the SolarPILOT optimization algorithm [87]. A drawback of this algorithm is that it is computationally expensive because it evaluates each heliostat individually rather than evaluating a larger groups of heliostats. The solar-field cost accounts for the largest fraction

(about 20-35%) of the total system cost, so the field geometry must be optimized appropriately to improve the optical efficiency and therefore reduce the solar-field cost.

The optimized heliostat-field layout is shown in the Figure 56 along with the associated optical efficiencies.

Figure 56. Heliostat-field layout with optical efficiency (colors) As shown in Figure 56, heliostat mirrors are distributed evenly around the solar tower stimulatingly with the optimization of tower height, receiver height, and receiver diameter. In total, 5,388 heliostat mirrors are installed with an average yearly optical efficiency of 67.3%. Losses that adversely affect the optical efficiency (i.e.,., blocking, shadowing, and atmospheric attenuation) are taken into account when optimizing the field geometry. Figure 57 - Figure 61 show the main sources of solar-field losses.

Figure 57. Atmospheric attenuation efficiency of each heliostat As shown in Figure 57, the average yearly heliostat atmospheric attenuation efficiency is 93.8%. The atmospheric attenuation efficiency (radiation losses) is affected by both heliostat–receiver distance and sky visibility. As can be seen in Figure 57, the heliostat atmospheric attenuation efficiency decreases with the distance increase from a heliostat to the receiver. Heliostats that are 1.25 km or more away from the receiver loss about 10% of their efficiency due to atmospheric attenuation losses. Therefore, the recommendation is to install heliostats close to the receiver as possible. However, shading and blocking losses may increase with the decrease of heliostat-receiver distance. Overall, it is important to make the correct choice regarding the tradeoff between conflict factor losses.

Figure 58. Cosine efficiency of each heliostat Figure 58 shows the average total heliostat cosine efficiency is 81.3%. The cosine efficiency is affected by sun position and the heliostat-receiver distance. A Larger solar field results in lower cosine efficiency, so making smaller solar fields preferable. To reduce the solar-field size, heliostats can be distributed properly closer to each other, which is expected to cause a shading and blocking losses in some cases, so taken into consideration the incident angle for each heliostat at each hour is necessary. However, a tradeoff between the cosine and blocking/shading efficiencies is necessary to increase the total field efficiency. Of all the losses on the solar field, the cosine losses are the highest. An

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appropriate radially staggered distribution is essential to minimize the cosine losses and hence increase the field efficiency.

Another major factor affecting the solar field comes in the form of the shading and blocking losses, which are shown in Figure 59 and Figure 60, respectively.

Figure 59. Shading efficiency of each heliostat

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Figure 60. Blocking efficiency of each heliostat The total shading and blocking efficiencies are 99.7% and 100% respectively.

Shading and blocking losses are functions of the distance between heliostats, tower height, and incident angle [Power From]. A shading loss refers to part of a heliostat mirror being in the shadow of an adjacent heliostat, thereby depriving the receiver of some of sun rays.

A blocking loss refers to a portion of incident solar rays that blocked the reflected radiation by a nearby heliostat. As mentioned above, attempting to reduce the solar-field is order to reduce cosine and attenuation losses, and land costs, but doing so increase the shading and blocking losses. Therefore, during the optimization process, a tradeoff optimization among the most significant conflict factors that affect the field efficiency is conducted.

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Figure 61. Intercept efficiency of each heliostat

As can be seen in Figure 61, the total average heliostat intercept efficiency is 97.7%.

The intercept factor is the amount of solar flux reflected by a heliostat and captured by the receiver. Intercept loss is caused by surface nonuniformity (angle error), sun tracking, solar flux distribution, and receiver size. Also, Figure 61 shows that heliostats to the north have lower efficiencies than those to the west and east. Basically, higher intercept efficiency means higher optical efficiency and therefore higher performance. However, the receiver lifetime is expected to be reduced if the concentrated solar flux density exceeds the maximum value. Higher intercept efficiency means higher concentrated solar flux density focused on the central receiver, which may degrade the receiver. Careful design is necessary to extend the receiver lifetime and reduce the intercept (spillage) losses [102-

103].

