Thermo-economic assessment of supercritical CO2 power cycles for concentrated solar power plants

Department of Energy Enegineering School of Engineering - ETSI University of Seville Thermo-Economic Assessment of Supercritical CO2Power Cycles for Concentrated Solar Power Plants Francesco Crespi Seville, October 2019 Research work submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy PhD programme in Energy, Chemical and Environmental Engineering Department of Energy Enegineering School of Engineering - ETSI University of Seville Thermo-Economic Assessment of Supercritical CO2 Power Cycles for Concentrated Solar Power Plants Author: Francesco Crespi Supervisor: Prof. David Sánchez Martínez, University of Seville Co-Supervisor: Prof. Tomás Sánchez Lencero, University of Seville Seville, October 2019 Research work submitted to the Department of Energy Engineering, School of Engineering, of the University of Seville in partial fulfillment of the requirements for the degree of Doctor of Philosophy Non al denaro, non all’amore né al cielo... ...ma ai miei genitori. Senza di voi tutto questo non sarebbe stato possibile. Acknowledgements I wish to acknowledge the main supervisor of this thesis, Prof. David Sánchez, for the long time motivation, guidance and help throughout the course of my doctoral studies. I am also grateful to Dr. Tomás Sánchez, second supervisor of this thesis, for his support from the very beginning of my research. I would also like to express my gratitude for the academic support received at the University of Seville and to sincerely thank my colleagues (and friends) at the Thermal Power Group (GMTS). I am also grateful to all the people I’ve worked with at TU Delft, in particular to Sebastian Bahamonde, for his precious help and advice during my short visit to The Netherlands. Above all, I am grateful to my family for their continuous support and confidence. Last but not least, I sincerely thank my friends here in Seville and in Italy. This would have not been possible without their help, support and understanding. Seville, 23th October 2019 F. C. i Resumen Los sistemas de concentración solar basados en campos de heliostatos y receptor central (comúnmente denominados sistemas de torre) permiten alcanzar grandes relaciones de concentración, asociadas a elevadas temperaturas del fluido de trabajo empleado en el receptor. La utilización de este tipo de sistemas de concentración en combinación con ciclos de potencia basados en dióxido de carbono (CO 2 ) en condiciones supercríticas es una forma realmente prometedora de maximizar la eficiencia total de una planta termosolar de concentración (solar-to-thermal-to-electricity), reduciendo al mismo tiempo su tamaño y el coste de la electricidad (Levelized Cost of Electricity). A la vista de semejante interés, en los últimos quince años, se han publicado gran cantidad de artículos científicos sobre este tema, se han organizado varios congresos internacionales y se ha construido un número significativo de instalaciones experimentales en todo el mundo, hasta el punto de que el ciclo de potencia de sCO 2 , se considera hoy en día como una de las alternativas más interesantes para un producir potencia eléctrica a partir de un buen número de fuentes de energía, entre ellas la energía solar. No obstante, el rápido crecimiento del interés de la comunidad científica e industrial alrededor de los ciclos de sCO 2 se ha basado inevitablemente en una búsqueda no estructurada de ciclos más eficientes y técnicamente viables, más allá de los propuestos originalmente por los precursores de la tecnología: Gianfranco Angelino y Edward Feher. Observando este escenario, la presente tesis se centra en el análisis de los fundamentos termodinámicos del ciclo de potencia de CO2supercrítico, con el objetivo de proporcionar una vía estructurada para el estudio de viabilidad termo-económica de este último aplicado a centrales termosolares de concentración. De este modo, se pretende responder a la pregunta de si la tecnología termosolar para producción de energía eléctrica puede llegar a ser competitiva con otras tecnologías convencionales a medio y largo plazo, en un mercado carente de subsidios e incentivos. Con estas consideraciones, este documento se estructura en cuatro secciones claramente definidas. En primer lugar, se realiza una revisión exhaustiva del estado del arte de la tecnología de ciclos de potencia de CO 2 supercrítico, no solamente revisando la información disponible en la literatura científica sino, también, proponiendo una nueva categorización basada en las características termodinámicas intrínsecas de estos ciclos, con el objetivo de detectar su potencial real y descartar aquellos ciclos que no resultan de interés para la aplicación considerada. De esta revisión se obtiene una preselección de doce ciclos de potencia. En segundo lugar, se presenta una comparación puramente termodinámica de los ciclos preseleccionados, tomando como parámetros de comparación (key performance indicators) el iii List of Figures 1.1 Global greenhouse gas emissions scenarios (adapted from [1]). . . . . . . . . . . 2 1.2 World population growth, 1750-2100 (adapted from [1]). . . . . . . . . . . . . . . 3 1.3 Evolution of World population and World Gross Domestic Product from 1850 to 2015 (based on data from [1]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 World distribution of GDP and Consumption of Electricity. . . . . . . . . . . . . 4 1.5 World Primary Energy Consumption in Mtoe (obtained from [2]). . . . . . . . . 5 1.6 World Energy Consumption by fuel in Btu (obtained from [3]). . . . . . . . . . . 5 1.7 Foreseen development of electricity generation under the IEA "Current Policies" and the Energy [r]evolution case (obtained from [4]). . . . . . . . . . . . . . . . . 7 1.8 Schematic representation of a typical SPT plant with TES (obtained from [5]). . 7 1.9 Heat balance of a solar receiver. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.10 Receiver and Carnot cycle efficiencies ( ηrec and ηC ar not ) and their combined effect as a function of receiver temperature and CR. . . . . . . . . . . . . . . . . . 10 1.11 Dependence of cycle thermal efficiency ( ηth ) on turbine Inlet temperature, taking into account four different cycles. Minimum cycle temperature is set to 35 º C in all cases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 1.12 Performance of different carbon dioxide cycles in comparison with double reheat steam cycles and inter-cooled Brayton cycles at high turbine inlet pressure (300 atm) [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.1 Stand-alone R1 cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2 Standalone R1-IC cycles. General layout (top) and particular embodiments (center and bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.3 Stand-alone R1-RH cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4 Stand-alone R1-IC-RH cycles. General layout (top) and particular embodiments (center and bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5 Stand-alone R1-SFH and R1-SFE cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.6 Stand-alone R2 cycles. General layout (top) and particular embodiment (bottom). 29 2.7 Stand-alone R2-SFC cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.8 Stand-alone R2-IC cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.9 Stand-alone R2-IC-SFC cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 xi List of Figures 2.10 Stand-alone R2-RH-SFC cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.11 Stand-alone R2-SFH and R2-SFC-SFH cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.12 Stand-alone R2-SFHE cycles. General layout (top left) and particular embodiments (top right and bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.13 Stand-alone R2-SFC-SFE and R2-IC-SFC-SFE cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.14 Stand-alone R2-IC-RH-SFC cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.15 Stand-alone R3-SFC (left) and R3-IC-SFC (right) cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . 36 2.16 Stand-alone R3-SFC-SFHE (left) and R3-SFC-SFH (right) cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . 37 2.17 Stand-alone R3-IC-RH-SFC-SFE cycles. General layout (top) and particular embodiment (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.18 Stand-alone R3-IC-RH-SFC-SFHE cycles. General layout (top) and particular embodiment (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.19 Stand-alone RH and SFC-SFH cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.20 Stand-alone IC and IC-RH cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 2.21 Topping R3-SFC cycle. General layout (top) and particular embodiments (bottom). 43 2.22 R3-IC-SFC-SFH Topping cycles. General layout (top) and particular embodiment (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.23 Simple and R1-SFH bottoming cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.24 R1-SFHE and R1-SFC-SFH Bottoming cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.25 R2-SFHE Bottoming cycles. General layout (top) and particular embodiments (center and bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.26 R2-IC-SFHE Bottoming cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.27 R2-SFC-SFHE Bottoming cycles. General layout (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.28 R2-IC-SFH-SFHE and R3-SFHE Bottoming cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.29 R3-RH-SFC and R3-SFC-SFHE Bottoming cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.30 R3-RH-SFC-SFHE Bottoming cycles. General layout (top) and particular embodiment (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.31 Nested simple (left) and R1-SFH (right) cycles. General layouts (top) and particular embodiments (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.32 Stand-alone cycles. Summary of thermal efficiencies (Correspondence of cycle number in Table 2.4). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 xii List of Figures 2.33 Influence of turbine inlet temperature on thermal efficiency for the stand-alone cycles considered. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.34 Combined cycles. Summary of sCO 2 and overall thermal efficiencies (Correspondence of cycle number in Table 2.5). . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.35 Chronological development of sCO 2 cycles: thermal efficiencies and Turbine Inlet Temperatures. Cycle numbers refer to Table 2.10, and are different from those in Table 2.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.1 Layouts of selected cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.2 Diagrams of Thermal Efficiency vs. Specific Work, as originally proposed by Angelino [6]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 3.3 Relationship between isentropic and polytropic efficiency in compressors and turbines (taken from [7]). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.4 Dependence of thermal efficiency on split-flow Fraction, considering a Recompression cycle operating at 550ºC and 20 MPa (taken from [8]). . . . . . . . . . . 71 3.5 Dependence of split-flow fraction and thermal efficiency on maximum pressure for different configurations. Turbine inlet temperature is set to 750ºC. . . . . . . 72 3.6 Verification of the code: comparison between original ( ηth,0 ) and computed thermal efficiencies (ηth). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.7 Dependence of thermal efficiency upon compressor inlet temperature and pressure for different cycle layouts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.8 ηth vs Wsdiagrams for the Simple Recuperated cycle. . . . . . . . . . . . . . . . . 77 3.9 ηth vs Wsdiagrams for the Transcritical CO2 cycle. . . . . . . . . . . . . . . . . . 77 3.10 ηth vs. Wsdiagrams for the Precompression cycle. . . . . . . . . . . . . . . . . . . 78 3.11 ηth vs. Wsdiagrams for the Recompression cycle. . . . . . . . . . . . . . . . . . . 78 3.12 ηth vs. Wsdiagrams for the Recompression+RH+IC cycle. . . . . . . . . . . . . . 79 3.13 ηth vs. Wsdiagrams for the Partial Cooling cycle. . . . . . . . . . . . . . . . . . . 79 3.14 ηth vs. Wsdiagrams for the Partial Cooling + RH cycle. . . . . . . . . . . . . . . . 80 3.15 ηth vs. Wsdiagrams for the Schroder-Turner cycle. . . . . . . . . . . . . . . . . . 80 3.16 ηth vs. Wsdiagrams for the Double Reheated Recompression cycle. . . . . . . . . 81 3.17 ηth vs. Wsdiagrams for the Allam cycle. . . . . . . . . . . . . . . . . . . . . . . . . 81 3.18 ηth vs. Wsdiagrams for the Matiant cycle. . . . . . . . . . . . . . . . . . . . . . . 82 3.19 ηth vs. Wsdiagrams for the Quasi-Combined cycle. . . . . . . . . . . . . . . . . . 82 3.20 Comparison of cycles operating at TIT=550 ºC and TIT=750ºC. . . . . . . . . . . 84 3.21 Comparison of cycles operating at TIT=950ºC and TIT=1150ºC. . . . . . . . . . . 85 3.22 Comparison of cycles operating at TIT=950 º C. Operating conditions yielding recuperators with hot inlet temperatures higher than 800ºC have been removed. 86 3.23 Comparison of cycles operating at TIT=1150 º C. Operating conditions yielding recuperators with hot inlet temperatures higher than 800ºC have been removed. 87 3.24 Carnot Factor comparison of cycles operating at TIT=550ºC and TIT=750ºC. . . 88 3.25 Carnot Factor comparison of cycles operating at TIT=950 º C and TIT=1150 º C. Operating conditions yielding recuperators with hot inlet temperatures higher than 800ºC have been highlighted in red. . . . . . . . . . . . . . . . . . . . . . . . 89 3.26 Comparison of cycles operating at TIT=750 º C, showing envelope curve for 40 MPa and margin for future performance enhancement. . . . . . . . . . . . . . . 90 4.1 Solar Field Cost function as produced by SAM. . . . . . . . . . . . . . . . . . . . . 96 xiii List of Figures 4.2 Solar Tower Cost function as produced by SAM. . . . . . . . . . . . . . . . . . . . 97 4.3 Solar Receiver Cost function as produced by SAM. . . . . . . . . . . . . . . . . . 97 4.4 Cost of Thermal Energy Storage system. . . . . . . . . . . . . . . . . . . . . . . . . 