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Table 18. Breakdown of yearly heliostat-field efficiency

Heliostat-field efficiency Case 1 Cosine efficiency [-] 81.3% Blocking efficiency [-] 99.7% Shading efficiency [-] 100% Atmospheric attenuation efficiency [-] 93.8% Intercept efficiency [-] 97.7% Optical efficiency [-] 67.3% The sub-system cost is derived from internationally deployed data. The CSP-TES systems to utilize the sCO2 recompression Brayton cycle costs $0.1078/kWh; without a

TES, the system costs $0.20/kWh. This relatively large LCOE reduction shows the importance of integrating TES with CSP. CSP surpasses other renewable energy sources because TES is readily coupled into the operation, thereby increasing the capacity factor and reducing the cost. To achieve low-cost electricity, the total system cost is broken down to locate the highest fractional contribution to the capital cost.

Figure 62. Breakdowns of capital cost

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As shown in Figure 62, the heliostat field accounts for 31% of the system’s capital cost, followed by the power block (15%) and the receiver (10%), respectively. To reduce the LCOE, attentions should paid directly to improving the solar field. Sandia

National Laboratories (SNL) [93] proposed various technology improvement opportunities

(TIOs) to reduce the LCOE of the SPT plants. The three main TIOs to reduce the LCOE by reducing both capital and O&M costs involved glass/metal heliostats, stretched- membrane (SM) heliostats, and innovative concepts. For the glass/metal heliostat TIOs, experts recommended two aspects that could reduce the heliostat cost: (i) improve the driver cost and (ii) examine the pipe in the pipe driver. For the SM-heliostat TIO, the recommendation was to evaluate the economy of a large solar-tower module versus smaller modules. For the innovative-concepts TIO, the recommendations were to consider using new low-cost materials and to examine single-mirror technologies and hydraulic drives.

Table 19. Summary of the optimized model

Value Comment Location (city) Riyadh, Saudi Arabia 24.5°N/46.5°E Direct normal irradiance [W/m2] 960 7.65 kWh/m2/day Cycle thermal power [MWt] 108.7 Design turbine gross output [MWe] 50 sCO2 Brayton cycle (η = 46%) Heat transfer fluid Molten salt 60% NaNO3 40% KNO3 Inlet/outlet fluid temp [°C] 287/565 Stainless AlSl316 Storage type Two-Tank ∆T = 223 °C Thermal energy storage capacity [MWht] 1,413 26.7m diameter 13m height Thermal energy storage full load [h] 13 Thermal energy storage volume [m3] 7264 2 Heliostat number [-] 5,338 Ah = 108 m (12.84w * 9.45h) Total plant land area [km2] 3.32 Solar multiple 3 Tower/receiver height [m] 159.8/13.8 Capacity factor [-] 61.1% 90% availability Installed cost [$/kW] $7,700/kW LCOE [$/kWh] $0.1078/kWh

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A detailed analysis has been conducted to evaluate the impact integrating TES with

CSP to mitigate the intermittent solar source. Integrating a TES with a SPT shows a high positive impact on both system LCOE and production, as shown in Table 20 and Figure

63.

Table 20. Economic and performance summary of different thermal energy storage (TES) options Case 1 Case 2 Case 3 Case 4 Case 5 TES option No TES 4 hours 8 hours 12 hours 16 hours Solar multiple 1.2 1.8 2.3 3 3.5 Capacity factor [-] 18.9% 34% 45.9% 59% 70.4% Installed cost [$/kW] $4,118/kW $5,214/kW 6,260/kW $7,488/kW $9,100/kW LCOE [$/kWh] $0.2045/kWh $0.14/kWh $0.121/kWh $0.11/kWh $0.1112kWh

Figure 63. Breakdown of the solar power tower system cost for different thermal energy storage capacity

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Figure 64. Breakdown of the solar power tower system cost fraction for different thermal energy storage capacity

5.4 Conclusions

The primary goal of this research has been to develop comprehensive CSP models in System Advisor Model (SAM), Engineering Equation Solver (EES), and SolarPoilot to study the feasibility of an SPT plant with a sCO2 power cycle. The models optimize the heliostat field and the TES dispatch and calculate the solar-field power output for continuous year-round operation. The valuable outcomes of the models developed are listed below.

First, an adequate molten-salt TES incorporated into SPT plant (TES-CSP) shows a strong positive impact on plant performance and economy relative to non-TES CSP. In addition, there is a 50% reduction in the LCOE from $0.209/kWh (non-TES CSP) to

$0.1078/kWh (TES-CSP). Therefore, CSP-TES is a practical approach that is technically and economically feasible.