99 4.5 Section of a counter-flow PCHE. Taken from [9]. . . . . . . . . . . . . . . . . . . . 99 4.6 Section of the counter-flow PCHE taken into account in the in-house model. Dc , Pcand tcare channel diameter, pitch and plate thickness. . . . . . . . . . . . . . 100 4.7 Maximum allowable mechanical stresses of materials employed in HX design, as a function of temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4.8 Forces on a cascade of turbine blades. . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.9 ηth and ∆Tsolar as a function of peak cycle pressure. . . . . . . . . . . . . . . . . 105 4.10 OCC and PB costs as a function of peak cycle pressure. . . . . . . . . . . . . . . . 106 4.11 Cumulative probability distribution of Overnight Capital Costs per kilowatt. All cycles (see Figure 3.1 to identify labels). . . . . . . . . . . . . . . . . . . . . . . . . 110 4.12 Cumulative probability distribution of Overnight Capital Costs per kilowatt. Close-up of Figure 4.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 4.13 Breakdown of Capital Costs. Labels refer to Figure 3.1. . . . . . . . . . . . . . . . 111 4.14 Breakdown of Power Block Costs. Labels refer to Figure 3.1. . . . . . . . . . . . . 112 4.15 Thermo-economic comparison of supercritical CO2cycles. . . . . . . . . . . . . 113 4.16 Thermo-economic comparison of supercritical CO 2 cycles. Trade-offs between key figures of merit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 A.1 Cross-sectional area of the counter-flow PCHE: actual heat exchanger and model. 126 A.2 Sub-HX model with counter-flow configuration [10]. . . . . . . . . . . . . . . . . 127 A.3 Thermal resistance in a subdivision of a PCHE. . . . . . . . . . . . . . . . . . . . 128 A.4 Flow chart of the PCHE design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 A.5 Predicted outlet temperatures of the selected recuperator. . . . . . . . . . . . . . 132 A.6 Average Reynolds number on both sides as predicted by the PCHE model at various load settings. In this figure, the hot side of the heat exchanger flows from left to right while the cold side of the heat exchanger flows leftwards. . . . . . . 132 B.1 Pressure-enthalpy and Enthalpy-entropy diagrams of the Partial Cooling cycle at partial load considering Inventory control strategy. . . . . . . . . . . . . . . . . 136 B.2 Pressure-enthalpy and Enthalpy-entropy diagrams of the Partial Cooling cycle at partial load considering By-pass control strategy. . . . . . . . . . . . . . . . . . 137 B.3 Pressure-enthalpy and Enthalpy-entropy diagrams of the Partial Cooling cycle at partial load considering Temperature control strategy. . . . . . . . . . . . . . . 138 B.4 Pressure-enthalpy and Enthalpy-entropy diagrams of the Partial Cooling cycle at partial load considering the best control strategy, a combination of Inventory and By-pass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 B.5 Partial load performance of compressor C1 in the Partial Cooling cycle - part 1. The three different control strategies are considered. . . . . . . . . . . . . . . . . 139 B.6 Partial load performance of compressor C1 in the Partial Cooling cycle - part 2. The three different control strategies are considered. . . . . . . . . . . . . . . . . 140 B.7 Partial load performance of compressor C3 in the Partial Cooling cycle - part 1. The three different control strategies are considered. . . . . . . . . . . . . . . . . 140 B.8 Partial load performance of compressor C3 in the Partial Cooling cycle - part 2. The three different control strategies are considered. . . . . . . . . . . . . . . . . 140 xiv List of Figures B.9 Partial load performance of compressors C1 and C3 in the Partial Cooling cycle for Inventory control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 B.10 Partial load performance of compressors C1 and C3 in the Partial Cooling cycle for By-pass control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 B.11 Partial load performance of compressors C1 and C3 in the Partial Cooling cycle for Temperature control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 B.12 Part-load performance of compressors C1 and C3 in the Partial Cooling cycle when using the best control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . 142 C.1 Pressure-enthalpy and Enthalpy-entropy diagrams of the Allam cycle at partial load considering Inventory control strategy. . . . . . . . . . . . . . . . . . . . . . 144 C.2 Pressure-enthalpy and Enthalpy-entropy diagrams of the Allam cycle at partial load considering By-pass control strategy. . . . . . . . . . . . . . . . . . . . . . . . 145 C.3 Pressure-enthalpy and Enthalpy-entropy diagrams of the Allam cycle at partial load considering Temperature control strategy. . . . . . . . . . . . . . . . . . . . 146 C.4 Pressure-enthalpy and Enthalpy-entropy diagrams of the Allam cycle at partial load considering best control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . 147 C.5 Partial load performance of compressor C1 in the Allam cycle - part 1. The three different control strategies are considered. . . . . . . . . . . . . . . . . . . . . . . 147 C.6 Partial load performance of compressor C1 in the Allam cycle - part 2. The three different control strategies are considered. . . . . . . . . . . . . . . . . . . . . . . 148 C.7 Partial load performance of compressor C2 in the Allam cycle - part 1. The three different control strategies are considered. . . . . . . . . . . . . . . . . . . . . . . 148 C.8 Partial load performance of compressor C2 in the Allam cycle - part 2. The three different control strategies are considered. . . . . . . . . . . . . . . . . . . . . . . 148 C.9 Partial load performance of compressors C1 and C2 in the Allam cycle for Inventory control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 C.10 Partial load performance of compressors C1 and C2 in the Partial Cooling cycle for By-pass control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 C.11 Partial load performance of compressors C1 and C2 in the Partial Cooling cycle for Temperature control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 C.12 Part-load performance of compressors C1 and C2 in the Allam cycle when using the best control strategy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 D.1 System Design menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 D.2 Location and Resource menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . 152 D.3 Heliostat Field menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 D.4 Tower and Receiver menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 D.5 Parameters of the Power Cycle in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . 156 D.6 Thermal Storage menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 D.7 System Costs menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 D.8 Financial Parameters menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . 159 D.9 Incentives menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 D.10Depreciation menu in SAM. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161 xv List of Tables 2.1 Categorization criteria. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.2 Summary list of stand-alone cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.3 Summary list of combined cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.4 Stand-alone cycles. Original boundary conditions (P[MPa], T[°C]). . . . . . . . 54 2.5 Combined cycles. Original boundary conditions (P[MPa], T[°C]). . . . . . . . . 55 2.6 Stand-alone cycles: Strengths-Weaknesses analysis (Part 1). . . . . . . . . . . . . 58 2.7 Stand-alone cycles: Strengths-Weaknesses analysis (Part 2). . . . . . . . . . . . . 59 2.8 Combined cycles: Strengths-Weaknesses analysis (Part 1). . . . . . . . . . . . . . 60 2.9 Combined cycles: Strengths-Weaknesses analysis (Part 2). . . . . . . . . . . . . . 61 2.10 Survey of sCO 2 cycle layouts published in the public domain. Where two references are provided, the first one indicates the year of first publication whilst the reported thermal efficiency is taken from a more recent source. . . . . . . . . . 62 3.1 Verification of the simulation code employing the efficiencies reported in literature ( ηcompr , ηtur b and ηrec ). Note that, for the Simple Recuperated cycle a , reference [ 11 ] is used instead of [ 12 ] and that all the values in the table are displayed as percentages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.2 Parameters used in the sensitivity analysis. Note that turbomachinery efficiency is polytropic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.1 Specifications of the reference power plant. . . . . . . . . . . . . . . . . . . . . . 94 4.2 Comparison between a standard molten salt and FLiNaK. Price of FLiNaK calculated from data available in [13]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 4.3 Uncertainty analysis: limits of the uniform probability distributions. . . . . . . 108 4.4 Parameters used in the economic analysis. . . . . . . . . . . . . . . . . . . . . . . 109 A.1 Operating conditions of the selected recuperator. . . . . . . . . . . . . . . . . . . 131 A.2 Operating conditions of the selected recuperator. . . . . . . . . . . . . . . . . . . 131 D.1 System Design parameters for the three different cycles considered, see Figure D.1. 152 D.2 Parameters of the Heliostat Field for the three different cycles considered, see Figure D.3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 D.3 Parameters of the Tower and Receiver for the three different cycles considered, see Figure D.4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 D.4 Parameters of the Power Cycles for the three different cycles considered, see Figure D.5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 xvii List of Tables D.5 Parameters of the Thermal Storage system for the three different cycles considered, see Figure D.6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 xviii Nomenclature Introduction - symbols αAbsorptance [−] ˙ QThermal radiation [W] ²Emissivity [−] ηEfficiency [%] λReflectance [−] ASME American Society of Mechanical Engineers [−] BP British Petroleum [−] CO2Carbon dioxide [−] COP Conference of the Parties [−] CR Concentration Ratio [−] CSP Concentrated Solar Power [−] DOE US Department of Energy [−] GDP Gross Domestic Product [$] ISolar radiation [W] IE A International Energy Agency [−] K AERI Korea Atomic Energy Research Institute [−] K AIST Korea Advanced Institute of Science and Technology [−] LCoE Levelized Cost of Energy [ ¢ kW h ] LFR Linear Fresnel Reflector [−] NET L National Energy Technology Laboratory [−] NREL National Renewable Energy Laboratory [−] PC HE Printed Circuit Heat Exchangers [−] xix List of Tables BMPC Bechtel Marine Propulsion Corp [−] CF Capacity factor [%] C IP Compressor Inlet Pressure [Pa] CRM Conductance Ratio Method [−] DN I Direct Normal Irradiance [ W m2] Eyear Annual Energy Production [GW h] fFunction [−] FdThermal properties contribution term [−] ∆hEnthalpy [ J kg ] hHeat transfer coefficient [ W K m2] Inv. Inventory [−] IRR Internal Rate of Return [%] IST Integrated System Test [−] kHeat exchanger sub-division [−] LHS Latin Hypercube Sampling [−] NRotational speed [r pm] Ncorr Corrected rotational speed [r pm·s m] NPV Net Present Value [$] Nu Nusselt number [−] PD Percentage Deviation [%] PPA Purchase Price Allocations [$] Pr Prandtl number [−] qAS object function [−] RIdeal Gas Constant [ J K·mol ] Rtot Total thermal resistance [K m2 W] Rwall Wall thermal resistance [K m2 W] Re Reynolds number [−] T D Mean temperature difference [K] xxvi List of Tables T IP Turbine Inlet Pressure [Pa] TOD Time-of-delivery factors [−] tol Tolerance [−] UThermal transmittance [ W K m2] VVolume [m3] xReynolds scaling exponent [−] xAC Active variables [−] yPrandtl scaling exponent [−] Partial Load Analysis - subscripts 0Calculated in off-design conditions [−] AC Active [−] Al Allam cycle [−] Cooler1 First cooler after LT Rec [−] corr Corrected parameter [−] dDominant [−] HT Rec High Temperature Recuperator [−] in Inlet [−] kHeat exchanger sub-division [−] LT Rec Low Temperature Recuperator [−] o f f Off-design [−] on On-design [−] PC Partial Cooling cycle [−] sSecondary [−] TTurbine [−] tot Total [−] T T Total-to-total [−] wall Wall surface [−] x,→yHX side between point x to y [−] xxvii List of Tables Appendix - symbols ∆LiLength of sub-HX [m] ˙ CHeat capacity [W K] ˙ C∗Ratio between minimum and maximum heat capacity [−] ˙ QHeat duty [ W m2] ²Heat exchanger efficiency [%] σM AX Maximum allowable mechanical stress [MPa] AArea [m2] DcChannel Diameter [mm] Dhyd Hydraulic diameter [m] fcFriction factor [−] HPCHE cross sectional area height [mm] NNumber of sub-HX divisions [−] Nch Number of channels [−] NTU Number of Thermal Units [−] PcChannel Pitch [mm] pcDifference between Channel Pitch and diameter [mm] tcPlate thickness [mm] UThermal transmittance [ W K m2] WPCHE cross sectional area width [mm] Appendix - subscripts CHX cold side [−] cond Conductive [−] conv Convective [−] HHX hot side [−] hor Horizontal [−] iRefers to i sub-HX division [−] tot Total [−] ver Vertical [−] xxviii 1Introduction This first chapter presents the general background of the thesis -in terms of sustainable development and energy utilizationand a justification of its research topic, along with a discussion of the specific objectives and associated general methodology . Also in this chapter, a brief description of the structure of the document and of the original contribution to knowledge provided by the thesis are presented. 1.1 Background The themes of sustainable energy and climate change are gaining increasing importance in the international, scientific debate in recent years, thanks also to the creation of several summits and conferences focused on these topics. Among these, the Earth Summits, consisting in decennial meetings of world leaders organized since 1972 with help of the United Nations, and the United Nations Climate Change Conferences (COP, Conference of the Parties), a series of yearly conferences developed by the United Nations Framework Convention on Climate Change (UNFCCC), are worth noting. The main accomplishment of these conferences, started in 1995, was the signature of the world-widely known Kyoto Protocol in 1997. This managed to move the public opinion, attracting the interest of a great majority of the scientific community and mass media, converting climate change and sustainable development into a worldwide topic of debate. All of a sudden, concepts like greenhouse gas emissions and global warming were on everyone’s lips and several campaigns to raise awareness were initiated. This process continued during the past twenty years and is still ongoing nowadays, as demonstrated by the recent signing Paris Agreement in March 2019, where the climate change was universally recognized as a concrete threat to our planet. The agreement, proposed in 2015 during the COP17, focuses on mitigating global warming and establishes a long-term goal that is as necessary as it is challenging: on one hand, keeping the global average temperature raise to well below 2 ° C above pre-industrial levels; on the other, limiting this increase to 1.5 ° C, since this would substantially reduce the risks and effects of climate change. Figure 1.1 represents potential future emissions pathways of global greenhouse gas emissions in the case of no climate policies, with the currently implemented policies, with the national pledges set forth in the Paris Agreement and with the aforediscussed 2 º C and 1.5 º C consistent pathways. Values are expressed in gigatonnes of equivalent CO 2 , while high, intermediate an low pathways represent ranges for a given scenario. The temperatures quoted to the right of the chart report the estimated average global temperature rise by 2100 (from pre-industrial levels). As claimed by several environmental organizations, an increase of only 2 º C would cause a tremendous damage to the ecosystem (extreme heat, water scarcity, extinction of the coral reef and of 1 Chapter 1. Introduction several vegetal and animal species [ 14 ]), while a 3 º C rise would be able to initialize an irreversible process as a consequence of which areas inhabited by more than 275 million people worldwide would potentially be flooded [ 15 ]. Observing such a destructive scenario from an engineering standpoint, it seems to be mandatory to seriously question ourselves about what sustainable development really means and, above all, what pragmatic actions could possibly give solutions to this looming problem. Figure 1.1: Global greenhouse gas emissions scenarios (adapted from [1]). It is widely acknowledged that sustainable energy is a principle whereby the human use of energy "meets the needs of the present without compromising the ability of future generations to meet their own needs" [ 16 ]. In this definition, the needs of the present must be thoroughly discussed in order to completely understand the real extent of the problem. The population of the world has been growing steadily in the last centuries, increasing from 0.9 billion in 1800 to 7.4 billion in 2015 as reported in Figure 1.2, and there is no evidence of a decline in the near future. In fact, according to the last projections provided by [ 1 ], the world population will be increasing in the next decades, even if at a lower annual growth rate, at least until 2100. Interestingly, the steep increase in world population has translated into a parallel economic growth in the last century, in particular after World War II, as shown in Figure 1.3. The World Gross Domestic Product (GDP) is usually employed as a figure of merit for the world’s wealth, calculated as the total output of the world economy, adjusted for inflation and expressed in 2011 international dollars. From 1850 to 1950, world population doubled (from 1.26 to 2.52 billion) while GDP experienced an almost five-fold increase, reaching 9,250 billion dollars (USD). Nevertheless, the exponential growth was yet to come: from 1950 to nowadays, the world population tripled, while GDP experienced a tremendous twelve-fold increase, reaching 110,000 billion dollars (USD). Such worldwide economic growth has, nonetheless, not been distributed evenly throughout the world. This is shown in Figure 1.4(a) where inequalities between the wealthiest and underdeveloped regions is very visible. Interestingly, there is a very clear parallelism between wealth 2 1.1. Background Figure 1.2: World population growth, 1750-2100 (adapted from [1]). Figure 1.3: Evolution of World population and World Gross Domestic Product from 1850 to 2015 (based on data from [1]). and consumption of energy (electricity), as observed in Figure 1.4(b), and the same can be claimed for other goods like the number of motor vehicle ownership, connections to internet, etc. 1 Further to the previous discussion, Figure 1.5 presents the evolution of world GDP and Primary Energy Consumption in the last forty years, showing an undeniable similarity between the two trends. The data, taken from the British Petroleum Statistical Review of World Energy [ 2 ], confirms that the Primary Energy Consumption has more than doubled in this period, exceeding 13,000 Mtoe in 2015, against an almost four-fold increase of GDP. Interestingly, the same plot shows a temporary decline of both figures or merit, due to the Global Financial 1 A complete data-set can be found in [ 1 ], even if the author decided to not include the corresponding diagrams here to limit the extension of the present chapter. 3 Chapter 1. Introduction (a) World GDP per Capita in 2016 (adapted from [ 1 ]). Real GDP per capita is measured in USD, inflation adjusted to USD2011. (b) World Electricity Consumption per capita in 2015 (adapted from [1]). Figure 1.4: World distribution of GDP and Consumption of Electricity. Crisis that took place around 2009. In order to analyze possible strategies in the frame of sustainable development, it is mandatory to understand the contribution of each energy source to the cumulative consumption of primary energy and the extent to which this is affecting climate change. According to the technical report by BP, world energy consumption is characterized by the following scenario: fossil fuels provide the great majority of energy, reaching a total of 84.2 %, 34.2% of which obtained from Oil, 27.6% from Coal and 23.4% from Natural Gas; 10.4% of the total energy consumed is produced from renewable energies, and only 4.4% is provided by Nuclear. Figure 1.6 shows the evolution of this overall scenario in the last thirty years, and a possible projection to 2040, as declared by the International Energy Agency (IEA). 4 1.1. Background Figure 1.5: World Primary Energy Consumption in Mtoe (obtained from [2]). Figure 1.6: World Energy Consumption by fuel in Btu (obtained from [3]). According to the data provided in this section, it becomes clear that even if renewable energies will increase their share of the World energy consumption significantly, fossil fuels still represent more than 75% of the primary energy consumption worldwide (at least according to IEA studies), which continues to increase carbon dioxide and other greenhouse gas emissions rate as previously discussed in Figure 1.1. This puts forward a need to de-carbonize the world energy consumption through the use of effective carbon abatement technologies in fossil fuel power plants and the deployment of renewable energy generation capacity at a faster rate. To this end, a balanced approach is needed, far from biased or simplistic statements like that set forth in the Energy [R]Evolution report by Greenpeace[ 4 ], which claims that "there are no major economic or technical barriers to moving towards 100% renewable energy by 2050". Such declarations are warmly welcomed by the general public and certainly work at a macroeconomic level, but energy supply is a very local task for which many hurdles and challenges remain unsolved 2 . Nevertheless, this being said, there is consensus in the urgent need to 2 The discussion held between the scientific groups led by Prof. M.Z. Jacobson and Dr. C.T.M. Clack in regards to 5 Chapter 1. Introduction find and develop new technologies to help deploy renewable electricity at the highest possible pace and to the largest possible extent, and this is the stage in which this thesis is presented. 1.2 Motivation for this research Solar energy is acknowledged as the most abundant and competitive alternative amongst renewable energy sources, due to its characteristic features such as low-cost and large availability and the extremely low greenhouse gas emissions (from a Life Cycle Analysis perspective). Nowadays, photovoltaic panels are the technology of choice for the large majority of solar power generation facilities, in terms of installed capacity and energy produced [ 3 ]. Nevertheless, this technology also presents weaknesses, among which low dispatchability is without a doubt one of the most salient. Comparing the scenario proposed by Greenpeace [ 4 ] and the projections by IEA [ 3 ], Figure 1.7, it looks clear that Concentrated Solar Power (CSP) is also called to play a leading role along with PV in the intent to partially (or fully, in the most optimistic projection) replace fossil fuels. CSP presents all the features that PV is currently lacking in order to enhance the performance of Solar energy technology, both individually [ 19 , 20 ] or in hybrid-configurations [ 21 ]. CSP is much more dispatchable than PV, thanks to a mature Thermal Energy Storage technology that allows Solar Tower plants to work really close to nominal conditions 24 h per day [ 22 ]. Moreover, CSP power plants can be designed for much larger power ratings, comparable to steam or gas turbine power plants; such is the case of like Ouarzazate Solar Power Station [ 23 ] and Ivanpah Solar Power facility [ 24 ], with outputs of 510 and 392 MW respectively (gross electric power) and using parabolic trough and solar tower technologies (Ouarzazate also employs thermal energy storage). Among all the CSP technologies -Linear Fresnel Reflectors (LFR), Solar Parabolic Dishes (SPD), Parabolic Trough Collectors (PTC) and Solar Power Tower (SPT)- parabolic trough and central receiver systems have the largest share of installed capacity and also the largest potential for future development and mass deployment [ 19 ]. Among the two, this thesis focuses on central receiver systems (Solar Towers) because of their inherent thermodynamic potential enabling higher efficiency and the utilization of innovative power cycles. As a downside, it is acknowledged that the costs of central receiver systems are currently higher than those of parabolic trough power plants. A typical commercial SPT with TES is presented in Figure 1.8. A solar field composed by a large number of heliostats concentrates solar radiation onto the external receiver surface, located in the upper part of the tower. In a standard configuration with TES enabled, molten salts flowing inside the receiver (usually referred to as Solar Salts, NaNO3-KNO3) absorb this energy in the form of sensible heat, increasing their temperature up to 565 º C. The high temperature salts are then stored in a hot tank from which they are then sent to a steam generator. Energy is transferred from the molten salts to the feed-water stream. The low temperature salts are sent to storage in a cold tank at 290 º C and the high pressure, high temperature live steam is used to drive the turbine in a >40% efficient Rankine power cycle. The installation cost and Levelized Cost of Energy (LCoE) of these plants is in the order of 5800 $/kW and 13-15 ¢ /kWh [ 25 ] respectively, values that are not really appealing if compared to 3800 $/kW [ 26 ] the potential electrification of United States based on renewable energy only [ 17 , 18 ] is another recent example of this. 6 1.2. Motivation for this research Figure 1.7: Foreseen development of electricity generation under the IEA "Current Policies" and the Energy [r]evolution case (obtained from [4]). and 6-7 ¢ /kWh [ 27 , 3 ] for a coal power plant or 1600-1800 $/kW [ 25 ] and 8-9 ¢ /kWh [ 28 ] for a photovoltaic farm. Moreover, these figures of merit can be drastically increased in unfavorable locations with a low availability of solar irradiation. Figure 1.8: Schematic representation of a typical SPT plant with TES (obtained from [5]). In order to tackle their potentially unfavorable economics, several solutions to reduce the 7 Chapter 1. Introduction a sCO 2 power cycle, obtained from DOE data as obtained from vendors. Regarding concentrated solar power, NREL’s System Advisor Model (SAM) [ 75 ] is the most common tool employed in literature for techno-economic analysis, also when using sCO2 cycles [76]. Further to the works cited above, it is worth noting that the vast majority of references in literature use cost estimates adapted to current-state-of-the-art CSP technology, with temperatures around 550 º C and standard solar salts. When a sCO 2 power cycle is used, turbine inlet temperature must be increased in order to attain a significant thermodynamic gain (Fig. 1.12), and therefore alternative molten salts must also be employed. These features are loosely studied in literature, which raises the complexity of providing an accurate estimate of the installation costs of sCO 2 -based CSP power plants. This is why, in the present dissertation, the cost estimation of all the major equipment, based on standard CSP technology and performed with SAM or with an in-house models, has been upgraded with a series of correction factors and uncertainty quantification to account for the singularities of sCO 2 blocks as opposed to those using steam turbines. This is considered an original contribution of this thesis. •Off-design Conditions: as it can be deduced from the current state of development of the technology, the information about control of sCO 2 power cycles in partial load and transient conditions available in literature is limited. A number of publications have been produced in the last years, providing a small amount of test data coming from either theoretical analyses [ 77 ] or from the main experimental facilities mentioned earlier in this section. Amongst them, the contributions by SANDIA [ 78 , 79 , 80 ], Bechtel Marine Propulsion Corporation [ 57 ], Echogen [ 81 ] and KAIST [ 82 ] are worth noting. Moreover, a few dynamic models have been developed with the aim to predict off-design performance, such as the work presented by Direby et al. [ 80 ], using SANDIA’s data for the compressors, and by Moyssetsev et al. [ 83 ], from Argonne National Laboratory. Other authors presented more specific studies as, for example, the transient characteristics during startup of one of the 100 kW class loops available in USA [ 84 ]. More recently, other publications have proposed other partial or complete dynamic models: Mahapatra et al [ 85 ] developed a software-based dynamic model of the STEP facility [ 45 ]; similarly, Zhang presented a dynamic model of a Recompression cycle employed in a CSP plant with thermal storage in Modelica Language [ 86 ]; finally, Wright et al. [ 87 ] also proposed a model to predict off-design performance of sCO 2 cycles for waste heat recovery applications. A very recent work that is worth noting has been developed by Allison et al. [ 88 ] using experimental data from the 1 MWe-scale sCO 2 test loop at SwRI, for which the design/control requirements of the facility are discussed. A final comment in regards to off-design performance prediction is to highlight that very little data or ready-to-use information is actually available. Most of the experimental data are confidential and most models make very case-specific simplifying assumptions which are not applicable to a different case or set of boundary conditions. For this reason, the author decided to develop a series of in-house models to predict off-design performance of heat exchangers and turbomachinery, along with some general assumptions about cycle control in CSP applications. This original work is thoroughly presented in Chapter 5 of the thesis. 