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Second, a CSP system with an sCO2 power plant is economically and technically viable because it has a high capacity factor and provides a competitive LCOE. The CSP- sCO2 price per kWh is expected to fall further with improved receiver outlet temperature limit. A study by SNL expected an 8% reduction in the LCOE by increasing the nitrate salt outlet temperature limit to 650°C [94].

Third, molten salt (60% sodium nitrate (NaNO3) + 40% potassium nitrate (KNO3)) is suitable in the system as an HTF, reviver coolant, and thermal storage medium and technical and economic benefits (i.e. it is not toxic, has high heat capacity, and is compositionally stable). However, all equipment with which the molten salt comes into contact must be trace-heated and thermal insulated to avoid salt freezing (the salt freezes at 230°C).

Fourth, the heliostats contribute the highest fraction of the capital cost, which constitutes roughly 50% of the total system cost. More technical attentions should be paid to heliostats technologies improvements to reduce the SPT plant cost.

Finally, Riyadh in Saudi Arabia is a suitable city for CSP tower plants because it offers the key success factors. First, the DNI is relatively high (the yearly average is around

7.65 kWh/m2/day) and the yearly average wind speed is normal (~ 3 m/s). Second, introducing solar energy to Saudi Arabia community is part of the adapting to new Saudi vision 2030, which is part of economic diversification plans away from oil that aim to promote the use of renewable energy.

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CHAPTER VI

CONCLUSIONS AND FUTURE RECOMMENDATIONS

6.1 Conclusions

In this dissertation, a comprehensive efficient thermodynamic model developed based on a computational technique using constant conductance (UA) to represent heat exchanger performance in order to improve the accuracy of sCO2 analysis. An efficient heat exchanger modeling technique has been used to accommodate the sharp CO2 properties alteration near critical point, which each heat exchanger in the power cycles is divided into sub-heat exchangers. Then each sub-heat exchanger modeled independently.

A comparative analysis of four advanced cycles are executed based on three parametric analysis: 1) pressure ratio, 2) total conductance, and 3) maximum and minimum operating temperature. Parametric analysis suggests that designing for higher inlet temperature or coder inlet compressor have a positive impact on the thermal efficiency and power output.

Also, the results from chapter 3 suggest that total conductance (UA) has to be fixed for all cycles for an appropriate comparative analysis in order to compare them on an equivalent basis. The finding indicate that recompression sCO2 achieved the highest efficiency and power output under different operating condition.

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To enhance the performance of sCO2, a newly-conceived combined power cycle is proposed in chapter 4. The combined power cycle consists of a topping recompression sCO2 Brayton cycle and a bottoming split flow tCO2 Rankine cycle. Multi-objective optimizations based on genetic algorithm were used to maximize the power output and thermal efficiency. The proposed power cycle aim is to improve the overall thermal efficiency by minimizing internal and external irreversibilities, and waste heat as a consequence of the Second Law. The proposed new cycle improves overall thermal efficiency by 6% compared to the stand alone recompression configuration, and by 3% compared to a simple tCO2 Rankine cycle.

To study the feasibility of a CSP plant with a sCO2 power cycle, a comprehensive thermos-economic model is developed and the dynamic behaviors are studied, including the heliostat layout, tower and receiver optimization, and TES dispatch optimization. The findings show that CSP-TES to drive sCO2 power cycle is technically and economically feasible. Also, the findings indicate that molten salt TES has a positive influence on the system cost and performance. Technical developments are needed to reduce the LCOE of the CSP-sCO2 system to be competitive with the conventional power plants.

6.2 Future Recommendations

6.2.1 Pressure Drop

To make the power cycles calculation more accurate, a further step of calculating the pressure drop through the connection tubes and heat exchangers is recommended.

Pressure drop occurs in any heat exchanger in the flow direction, which has an adverse effect on the system’s component geometry. Correctly evaluating pressure drops through

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the system leads to an appropriate selection of heat exchangers. The main two types of pressure drops (local pressure drop, frictional pressure drop) should be taking into account.

The frictional pressure drop for internal flow (tubes) is expressed as:

푓 (58) Δ푃 = 2 퐿 𝜌 푉푚̇ (퐷) ( 2 )

where 푓 is the Moody-friction factor (obtained from a correlation), 푉푚̇ is the mean velocity of the flow, 𝜌 is the fluid density, D is the tube diameter, and L is the tube length.

There are many generic correlations to determine the friction factor depending on the geometries, and flow conditions.