14 1.4. Structure of the dissertation In the light of this brief review of the current state of the art of sCO 2 technology, it becomes evident that no certain and univocal answers can be provided to the questions posed in the previous section. A deeper analysis of these three aspects (cycle configuration, cost estimation and off-design performance) seems therefore mandatory in order to understand the real potential and feasibility of Supercritical CO 2 power cycles for CSP power plants. This is the actual topic of the dissertation. 1.4 Structure of the dissertation This thesis is divided into six chapters, each one of which corresponds to the different stages of the research: •Chapter 2 - State of the art . This chapter presents a literature review focused on the sCO 2 power cycle technology. All the cycle layouts found in literature are described and categorized, providing a comprehensive classification with the aim to facilitate the comparison between different layouts. Both stand-alone and combined cycles configurations are taken into account. •Chapter 3 - Thermodynamic comparison . The most interesting cycles amongst those reviewed in Chapter 2 are compared from a purely thermodynamic standpoint, considering steady-state conditions. First and Second Law efficiencies are used as figures of merit of this analysis, along with specific work. The aim of this study is to isolate the thermodynamic potential of each cycle from the inherent technical constraints brought about by the realization of the technology, hence providing a clear insight into the true potential of each cycle, regardless of the application. •Chapter 4 - Thermo-economic comparison . In this chapter, the sCO 2 power cycle is integrated in a CSP plant with Thermal Energy Storage and a new thermo-economic comparison is carried out. On one hand, the installation costs for all the major equipment are assessed, calculating the Overnight Capital Cost per kW installed; on the other hand, the analysis is enriched with a new figure of merit, found to be extremely important both for the thermodynamic performance of the cycles and for their installation cost: the temperature rise experimented by molten salts in the solar receiver. •Chapter 5 - Partial Load Analysis and LCoE Assessment . Among all the cycles considered in the previous chapters, two configurations are selected and their performance in off-design conditions are analyzed. This chapter presents off-design performance models of both heat exchangers and turbomachinery and different control strategies of the power cycle are discussed. Finally, the Levelized Cost of Electricity of a CSP power plant employing a sCO2power cycle is assessed using the free software SAM. •Chapter 6 - Conclusions . The main findings of the research are discussed. Suggestions for future work are also given. •Appendix A - Heat Exchangers model . Design and performance models of Printed Circuit Heat Exchanger are described in detail in this Appendix. •Appendix B - Off-design performance of the Partial Cooling cycle . This Appendix provides all the results corresponding to the off-design performance of the Partial 15 Chapter 1. Introduction Cooling cycle that are not included in Chapter 5. Providing these results in an appendix is aimed at reducing the overall length of the main report. •Appendix C - Off-design performance of the Allam cycle . Akin to Appendix B, this annex provides the results corresponding to the Allam cycle. •Appendix D - Input Parameters to the System Advisor Model . This appendix provides all the input parameters of the software used to perform techno-economic simulations in Chapter 5, in order not to increase the length of this part of the report. 1.5 Original contribution to knowledge The core work of the present doctoral research is almost entirely original, even if some alreadyexisting simulation tools have been adapted to be used in the parallel cycle analysis. For instance, the design model of Printed Circuit Heat Exchangers is developed with an in-house code based on an already existing model found in literature (see Appendix A). Nonetheless, the non-original content is explicitly highlighted throughout the dissertation, in order to separate original and non-original contents of the research. The author would like to emphasize that the most salient original feature of this work is the approach used. Indeed, from the beginning, the dissertation tries to avoid preconceived ideas and to follow the mainstream research path defined by literature. Thus, in each step of the research, scientific questions are genuinely outlined, sometime even naively, and the answers obtained constantly shape the actual strategy and direction of the research, not vice-versa. As said, the result of this unconstrained thinking is a novel approach to the analysis of sCO 2 power cycle technology, which is thought to provide a clear insight into the most interesting layouts from a thermodynamical point of view, regardless of the application, and also into the actual techno-economic feasibility of the most suitable ones for CSP plants. Finally, it is also to note that the content of this dissertation has partially been presented in several scientific papers, published in either high-caliber journals such as Applied Energy, Renewable Energy and the ASME Journal of Engineering for Gas Turbines and Power or presented at leading conferences, as commented in the introduction of each chapter. This is regarded as an indirect (or maybe direct) measurement of the originality and archival value of the research. 1.6 List of publications Parts of this work have already been published in scientific journals and presented at technical conferences, as indicated at the beginning of each chapter. The following five publications have been produced by the author with assistance by the supervisors of the thesis and other peers at the University of Seville, plus a collaboration with SwRI and Alpha Laval (paper presented at ASME Turbo Expo 2017): • F. Crespi, G. Gavagnin, D. Sánchez, G.S. Martínez, Supercritical carbon dioxide cycles for power generation: A review,Applied Energy 195, 152–183 (2017). • F. Crespi, D. Sánchez, J.M. Rodríguez, G. Gavagnin, Fundamental Thermo-Economic 16 1.6. List of publications Approach to Selecting sCO2 Power Cycles for CSP Applications, Proceedings of 4th International Seminar on ORC Power Systems, Milan, IT, (2017). • F. Crespi, D. Sánchez, K. Hoopes, B. Choi, N. Kuek The Conductance Ratio method for off-design heat exchanger modeling and its impact on an sCO2 Recompression cycle, Proceedings of ASME Turbo Expo 2017 : Turbomachinery Technical Conference and Exposition, Charlotte, NC, (2017). • F. Crespi, D. Sánchez, J.M. Rodríguez, G. Gavagnin, A Thermo-Economic Methodology to Select sCO2 Power Cycles for CSP Applications, Renewable Energy , (2018). (This paper is an extended version of the one included in the Proceedings of 4 th International Seminar on ORC Power Systems in 2017) • F. Crespi, G. Gavagnin, D. Sánchez, G.S. Martínez, Analysis of the Thermodynamic Potential of Supercritical Carbon Dioxide Cycles: a Systematic Approach, Journal of Engineering for Gas Turbines and Power 140, 051701-1–10 (2018). • F. Crespi, D. Sánchez, T. Sánchez, G.S. Martínez, Capital Cost Assessment of Concentrated Solar Power Plants Based on Supercritical Carbon Dioxide Power Cycles, Journal of Engineering for Gas Turbines and Power 141, 071011-1–9 (2019). The author would also like to highlight another work produced by the author himself in collaboration with other peers of Politecnico di Milano after his M.Sc. thesis, that, in spite of not being directly connected with the main topic of the present dissertation, helped the author to better understand construction and operation issues of CSP technology: • F. Crespi, A. Toscani, P. Zani, D. Sánchez, G. Manzolini, Effect of passing clouds on the dynamic performance of a CSP tower receiver with molten salt heat storage, Applied Energy 229, 224–235 (2018). 17 2Thermodynamics of Supercritical CO2 Cycles. Literature Review This second chapter presents the review of the state of the art of sCO2power cycles . Firstly, the pathway from closed cycle gas turbines to sCO 2 cycle is discussed, along with an analysis of the seminal works of Angelino and Feher . Secondly, a total of forty two stand-alone layouts and thirty eight combined cycles resulting from a thorough literature search are categorized following original criteria aimed to unambiguously describe the configurations based on their thermodynamic characteristics. Finally, a quantitative and qualitative comparison between all the cycles taken into account is made, based on the data available in literature. The contents of this chapter are partially available in: F. Crespi, G. Gavagnin, D. Sánchez, G.S. Martínez, 2017, Supercritical carbon dioxide cycles for power generation: A review, Applied Energy 195, pp. 152–183. 2.1 Historical approach to the closed cycle gas turbine Closed cycle gas turbines were proposed some seventy five years ago by Dr. Curt Keller from Escher-Wyss, Switzerland, as a means to increase efficiency beyond the values achieved by contemporary steam turbines [ 89 ]. Numerous advantages over steam and open cycle gas turbines were claimed: high part load efficiency, efficient fuel utilization, reduced environmental impact, modular small-scale design, high efficiency over a wide range of power-to-heat ratios and compressor/turbine isolated from combustion products and environmental contamination. The closed cycle gas turbine technology was nevertheless obscured in the late 1960s by a step improvement of open cycle combustion turbines thanks to the introduction of new materials and blade-cooling technologies, which enabled higher firing temperatures. All of a sudden, conventional gas turbines reached comparable and even higher efficiencies with much lower installation costs, and superseded the formerly leading technology, also due to the low prices of natural gas. A new technology based on the closed cycle gas turbine was however proposed in this period: the supercritical CO 2 power cycle. It was actually an update of the already existing closed cycle engines with the introduction of this novel working fluid,carbon dioxide, which presented dense (real) gas behavior throughout the compression process due to the vicinity of the critical point. This particular feature enabled large reductions in compression work, therefore 19 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review increasing the overall thermal efficiency even at moderate turbine inlet temperatures. Even if the first sCO 2 cycle ever proposed was a partial condensation Brayton cycle patented by Sulzer in the late 1940s [ 90 ], the first landmark in the development of the supercritical CO 2 power cycle was set by the original works by Gianfranco Angelino (1968) [ 38 , 6 ] and Edward Feher (1967-1969)[ 12 , 91 ]. These authors, working in Europe (Politecnico di Milano, Italy) and United States (Douglas Aircraft Co.) respectively, presented the theoretical fundamentals of this innovative technology and proposed a series of possible configurations of the working cycle. They drew attention to the great potential of carbon dioxide used as working fluid in supercritical and transcritical power cycles, thanks to its advantageous thermodynamic properties. Soon after Angelino and Feher’s seminal works, a few studies were developed by Strub and Frieder [ 92 ], a team at General Electric [ 93 ] and others but after little time the interest decayed and the technology was almost abandoned. It was not until forty years later that Vaclav Dostal revived the interest in the sCO 2 power cycle with the publication of his doctoral thesis in 2004 [ 67 ]. Dostal did a thorough review of the works by Angelino and Feher, both thermodynamically and technologically, and proposed some modifications in the cycle layouts. Starting from this publication, aimed at finding alternative technologies for nuclear reactors of a new generation, the sCO 2 Brayton power cycle has captured increasing attention by the scientific and industrial communities. As of today, this cycle is acknowledged as one of the most promising technologies for the next generation of power systems, provided that the technical challenges inherent to the high pressures and temperatures are successfully overcome. 2.2 The sCO2power cycle 2.2.1 Original works by Angelino and Feher Most of the thermodynamic cycles studied by the scientific community today and those implemented in the few experimental loops available derive from the initial proposals of Angelino and Feher [ 38 , 12 ]. For this reason, and in order to better understand the evolution of sCO 2 technology, it is worth starting from a comprehensive review of their work. Several configurations of condensation (transcritical) cycles were set forth by Angelino in [ 38 ], with the main argument that standard Brayton cycles (gas turbines) yielded lower efficiency than Rankine cycles (steam turbines) when considering similar turbine inlet temperatures. As opposed to these though, the utilization of carbon dioxide at supercritical pressures was claimed to be able to provide the same or even higher efficiency than steam turbines whilst still retaining the simplicity of closed cycle gas turbines. Initially, Angelino considered a simple transcritical condensing cycle with a recuperative layout for which it was observed that the main contribution to inefficiency (irreversibility) came from the recuperative heat exchanger. For this reason, a series of layout modifications were devised by Angelino, aimed at reducing these losses and increasing cycle efficiency. To this end, a Partial Condensation cycle was proposed, with a reduced mass flow in the low temperature recuperator that managed to largely reduce the losses in this equipment. This cycle was actually the forerunner of the modern Recompression cycle where the low pressure carbon dioxide stream is split into parallel compression processes in order to achieve the same effect on the irreversibility of the low temperature recuperator. 20 2.2. The sCO2power cycle The main shortcoming of the previous cycle was that turbine exhaust pressure was imposed by condenser pressure. Therefore, in order to make these two pressures independent from one another, a modification of the cycle layout was proposed whereby an additional compressor ensured pressure flexibility and convergence at the same time. This modified layout can be named Partial condensation with precompression 1 cycle and its modern evolution is the Partial Cooling cycle. Moreover, in order to attenuate sthe effects of high temperatures and pressures at turbine inlet, Angelino proposed a modification whereby the high pressure carbon dioxide flowing out from the high temperature recuperator was expanded (before entering the heat adder) in a high pressure, moderate temperature turbine. Thanks to this, turbine inlet pressure was reduced and hence the mechanical design of this component was made easier. This cycle can be named Partial condensation with pre-expansion cycle. Finally, the last modification of the base cycle layout in Angelino’s work is the Total condensation with precompression cycle, very similar to the Partial condensation with precompression though, in this case, without the low pressure flow-split before compression. The advantage of the Total condensation with precompression cycle is the reduction in the number of components; on the negative side, the condensation section operates with all the mass flow rate and therefore the equipment have larger size and duty. Contemporary to Angelino, Feher studied alternative power cycles which could potentially improve the performance of state-of-the-art Rankine and Brayton cycles [ 12 ]. The proposal of this author was built upon a purely supercritical cycle (halfway from Rankine to Brayton cycles) which could be implemented with either water-steam or carbon dioxide. The advantages of this cycle, as claimed by the author, were twofold. On one hand, the capability to overcome some of the limitations inherent to Rankine cycles such as temperature restrictions, turbine exhaust in saturated steam/vapor conditions and a large number of turbine stages (due to the large expansion ratios). On the other, the possibility to solve restrictions of Brayton cycles such as large compression work (fluid in gaseous state), high sensitivity of cycle performance to pressure drops and compressor efficiency and large heat transfer areas due to the low density at the usual operating pressures. A modified version of this cycle was also mentioned by the author, wherein pump inlet is below the critical pressure. This cycle, termed pseudo-Supercritical cycle by Feher, resembles the condensation cycle presented by Angelino in [38]. The final conclusions drawn by Feher are similar to those presented by Angelino. Both authors agree that the supercritical cycle enables higher efficiencies (ca. 50%) than conventional Brayton cycles with moderate turbine inlet temperatures. Also, with respect to Rankine cycles, supercritical carbon dioxide cycles offer potentially higher efficiencies at temperatures higher than some 600 º C but, more interestingly, with much smaller footprint. The main flaw of both analyses is nevertheless the oversimplification of the thermodynamic calculations as some of the assumptions are far from reality and yield misleading results. For instance, it is not realistic to neglect pressure drops in a system operating at 200 bar, or to consider ideal compression and expansion processes (both in Feher). This concern about the results obtained by Angelino is shared by Dostal et al. in [ 67 ] where it is stated that the assumptions made by the former author regarding turbomachinery efficiency must be updated (mainly for the compressor and pump) and the same applies to the pinch point differences in the high and low temperature 1 Note that this name was not given in the original work by Angelino. It is a term proposed by the author of this work to better track the different layouts. 21 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review recuperators. The same authors indicate that the pressure losses considered by Angelino are too optimistic and thus the efficiency of the more complex cycles would have to be corrected to a lower value. In any case, these observations are valid for thermal efficiency only as nothing is said about auxiliary power or mechanical losses. With all this in mind, it is concluded that the figures obtained by Angelino and Feher in their fundamental contribution provide a very good initial approach to the topic even if they cannot be extrapolated to a practical case. 2.2.2 Categorization criteria The sCO 2 power cycles taken into account in this work present a great variety of thermodynamic features. They can be fully supercritical or transcritical, with total/partial condensation or without it, simple or combined cycles, recuperative or not, etc. In order to properly analyze the differences between the various configurations, a categorization of the proposed layouts is required. The basic idea of the present work is therefore to organize the massive amount of information collected in literature, allowing a more comprehensive approach to sCO 2 cycles. To this end, the following assumptions have been made: •Fundamental division between simple and combined cycles. Firstly, the cycle proposals found in literature are divided in two main groups: simple and combined cycles. It is nonetheless possible that the same cycle layout (for instance Recompression) appears in both categories, depending on whether that layout is used as a stand-alone power system or if, on the contrary, it is used in combination with other systems in a combined cycle application. In the former, the objective is to achieve highest cycle efficiency whilst, in the latter, the aim is to achieve the best combined performance of the waste heat recovery unit and the bottoming cycle [94]. This will be further explained later. •No discrimination between purely supercritical and transcritical cycles. This means that, considering the same cycle layout, in the present categorization there is no difference between a Rankine or a Brayton cycle. Although it is acknowledged that from a component design standpoint this assumption is misleading, it is still valid conceptually. It enables a substantial reduction of the number of cycles taken into account and is based on two considerations: – The layouts used in a pseudo-Brayton or in a pseudo-Rankine sCO 2 cycle can be identical, except for the particular compression device (pump or compressor) and lowest temperature heat exchanger (cooler or condenser). This also makes it theoretically possible to shift from a transcritical to a supercritical cycle by merely changing the temperature and/or pressure at the inlet to the compressor [6, 95]. – The thermodynamic features that characterize a given layout remain essentially unaltered when changing from transcritical to supercritical working conditions [6, 96]. •No discrimination between cycles with or without condensation. Akin to the previous assumption, the proposed categorization remains focused on the layout of the cycle, neglecting whether or not there is condensation of CO 2 during the heat rejection process. This assumption is even more important in the context of the cycle being supercritical or transcritical. Transcritical and condensing are not synonyms [ 97 ] even if they are sometimes considered equivalent. A supercritical cycle, whose reduced pressures and 22 2.2. The sCO2power cycle temperatures are always higher than one, might feature condensation (supercritical condensation) whilst a transcritical cycle (reduced pressures and temperatures higher/lower than one depending on cycle station) might either present total/partial condensation (pseudo-Rankine) or just cooling without condensation (pseudo-Brayton). Thus, the same cycle layout can theoretically belong to either category, transcritical or supercritical, without this meaning that condensation is automatically implemented/discarded. •No discrimination based on the type of heat source. An important characteristic of the sCO 2 power cycle is its applicability to a large number of different heat sources, due to its high efficiency in a wide temperature range. As further explained in section 2.6 (Table 2.4), the applications already considered range from nuclear power to concentrated solar power, and also combined cycles with gas turbines or fuel cells. The result is that the same cycle layout is found several times in literature with different temperature and pressure levels, even if the associated thermodynamic fundamentals remain the same. For the sake of generality, and in order to avoid repetition, the cycles in this work are not categorized according to their application/heat source but focusing on the layout and thermodynamic fundamentals. A direct consequence of this assumption is that cycles presenting oxy-combustion (internal combustion) and others that are externally fired might fall in the same category. This means that cycles operating on gas mixtures (typically 92 –– 96% CO 2 and 4 –– 8% of H 2 O,N 2 and other combustion products) or CO 2 only are treated as a single cycle if they share the same layout. •Cycles labeled with a code based on thermodynamic features, excluding condensation. This last assumption is the main argument to assign a certain category. Taking inspiration from [ 98 ], a system of labels is set up by the authors in order to unambiguously describe the cycle layout based on its thermodynamic characteristics. The features considered are: internal heat recovery (and number of recuperators), reheat, intercooling, flow-split before compression, flow-split before expansion, flow-split before heating and flow-split before heating-expansion (Table 2.1). Using this system, a Simple Recuperated Brayton cycle comprising compressor, heater, turbine, recuperator and cooler would be termed "R1". Adding reheat would change the code to "R1-RH" and considering intercooled compression and a two-stage internal heat recovery (low and high temperature recuperators) would yield "R2-RH-IC". Symbol Thermodynamic Feature R Internal heat recovery (recuperator) IC Intercooled Compression RH Reheated expansion SFC Split-flow before compression SFE Split-flow before expansion SFH Split-flow before heating SFHE Split-flow before heating and expansion Table 2.1: Categorization criteria. 23 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review means that the flow is split in two for the compression process. The first stream flows into the cooler where its temperature is reduced to a value close to the critical temperature. The second stream is not cooled but compressed directly in the re-compressor. The benefits of this layout are twofold. First, the pinch point problem in the low temperature recuperator is attenuated due to the change in heat capacity that is brought about by the dissimilar mass flow rates on the high (reduced flow) and low pressure (full flow) sides of the equipment. Second, the thermal duty of the cooler is also reduced, hence reducing the size of this equipment. The Supercritical Recompression layout is the most extensively researched cycle in literature along with the Supercritical Simple Recuperated, as credited by the references in Table 2.2. Finally, the Supercritical Recompression configuration is used by Manente and Lazzaretto in the Part-flow cascaded sCO 2 power cycle [ 174 ], followed by a Supercritical Simple Recuperated cycle, and by Johnson and McDowell [ 177 ], followed by another Supercritical Recompression cycle. The BAS cycle [ 159 , 160 ] is essentially a Recompression cycle adapted to nuclear applications, Figure 2.7. The heating process is distributed in four different heat exchangers to better fit with the temperature limits imposed by the reactor layout. Figure 2.7: Stand-alone R2-SFC cycles. General layout (top) and particular embodiments (bottom). 