For laminar flow (푅푒 < 2100)

64 (59) 푓 = 푅푒

Where Re is the Reynolds number that can be defined as:

𝜌 푉푚 퐷 (60) 푅 = 푒 푉

The main flow velocity is calculated in equation (61)

푚̇ (61) Vm = 𝜌 ∗ 퐴푐

where 퐴푐 is the tube cross-sectional area, 푚̇ is the mass flow through the tube.

The local pressure drops which occur on the entrance and exit is expressed as [34]

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푉2 (62) Δ푃 = 퐶 𝜌 2 where V is the local velocity, and C is the local loss coefficient. The local loss coefficient.

6.2.2 Economic Calculating

Economic analysis of the sCO2 system and concentrated solar power system is recommended to evaluate the system against the basic conventional system. Three economic metrics should be taken into account for evaluation purpose: 1) Levelized Cost of Electricity (LCOE) 2) Internal Rate of Return (IRR), and 3) Net Present Value (NPV).

6.2.2.1 Levelized Cost of Electricity (LCOE)

Levelized Cost of Electricity is the assumed lifetime all-in cost of the net present value divided by the system energy production. It is important to use LCOE when comparing systems in different operating technologies.

The Levelized Cost of Electricity can be calculated by:

푇표푡푎푙 푙푖푓푒푡푖푚푒 푐표푠푡 ($) 푃 − 푇 + 퐶 − 푆 (63) 퐿퐶푂퐸 = = 푇표푡푎푙 푙푖푓푒푡푖푚푒 푒푛푒푒푟푔푦 푝푟표푑푢푐푡푖표푛 (푘푊ℎ) 퐸

Where P is the initial project cost, T represent the depreciation tax shield, C is the system annual operating cost, S is the salvage cost, and E is the electric production.

An advanced method to calculate the LCOE is proposed by Stanford [90].

Parameters included in the Stanford LCOE calculation are: assumed lifetime, depreciation tax shield, system price, system operating and maintenance cost, capacity factor, investment and production tax credits, discount rate, CO2 emission charge, Carbon

Intensity and fuel cost. Adding these parameters together yields the LCOE to equation to be:

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퐼 + 푂 + 푀 + 퐹 ∑푛 푡 푡 푡 푡 (64) 푡−1 (1 + 푟)푡 퐿퐶푂퐸 = 퐸 ∑푛 푡 푡−1 (1 + 푟)푡

where r represents the discount rate, n represents the assumed lifetime, 퐼푡 represents the investment expenditures in year t, 푂푡 represents the operating expenditures in year t,

푀푡 represents the maintenance expenditures in the year t, 퐹푡 represents the fuel cost in year t, and 퐸푡 represents the energy production in year t.

6.2.2.2 Net Present Value (NPV)

Net present value (NPV) is an economic metric that measures the present value of the investment’s future net cash flow. It involves the calculation of the annual negative and positive cash flow cost for the investment period. The project has to have a positive NPV to be accepted, which means the present value of the cash inflow has to be greater than the present value of the cash outflow.

∑푁 퐶퐹 퐶퐹 퐶퐹 퐶퐹 (65) 푁푃푉 = 푛=0 푛 = 0 = 퐶퐹 + 1 + 2 +. . . + 푛 (1 + 푟)푛 0 (1 + 푟)1 (1 + 푟)2 (1 + 푟)푛 where N represents the lifetime project in years, NPV represents the net present value, CF represents the cash flow, n represents each period (year), 퐶퐹0 represents the initial project cost, and r represent the discount rate.

6.2.2.3 Internal Rate of Return (IRR)

Internal rate of return (IRR) is another economic metric used to determine the rate of return of an investment. By calculating the IRR, an investor finds out whether the investment is profitable or not. If the IRR is above the interest rate then the project is profitable. It simply works by setting the positive and negative net present values of the cash flow from the project equal to zero.

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∑푁 퐶퐹 퐶퐹 퐶퐹 퐶퐹 (66) 푁푃푉 = 푛=0 푛 = 0 = 퐶퐹 + 1 + 2 +. . . + 푛 (1 + 퐼푅푅)푛 0 (1 + 퐼푅푅)1 (1 + 퐼푅푅)2 (1 + 퐼푅푅)푛 where N represents the lifetime project in years, NPV represents the net present value, CF represents the cash flow, n represents each period (year), 퐶퐹0 represents the initial project cost, and IRR represents the internal rate of return.

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