2.3.9 R2-IC The Supercritical Precompression cycle [ 67 ], Figure 2.8, is a further development of the Partial condensation with precompression cycle proposed by Angelino. It is a fully supercritical cycle that overcomes the restriction imposed by the compression process on turbine exhaust pressure. In effect, when the compressor inlet pressure is increased to supercritical values, either the expansion ratio is reduced or the turbine inlet pressure increases to prohibitive values. The outcome in the first case is a reduction in cycle specific work whereas, in the second case, the mechanical design of the components gets much more complex. 30 2.3. Stand-alone cycles The Recuperated CPOC cycle [ 149 ], where CPOC stands for Cryogenic Pressurized Oxy-Combustion, is another oxy-fuel based power cycle with integrated carbon capture, which combines the supercritical Recompression cycle concept with an advanced oxy-combustion process. The basic sCO 2 cycle is only slightly modified with the addition of a cyclone downstream of the combustor (for ash removal) and a water separator between the low temperature recuperator and the cooler. The cycle is fully supercritical and the bleed valve for carbon dioxide sequestration is located between the re-compressor and the high temperature recuperator, Figure 2.8. Figure 2.8: Stand-alone R2-IC cycles. General layout (top) and particular embodiments (bottom). 2.3.10 R2-IC-SFC The Supercritical Partial Cooling cycle [ 67 ] derives, again, directly from Angelino’s work. It is a modification of the Partial condensation with precompression cycle, very similar to the Supercritical Recompression layout but with the addition of a cooler and a pre-compressor before the flow-split, Figure 2.9. For this reason, this cycle can also be found in literature under the name Modified Recompression cycle [ 113 ]. The interest of the Partial Cooling cycle is a higher specific work [ 11 ] and a very low sensitivity of global efficiency to deviations of pressure ratio from the optimum value [115]. The Intercooling I layout proposed by Moisseytsev [ 97 ] is another split-flow, highly-recuperative cycle characterized by a multi-stage compression process. This configuration is very similar to the Recompression cycle but with the addition of intercooling in the main compression line, Figure 2.9. Originally investigated by Moisseytsev to better fit with sodium-cooled fast reactor applications, this cycle has also been considered for solar thermal power plants (Supercritical CO2Gas Turbine with intercooling [136]). 31 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review Figure 2.9: Stand-alone R2-IC-SFC cycles. General layout (top) and particular embodiments (bottom). 2.3.11 R2-RH-SFC The Reheating I cycle proposed by Moisseytsev [ 97 ] is a mere evolution of the Recompression cycle, characterized by the addition of a single reheat as shown in Figure 2.10. As already mentioned for the Intercooling I, this cycle is specifically designed for sodium-cooled fast reactor applications where reheating takes place in a Na-to-CO 2 heat exchanger. Dostal and Kulhanek also proposed a cycle identical to Reheating I, under the name of Split expansion cycle [ 111 , 99 ], and Padilla presented a comparison of Recompression cycles with and without reheating [ 154 ]. For the sake of simplicity, only the configuration proposed by Moisseytsev is considered in the present work. The Double Reheat Recompression cycle [ 121 ] adds a second reheat to the configuration originally proposed by Moisseytsev, Figure 2.10. Additionally, Mecheri and Le Moullec propose a by-pass valve before the low-temperature recuperator, which results in a secondary stream of CO 2 . This fraction of the main flow is split after the main compressor, heated up in another heater and re-injected before the high-temperature recuperator. The aim of this flow-split is to overcome the usual pinch-point problems and associated irreversibility in the internal heat recovery process, and it is also proposed in other cycles such as the Simple Recuperated, the Recompression and the Double Recompression [121] layouts. 2.3.12 R2-SFH The Driscoll cycle, proposed by Dostal et al. [ 162 ], is a modification of the Recompression layout with a single compressor. The sCO 2 flow is split into two streams downstream of the compression process and merged later between the two recuperators, Figure 2.11. The aim is to prevent the development of an internal pinch-point in the low temperature recuperator, 32 2.3. Stand-alone cycles but it results in a significant decrease of the thermal efficiency of the cycle [162]. Figure 2.10: Stand-alone R2-RH-SFC cycles. General layout (top) and particular embodiments (bottom). Figure 2.11: Stand-alone R2-SFH and R2-SFC-SFH cycles. General layouts (top) and particular embodiments (bottom). 2.3.13 R2-SFC-SFH As already explained for the Preheating cycle, the SF H is usually employed to better fit with the temperature range imposed by the thermal source. In the case of the REC2 cycle designed for fusion reactors [ 150 , 163 ], a standard Recompression configuration is modified with the addition of four heaters, one of them in parallel with the second recuperator. This is shown in 33 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review Figure 2.11. 2.3.14 R2-SFHE The Turbine Split Flow I, II and III cycles are three highly-recuperative configurations characterized by a flow-split situated between compressor and recuperator [ 101 ]. The sCO 2 flow is divided in two different streams that are then heated up and expanded separately, before being finally mixed together before the cooler, Figure 2.12. These layouts increase the expansion work (a second turbine is added) but this does not result in an increase in thermal efficiency [ 101 ]. The three cycles differ from one another in the layout of the recuperation/expansion process. Figure 2.12: Stand-alone R2-SFHE cycles. General layout (top left) and particular embodiments (top right and bottom). 2.3.15 R2-SFC-SFE The RC-EJ cycle is another configuration proposed by Vasquez in [ 143 ], consisting in a Recompression cycle assisted by an ejector. This configuration, shown in Figure 2.13, is characterized by the same features as the S-EJ (ejector) and Recompression (split-flow) cycles. 2.3.16 R2-IC-RH-SFC This category contains two layouts proposed by Turchi [ 116 ] initially and then also by Padilla et al. [ 108 ] and Shelton et al. [ 120 ]. The general layout is aimed at enhancing the performance of the Recompression and Partial Cooling cycles by merely adding multi-stage intercooled compression and reheated expansion processes (Figure 2.14). The benefits provided by these configurations, named Recompression with IC and RH and Partial Cooling with RH respec34 2.3. Stand-alone cycles tively, are the same as those previously discussed for their standard configurations without reheat. Figure 2.13: Stand-alone R2-SFC-SFE and R2-IC-SFC-SFE cycles. General layouts (top) and particular embodiments (bottom). Figure 2.14: Stand-alone R2-IC-RH-SFC cycles. General layout (top) and particular embodiments (bottom). 2.3.17 R2-IC-SFC-SFE The MC-EJ cycle is the third configuration proposed by Vasquez [ 143 ] and consists in a Recompression cycle assisted by an ejector with the addition of intercooling in the main compression 35 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review line, Figure 2.13. It presents essentially the same characteristics as the RC-EJ cycle plus a reduction of compression work thanks to intercooling. 2.3.18 R3-SFC The Double Recompression cycle is a highly recuperative configuration proposed by Moisseytsev [ 97 ] where the standard high-temperature recuperator cycle is divided in two heat exchangers (intermediate and high temperature) in order to improve its effectiveness, Figure 2.15. In this layout, the stream of CO 2 is split twice, downstream of the intermediate and low temperature recuperators respectively, following the same idea as in the Recompression cycle. Nevertheless, this configuration does not have any beneficial impact on thermal efficiency (other than the enhanced heat transfer in the recuperator) [97]. Figure 2.15: Stand-alone R3-SFC (left) and R3-IC-SFC (right) cycles. General layouts (top) and particular embodiments (bottom). 2.3.19 R3-IC-SFC The Partial cooling with improved recuperation cycle [ 67 ] is again a further development of a configuration proposed by Angelino in [ 6 ]. Starting from a standard Partial Cooling layout, an additional three-stream recuperator is located between the second recuperator (now working at intermediate temperature) and the cooler. The aim of this configuration shown in Figure 2.15 is to attain higher thermal efficiency thanks to the recovery of the heat available at the outlet of the pre-compressor [ 111 ]. This is only possible if the outlet temperature of the latter is higher than the outlet temperature of the main compressor. In an alternative layout, the three-stream recuperator can be replaced by two recuperators connected in parallel [111]. 36 2.3. Stand-alone cycles 2.3.20 R3-SFC-SFHE The Cascade Supercritical CO 2 cycle proposed by Johnson et al. [ 105 ] was included in the sCO 2 cycle development programme at Pratt & Whitney Rocketdyne for solar thermal applications. It is a further development of the Supercritical Recompression cycle with the addition of a flow-split valve downstream of the low temperature recuperator (cold side). As shown in Figure 2.16, this valve divides the flow into two streams, both of which follow the layout of a Supercritical Simple recuperated cycle independently (i.e., recuperator, heater and turbine) rejoining upstream of the low temperature recuperator (low pressure, high temperature side). The aim of this configuration is to recover heat from the solar plant with two heaters, in order to better fit with the large ∆Tthat is typical of this technology. Figure 2.16: Stand-alone R3-SFC-SFHE (left) and R3-SFC-SFH (right) cycles. General layouts (top) and particular embodiments (bottom). 2.3.21 R3-SFC-SFH The REC3 cycle is the second configuration proposed in [ 150 ]. It is very similar to the REC2 layout but incorporates a third recuperator at intermediate temperature. Differently from the Double Recompression cycle, the REC3 configuration presents two compressors only and can be considered a development of the Recompression cycle with a more complex layout of the recuperation process, Figure 2.16. 2.3.22 R3-IC-RH-SFC-SFE The Schroder-Turner cycle is an evolution of the Partial cooling with improved recuperation system, the main difference being the presence of three compressors and one power turbine only as shown in Figure 2.17. It is an extremely recuperative cycle, capable of taking advantage of the specific heat mismatch between the various streams in the recuperators thanks to several flow-splits [ 166 , 167 ]. In an alternative embodiment, the Schroder-Turner cycle can be simplified by removing the low-temperature recuperator [ 167 ]. This latter configuration is the 37 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review one considered in Table 4. Figure 2.17: Stand-alone R3-IC-RH-SFC-SFE cycles. General layout (top) and particular embodiment (bottom). 2.3.23 R3-IC-RH-SFC-SFHE The Quasi-combined system is an oxy-combustion cycle proposed by Zhang and Lior [ 168 ] whose complex layout incorporates several components as shown in Figure 2.18. The compression process is similar to the Partial Cooling cycle where the flow is split into two streams after a first compressor. The first stream is condensed thanks to the heat absorbed by an LNG evaporator, and then pumped and heated in the low and intermediate temperature recuperators. Then, this stream is expanded in a high-pressure turbine and heated in the high-temperature recuperator before rejoining the second stream (as in the Matiant cycle). This second stream is compressed after the flow-split valve, heated up in the intermediate temperature recuperator and finally mixed with the first stream. Once mixed, the entire flow enters the oxy-combustion chamber along with methane and pure oxygen (from an Air Separation Unit) and the resulting combustion gases are expanded across the low pressure turbine. After this, the working fluid is used (as if it were a pseudo-topping-cycle) to heat up the low temperature, high pressure flow in three recuperators before being finally directed to the water separator, cooler (again working with evaporating LNG) and first compressor. The name Quasi-combined derives from the fact that the mixed flow of sCO 2 and H 2 O coming from low pressure turbine and flowing towards the water separator acts as a sort of Brayton-like "topping cycle", heating the pure sCO2flow that acts as the corresponding Rankine-like "bottoming cycle" [168]. 38 2.3. Stand-alone cycles Figure 2.18: Stand-alone R3-IC-RH-SFC-SFHE cycles. General layout (top) and particular embodiment (bottom). 2.3.24 RH Tuo proposes the Rankine with Reheat cycle for low-temperature waste heat recovery applications as a sort of evolution of the Transcritical CO2layout with the addition of a single reheat [169], Figure 2.19. 2.3.25 SFC-SFH The Rankine with ejector cycle was proposed by Li et al. for low-grade heat applications (ca. 100 ° C) [ 170 ]. It consists of a simple non-recuperative Rankine cycle where the flow is split before the compression process: one stream is compressed, heated, expanded in the turbine and directed to the ejector whereas the other is compressed, heated in a second heater working at lower temperature and then sent to the ejector. This is shown in Figure 2.19. The two streams are mixed in the ejector and the cycle is closed by a cooling process that can either be implemented in a cooler or a condenser (Supercritical or Transcritical layouts respectively). 2.3.26 IC The Cryogenic Pressurised Oxy-Combustion cycle [ 149 , 161 ] is the ancestor of the Recuperative CPOC cycle presented earlier, Figure 2.20. It is a non-recuperative cycle and, in spite of a possible utilization in combined cycle applications, it does not bring about further benefits than the recuperative configuration. 39 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review 2.24. A flow-split valve divides the main flow in two downstream of the compressor. The first stream flows into the recuperator, is heated up in the heater and then expanded in a turbine before it finally returns to the recuperator. The other fraction of the flow follows a similar path but without the first step (recuperator): it is heated up and then expanded in a second turbine before rejoining the first stream upstream of the recuperator. Figure 2.24: R1-SFHE and R1-SFC-SFH Bottoming cycles. General layouts (top) and particular embodiments (bottom). R1-SFC-SFH The Combined Recompression and Preheating cycle is another proposal made by Kim et al. [ 190 ]. This configuration, as suggested by its name, results from the combination of the stand-alone cycles that are contained in the name, Figure 2.24. The compression process is taken from the Recompression cycle, retaining the flow-split valve that divides the main stream before the compression stage. One fraction is cooled, compressed and then heated up with the exhaust of the topping cycle (not in a low temperature recuperator as in the Recompression cycle). The second fraction is compressed only (not heated) before it rejoins the first stream downstream of the heater. After compression, the flow is divided again in two streams, closing the cycle with the known configuration of a Preheating cycle. R2-SFHE The Cascade I cycle in [ 94 ] presents a flow-split after the compressor, where the sCO 2 flow is divided in two streams. The first stream is heated up thanks to the recovery of waste heat from the topping cycle, and then expanded in a turbine downstream of which it is sent to two recuperators in series. The second stream raises its temperature across the cited recuperators 46 2.4. Combined cycles and is then expanded in a second turbine before being mixed with the first stream downstream of the high temperature recuperator, Figure 2.25. The main benefit of this configuration is that the waste heat recovery process is strongly enhanced thanks to the absence of recuperation in the first sCO 2 stream. On the negative side, the main shortcoming is the lower efficiency of the low temperature recuperator, which is negatively affected by the different mass flow rates on each side (hot and cold) [94]. Figure 2.25: R2-SFHE Bottoming cycles. General layout (top) and particular embodiments (center and bottom). Another configuration proposed by Kimzey is the Cascade II cycle [ 94 ]. This is an evolution of the previous Cascade I cycle with the addition of another heat exchanger connected with the topping cycle. This second heat exchanger is located just upstream of the second turbine (downstream of the recuperator in the second sCO2stream), Figure 2.25. The layout of the Dual Stage cycle presented in [ 189 , 41 ] is very similar to that of the Cascade I layout. The only difference is the existence of a recuperator in both sCO 2 streams rather than just one, Figure 2.25. Therefore, the temperature of sCO 2 at the inlet of the waste heat recovery process is higher than in the Cascade I configuration. The Partial Recuperation cycle is the last proposal made by Kim et al. in [ 190 ]. The flow is divided in two after the compressor. The first stream flows into the high pressure side of the high temperature recuperator, is heated up in a heater, expanded in a turbine and, finally, it flows across the low pressure side of the high temperature recuperator. The second stream 47 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review enters the low temperature recuperator (high pressure side), then the heater and, finally, the second turbine. The two streams mix before flowing into the low temperature recuperator, Figure 2.25. R2-IC-SFHE The Cascade I with intercooling and the Cascade II with intercooling cycles are two configurations proposed by Kimzey, identical to the ones presented previously with the simple addition of intercooling, Figure 2.26. The benefits of this layout are twofold. On one hand, the total compression work decreases, with a consequent increase of net power output. On the other, the temperature of the sCO 2 flow after compression is lower so the waste heat recovery from exhaust gases of the topping cycle is enhanced [94]. Figure 2.26: R2-IC-SFHE Bottoming cycles. General layout (top) and particular embodiments (bottom). R2-SFC-SFHE Moroz et al. propose a series of novel configurations for the bottoming cycle of a combined system in [ 188 ]. The main idea is to combine different stand-alone cycles in a unique layout by using several flow-splits, Figure 2.27. In the Composite bottoming II configuration, the standard layout of a Recompression cycle is used and a second turbine is then inserted in the main-compressor line by splitting the flow in two streams. Therefore, the resulting configuration is a combination of a Recompression cycle and a simple non-recuperative Brayton cycle. Both heaters (each one specific to the main and secondary turbines) are both thermally connected to the topping cycle, thus enhancing waste heat recovery. The Composite bottoming III cycle is an evolution of the previous configuration, with the addition of another flow-split valve downstream of the low-temperature recuperator. This enables splitting the expansion process in two turbines whilst also increasing the recovery of heat from the flue gases of the topping system. 48 2.4. Combined cycles Figure 2.27: R2-SFC-SFHE Bottoming cycles. General layout (top) and particular embodiments (bottom). R2-IC-SFH-SFHE The last configuration proposed by Kimzey is the Cascade III cycle, also reconsidered by Huck in [ 197 ]. The latter is similar to the Cascade I with intercooling layout due to the flow-split after the compression process and the fact that only one of the two sCO 2 streams recovers heat from the topping cycle. The novel feature of this configuration is the division of the heat recovery process in two heat exchangers, in between which the two sCO 2 streams are mixed, Figure 2.28. This allows to control the temperature profiles of the recuperators by varying the mass flow rates of the two streams, hence reducing the irreversibility of the internal heat exchange process [94]. R3-SFHE The Three stage configuration presented in [ 181 ] is a modification of the Dual Stage layout. In this configuration, the sCO 2 flow that does not receive thermal energy from the topping cycle is divided in two streams, each one expanded in a different turbine and sent to a different recuperative heat exchanger. These two secondary streams are finally mixed together with the main stream before flowing into the condenser, Figure 2.28. R3-RH-SFC Another configuration proposed by Moroz et al. is the Bottoming recompression with reheat cycle [ 188 ]. Contrary to the proposals presented previously, the latter does not result from the combination of different cycles but from the modification of the standard Recompression 49 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review Figure 2.28: R2-IC-SFH-SFHE and R3-SFHE Bottoming cycles. General layouts (top) and particular embodiments (bottom). cycle. A reheating process is enabled by merely adding a high temperature recuperator, a new heat exchanger connected to the topping cycle and a second turbine, Figure 2.29. Figure 2.29: R3-RH-SFC and R3-SFC-SFHE Bottoming cycles. General layouts (top) and particular embodiments (bottom). 50 2.4. Combined cycles R3-SFC-SFHE The Composite bottoming I cycle in [ 188 ] is essentially the same as the Composite bottoming II, with the addition of a recuperator before the secondary turbine, Figure 2.29. Therefore, it results from the combination of the Recompression and Simple Recuperated cycles. R3-RH-SFC-SFHE The Composite bottoming IV cycle is the last configuration proposed by Moroz et al. in [ 188 ]. It is obtained by adding a reheating process to the Composite bottoming III layout in Figure 2.30. The flow at the outlet of the last turbine flows through a new recuperator, after which it is heated up by the flue gas stream of the topping cycle and then expanded in a new turbine. This increases the waste heat recovery potential and the net power output of the combined cycle. Figure 2.30: R3-RH-SFC-SFHE Bottoming cycles. General layout (top) and particular embodiment (bottom). 2.4.3 Nested cycles The previous sections have presented several configurations for topping and bottoming sCO 2 cycles in combined cycle applications with somewhat standard integration layouts: heat is supplied to a topping system which produces work and rejects heat to a bottoming system that further converts a fraction of this into useful work. Alternative proposals can be found in literature though. For instance, Stapp proposes two nested configurations where a sCO 2 cycle is combined with a gas turbine in such a way that a standard topping/bottoming cycle structure cannot be defined, Figure 2.31. 51 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review Figure 2.31: Nested simple (left) and R1-SFH (right) cycles. General layouts (top) and particular embodiments (bottom). The combined system proposed by Peregrine Turbine is formed by two Brayton cycles: the topping cycle is a low pressure ratio gas turbine whilst the bottoming system presents a closed sCO 2 Brayton layout. Although none of the cycles is recuperative, they are nested into one another to yield a "globally recuperative" cycle [ 198 ]. In fact, this could be seen as a crossrecuperative layout in the sense that there are two recuperators where the working fluids of different cycles exchange heat to increase the global system efficiency. Thanks to this smart integration, the Peregrine Turbine system is able to achieve high thermal efficiencies. An evolution of this configuration is the Recuperated Peregrine Turbine cycle which presents the same fundamentals but is based on a Simple Recuperated sCO 2 cycle and makes use of four heat exchangers (rather than two) to connect the CO2system to the gas turbine. 2.5 Other cycles Besides power production, sCO 2 systems have been investigated for several alternative applications. For instance, various systems have been proposed to store energy in different ways: thermal energy storage (TES) [ 200 , 201 ], bulk energy storage [ 41 ], heat-pump based energy storage [ 202 , 203 ] and thermo-electric energy storage (TEES) [ 204 ]. Also, a number of sCO 2 combined systems have been looked into for mobile applications (cooling and power production [ 205 ], fuel savings [ 206 ]), ship propulsion [ 207 ] and waste heat recovery in the aero and naval industries [ 208 , 209 ]. The feasibility of less conventional power plants based on sCO 2 cycles has been studied in [ 210 , 155 , 211 , 212 , 213 ] for co-generation, [ 214 ] for geother52 2.6. Comparison mal power and [ 215 ] for combined heating, cooling and hot water production. Finally, other applications under investigation are hydrogen production [ 216 ], refrigeration [ 217 ] and novel dual-evaporator systems [218]. 2.6 Comparison 2.6.1 Thermal performance The review presented in this chapter confirms that sCO 2 power cycles have been proposed in literature for a number of different applications. From Nuclear power plants to Waste Heat Recovery, from Concentrated Solar Power to oxy-combustion plants, this technology always shows great potential in comparison to the default technologies employed in those fields. Tables 2.4 and 2.5 summarize the boundary conditions (minimum and maximum temperatures and pressures of the cycle) and thermal efficiencies declared in the original papers for the stand-alone and combined cycles 3 , along with the application proposed for each of them. In both cases, some standardization of the minimum cycle temperature is observed and there is also certain uniformity in the maximum pressure. For combined cycles, the minimum cycle pressure does not vary largely from one layout to another. Nevertheless, large discrepancies in turbine inlet temperature are observed; even if these are larger for stand-alone applications (Table 2.4), they also arise in combined cycle configuration (Table 2.5). Figure 2.32 puts together the declared thermal efficiency of each stand-alone power cycle considered in this work. The large dispersion observed in the chart is interesting: even if most cycles exhibit efficiencies in the range from 40 to 50%, some reach 60% whilst others are well below 10%. This is due to the different layout of each cycle but, also, the very different boundary conditions considered by the authors, in particular turbine inlet temperature (TIT) but also other parameters like cooling medium available (sink temperature) isentropic efficiencies of turbomachinery and effectiveness (or terminal temperature difference) of heat exchangers. Actually, this is further assessed in Figure 2.33 where efficiency is plotted against turbine inlet temperature for all the cycles considered, showing the clear impact of this parameter on cycle performance. The aforecited dispersion is still visible (for the cited reasons) but it is attenuated to a very large extent. Figure 2.34 presents the same information as Figure 2.32 for the combined cycle layouts considered, giving independent values for the sCO 2 and overall combined cycles whenever possible. Two aspects are worth noting. The efficiency of the sCO2cycles (in blue) is also not uniform, as it was the case for the stand-alone cycles. Also, regarding the global combined cycle efficiency, these combined systems using sCO 2 technology demonstrate that they are able to achieve comparable (but not substantially higher) efficiencies to state-of-the-art gas and steam combined cycle power plants. 3 Note that, in this case, minimum and maximum pressure and temperature correspond to the sCO 2 cycle only 53 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review Num. Cycle Name Pmin Tmin Pmax Tmax ηth Application Ref. 1Simple Recuperated 7.35 32.0 25.0 550 56.0 Not specified [12] 2Tr anscr i ti cal CO2 5.0 15.0 20.0 700 42.0 Nuclear [38] 3Hot day 6.5 28.0 25.0 510 37.3 WHR [109] 4Allam 3.0 20.0 30.0 1150 59.0 Oxy-combustion [132] 5Intercooling I I 7.5 32.0 25.0 500 37.0 Nuclear [101] 6Br ayton CO2GT 1.8 35.0 10.2 650 45.0 CSP [136] 7Reheating I I 7.5 32.0 25.0 500 37.5 Nuclear [101] 8Spli t −Expansion 7.5 32.0 25.0 500 34.0 Nuclear [101] 9Matiant 0.1 29.0 30.0 1300 44.3 Oxy-combustion [137] 10 Allam +RH 0.1 20.0 30.0 1150 60.0 Oxy-combustion [132] 11 ForcedCooler 6.7 -40.0 25.0 830 48.7 Nuclear/CSP [140] 12 DEMO 0.4 20.0 24.0 1250 52.0 Oxy-combustion [141] 13 Preheating 7.5 32.0 25.0 500 27.0 Nuclear [101] 14 S−E J 6.8 32.0 25.0 650 41.6 Nuclear/CSP [143] 15 Inter −Recuperated 7.5 32.0 25.0 500 38.0 Nuclear [101] 16 Recompression 7.8 32.0 25.0 550 46.5 Nuclear [11] 17 B AS 8.5 30.0 25.0 458 42.0 Nuclear [159] 18 Precompression 9.6 32.0 25.0 550 43.5 Nuclear [11] 19 Recuper ated CPOC 0.1 -62.0 17.5 1200 63.0 Oxy-combustion [161] 20 Par ti al Cooling 5.0 32.0 25.0 550 46.1 Nuclear [11] 21 Intercooling I 7.6 32.0 20.0 480 39.0 Nuclear [97] 22 Reheating I 7.6 32.0 20.0 415 37.0 Nuclear [97] 23 Double Reheated Recompression 7.5 32.0 30.0 620 52.4 Fossil Fuel (Coal) [121] 24 Dr i scoll 7.6 32.0 25.0 550 40.0 Nuclear [162] 25 REC2 8.5 30.0 25.0 550 45.7 Nuclear [150] 26 Tur bine Split Flow I 7.5 32.0 25.0 500 33.0 Nuclear [101] 27 Tur bine Spli t F low I I 7.5 32.0 25.0 500 30.5 Nuclear [101] 28 Tur bine Spli t F low I I I 7.5 32.0 25.0 500 29.0 Nuclear [101] 29 RC −E J 14.7 32.0 25.0 650 41.6 Nuclear/CSP [143] 30 Recompression +IC +RH 8.0 32.0 25.0 550 48.5 CSP [116] 31 Par ti al Cooling +RH 5.0 32.0 25.0 550 48.0 CSP [116] 32 MC −E J 5.6 32.0 25.0 650 41.6 Nuclear/CSP [143] 33 Double Recompression 7.6 32.0 20.0 466 39.0 Nuclear [97] 34 Par ti al Cooling w/Impr oved Recup. 4.4 32.0 15.0 550 45.0 Nuclear [99] 35 Cascade not declared 41.4 CSP [105] 36 REC3 8.5 32.0 22.5 600 46.0 Nuclear [159] 37 Schr oder −Tur ner 6.6 47.0 34.9 650 49.6 Solar [167] 38 Quasi −combined 0.1 -70.0 15.6 1300 65.6 Oxy-combustion [168] 39 Rankine w/Reheat 5.7 20 12 90 7.3 WHR [169] 40 Rankine w/e jector 7.2 30.0 12.5 72.0 6.4 WHR [170] 41 CPOC 0.1 -17.7 15.2 530 30.0 Oxy-combustion [161] 42 TCO 0.1 20.0 48.3 705 40.0 Oxy-combustion [171] Table 2.4: Stand-alone cycles. Original boundary conditions (P[MPa], T[°C]). 54 2.6. Comparison Num. Cycle Name sCO2Other Pmin Tmin Pmax Tmax ηth,sCO2ηth,over all Ref. 1Simple Recuperated Topp.ORC 4.0 35.0 30.0 727 32.5 42.8 [102] 2Simple Recuper ated +RH +IC Topp.ORC 3.0 35.0 27.0 727 n.d. 49.1 [102] 3Recompression Topp.ORC 7.4 30.0 25.0 500 43.3 43.5 [165] 4Par tial Cooling Topp.ORC 3.8 55.0 25.0 800 49.7 52.3 [179] 5Par tial Cooling +RH Topp.ORC 3.5 35.0 29.5 727 n.d. 50.5 [102] 6sCO2−ORC I I Topp.ORC 7.4 30.0 25.0 500 36.9 38.0 [165] 7sCO2−ORC I I I Topp.ORC 7.4 30.0 25.0 500 37.8 38.1 [165] 8sCO2−ORC IV Topp.ORC 7.4 30.0 25.0 500 37.3 39.2 [165] 9Brayton Bott.ST 7.8 32.0 20.0 300 n.d. 41 [185] 10 iso −Brayton Bott.GT 0.5 35.0 30.0 400 41.0 n.d. [187] 11(a)Simple Recuper ated Bott.GT 5.8 20.0 20.0 365 n.d. 48.9 [189] 11(b)Simple Recuper ated Bott.MCFC 7.5 35.0 22.5 650 39.9 59.4 [192] 12 Hot Day Bott.GT 6.5 28.0 25.0 510 n.d. 37.3 [109] 13 Preheating Bott.GT 7.7 32.0 24.0 390 27.8 21.2 [41] 14 Tr i ple Heating Bott.GT 8.9 36.9 27.6 346 26.9 n.d. [190] 15 Dual Expansion Bott.GT 8.9 36.9 27.6 398 27.5 n.d. [190] 16 Combined Recompr.and Preh.Bott.GT 8.9 36.9 27.6 346 n.d.n.d. [190] 17 Precompression Bott.GT 8.8 36.9 27.6 385 31.4 n.d. [190] 18(a)Recompression Bott.GT 8.4 30.0 32.0 450 33.9 51.7 [188] 18(b)Recompression Bott.MCFC 7.4 35.0 22.5 650 45.1 61.1 [195] 19 Par tial Recuper ation Bott.GT 8.9 36.9 27.6 498 29.7 n.d. [190] 20 Cascade I Bott.GT 8.5 36.9 27.6 604.9 28.4 n.d. [94] 21 Cascade I I Bot t.GT 8.4 36.9 27.6 604.9 31.2 n.d. [94] 22 Dual Stage Bott.GT 5.8 20.0 20.0 426 n.d. 50.0 [189] 23 Cascade I +IC Bott.GT 6.0 36.9 27.6 604.9 33.7 n.d. [94] 24 Cascade I I +IC Bott.GT 6.0 36.9 27.6 604.9 33.7 n.d. [94] 25 Composite Bott.I I Bott.GT 8.4 30.0 32.0 450 28.1 55.1 [188] 26 Composite Bott.I I I Bot t.GT 8.4 30.0 32.0 450 28.4 55.4 [188] 27 Cascade I I I Bot t.GT 5.0 36.9 27.6 604.9 35.2 n.d. [94] 28 T hree −Stage Bott.GT 6.4 20.0 20.0 480 26.0 23.7 [181] 29 Bott.Recompr.w/RH Bott.GT 8.4 30.0 32.0 450 35.6 52.9 [188] 30 Composite Bott.I Bott.GT 8.4 30.0 32.0 450 31.5 55.4 [188] 31 Composite Bott.IV Bott.GT 8.4 30.0 32.0 450 29.5 55.8 [188] 32 Simple Recuperated +Recompr.Bott.GT 8.4 30.0 32.0 260|450 32.3 55.3 [188] 33 Recompression +Preheating Bott.GT 7.8 32.0 28.0 307|570 34.1 57.9 [196] 34 Precompression +Preheating Bott.GT 7.8 32.0 28.0 333|570 33.4 57.6 [196] 35 sCO2+TCO2Bott.MCFC 6.4|8.1 25.0|55.0 22.5 650 46.1 61.5 [195] 36 RCO2+TCO2Topp.+Bott. 6.4|7.4 25.0|32.0 10.0|20.0 230|550 44.3 45.9 [107] 37 Pereg r ine Tur bine Nes.GT 7.5 32.0 25.4 750 n.d. 49.0 [198] 38 Recuper ated Per eg r ine Tur bi ne Nes.GT 7.8 32.0 26.7 750 n.d. 43.0 [198] Table 2.5: Combined cycles. Original boundary conditions (P[MPa], T[°C]). 55 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review costs due to the several high temperature heat exchangers that are needed. Finally, even if some interesting works with a formal approach to project appraisal have recently been published [ 41 ], assessing the economics of sCO 2 cycles is still very uncertain due to the lack of experimental facilities and standardization. Therefore, most of the attempts to evaluate the cost of the technology are based on mere extrapolations from other power generation technologies. It is precisely in this scenario that the qualitative comparison presented in this section, in combination with the numerical information provided in Section 2.6.1, provides hints to screen potential layouts for specific applications. With this information, a pre-selection of cycles is possible. Then, a more rigorous assessment of the on-design and off-design thermal performance should give way to a complete techno-economic evaluation for which considering specific boundary conditions would be mandatory. 2.7 Selection of the best cycle layout Reorganizing all the information discussed so far in chronological order, the lack of a clear development path of sCO 2 technologies from a thermodynamic performance standpoint becomes even more evident. Table 2.10, excerpted from Table 2.4, presents the following information for each cycle: name, most likely application, declared thermal efficiency, year of publication. Then, Figure 2.35 illustrates the chronological evolution of the thermal efficiency of the cycles, together with their corresponding peak temperatures. Thermal efficiencies are shown as blue bars and referring to the left axis, whilst turbine inlet temperatures are represented by markers whose values are given by the right axis. All these markers are then connected by a black dashed line4. #Name Application ηth[%] Year Ref. #Name Application ηth[%] Year Ref. 1 Simple Recuperated Not.spec. 40.4 1968 [12, 11] 22 Hot day WHR 37.3 2013 [130, 109] 2 Transcritical CO2 Nuclear 42.0 1968 [38] 23 Intercooling II Nuclear 37.0 2014 [101] 3 DEMO Oxy-comb. 52.0 1995 [141] 24 BraytonCO2GT CSP 45.0 2014 [136] 4 Matiant Oxy-comb. 44.3 1999 [137] 25 Reheating II Nuclear 37.5 2014 [101] 5 Quasi-Combined Oxy-comb. 65.5 2006 [168] 26 Split-Expansion Nuclear 34.0 2014 [101] 6 Intercooling I Nuclear 39.0 2009 [97] 27 Allam + RH Oxy-comb. 60.0 2014 [132] 7 Reheating I Nuclear 37.0 2009 [97] 28 Pre-heating Nuclear 27.0 2014 [101] 8 Double Recompression Nuclear 39.0 2009 [97] 29 Inter-recuperated Nuclear 38.0 2014 [101] 9 Recompression Nuclear 46.5 2011 [38, 11] 30 Recuperated CPOC Oxy-comb. 64.0 2014 [161] 10 Precompression Nuclear 43.5 2011 [38, 11] 31 REC2 Nuclear 45.7 2014 [150] 11 Partial Cooling Nuclear 46.1 2011 [38, 11] 32 Turbine Split Flow I Nuclear 33.0 2014 [101] 12 Driscoll Nuclear 40.0 2011 [162] 33 Turbine Split Flow II Nuclear 30.0 2014 [101] 13 Part. Cool. w/ impr. rec. Nuclear 45.0 2011 [6, 11] 34 Turbine Split Flow III Nuclear 29.0 2014 [101] 14 Rankine w/ reheat WHR 7.30 2011 [169] 35 Rankine w/ ejector WHR 6.40 2014 [170] 15 Cascade CSP 41.4 2012 [105] 36 CPOC Oxy-comb. 30.0 2014 [161] 16 TCO Oxy-comb. 40.0 2012 [171] 37 Forced Cooler Nuclear/CSP 46.3 2016 [140] 17 Allam Oxy-comb. 59.0 2013 [131] 38 S-EJ Nuclear/CSP 41.6 2016 [143] 18 BAS Nuclear 42.0 2013 [159] 39 RC-EJ Nuclear/CSP 41.6 2016 [143] 19 Recompression + RH + IC CSP 48.5 2013 [116] 40 MC-EJ Nuclear/CSP 41.6 2016 [143] 20 Partial Cooling+ RH CSP 48.0 2013 [116] 41 Double Reheated Recompr. Fossil Fuel 52.4 2016 [121] 21 REC3 Nuclear 45.5 2013 [159] 42 Schroder-Turner Solar 49.6 2016 [167] Table 2.10: Survey of sCO 2 cycle layouts published in the public domain. Where two references are provided, the first one indicates the year of first publication whilst the reported thermal efficiency is taken from a more recent source. The possible applications (i.e. energy source) of the cycles in Table 2.10 are easily deduced 4It is noted that turbine inlet temperature is not reported for the Cascade cycle, number 15 in Fig. 2.35. This is because values were not provided in the original work from [105] 62 2.7. Selection of the best cycle layout Figure 2.35: Chronological development of sCO 2 cycles: thermal efficiencies and Turbine Inlet Temperatures. Cycle numbers refer to Table 2.10, and are different from those in Table 2.4. from their corresponding TIT by merely observing Fig.s 2.33 and 2.35: oxy-combustion and fossil-fuel driven cycles present exhibit really high temperatures (above 1000 º C), Nuclear and CSP applications lie between 500 and 750 º C, and WHR options operate at extremely low temperatures, lower than 100 ºC. The scenario depicted in the foregoing tables and charts is certainly heterogeneous, and it pretty much looks as if each new cycle did not rely on the previously existing body of knowledge. This observation could arguably be explained by the absence of a thorough and rigorous analysis of the underlying thermodynamics principles of sCO 2 cycles. Indeed, even if a large number of works regarding cycle optimization have been published, virtually none has followed the path already set forth by Angelino and Feher [6, 12]. In spite of the comments set forth earlier in this section, the information contained in Table 2.10 and Figure 2.35, along with the qualitative comparison included in Tables 2.6 and 2.7, is now employed in the pre-selection of cycles, aimed at finding the best layouts that will be object of the thermodynamic and thermo-economic comparisons developed in the next chapters. Hence, those cycles with higher thermal efficiencies could easily be identified as the best candidates, but a selection based only on this figure of merit could turn out really misleading. In fact, configurations presenting high values of ηth are normally characterized by extremely high TIT, so choosing only amongst these cycles could limit the study to layouts specifically created for oxy-combustion applications. Moreover, keeping in mind that the actual topic of the present PhD dissertation is to analyze the feasibility of sCO2cycles applied to CSP plants with Thermal Energy Storage, extremely high temperatures might not be of interest. Based on this rationale, the author decided to select those cycles with highest thermal efficiency but trying a) to maintain in this portfolio representative cycles for the three main fields of application (oxy-combustion, CSP and Nuclear in Table 2.10), b) to take into account the real impact that the different configurations had in specific literature and c) to avoid extremely 63 Chapter 2. Thermodynamics of Supercritical CO2Cycles. Literature Review complex layouts. The result is a set of twelve different cycles, as described in the following paragraphs. Firstly, in order to retain the original works by Feher [ 12 ] and Angelino [ 38 ], the Simple Recuperated and the Transcritical CO 2 are selected, cycles number 1 and 2 in Figure 2.35. As discussed previously, the former is a Brayton-like cycle, while the second is a Rankine-like one. They share the same simple layout, with the only difference that the cooler and compressor of the Simple Recuperated cycle are replaced by a condenser and pump in the Transcritical CO 2 . Both cycles are reported to achieve intermediate thermal efficiency when operating with moderate turbine inlet temperature,so there may be margin for improvement of their thermodynamic performance. Moreover, these cycles have already been included in experimental facilities [ 50 , 53 , 54 , 52 ] discussed in Chapter 1, which means that they are at a higher Technology Readiness Level (TRL), and they have strongly influenced all the research done in sCO2technology in the last forty years. The Recompression,Precompression and Partial Cooling cycles (number 9, 10 and 11 in Figure 2.35) have been selected from the work by Kulhanek and Dostal [ 11 ]. Originally proposed by Angelino [ 38 ] with a transcritical configuration, these layouts are presented by Dostal in his PhD thesis as being the best candidates for Nuclear power plants [ 67 ]. If an intermediate turbine inlet temperature is considered (550 º C, [ 11 ]), these cycles have the potential to achieve fairly high thermal efficiency, 46.5, 43.5 and 46.1 % respectively. Together with the Simple Recuperated cycle, these layouts are the most referenced and studied ones in literature (see Table 2.2). In particular, the Recompression cycle is very likely the most famous configuration, and it has already been experimented several times by SANDIA [ 49 , 51 ]. This provides the cycle with a high TRL. For CSP applications, the following three cycles are selected: Recompression+RH+IC,Partial Cooling+RH and Schroder-Turner. The first two cycles are proposed by Turchi et al. [ 116 ]; they are mostly evolutions of the afore-described Recompression and Partial Cooling cycles, with the addition of intercooling and reheat. These features enhance their thermodynamic performance strongly, along with the fact that the double heater may be able to improve the performance of the solar receiver. On the other hand, the Schroder-Turner layout presents one of the best recuperator configurations among the cycles presented in literature, along with a high thermal efficiency, which may have a positive impact on its thermodynamic and thermo-economic features. Akin to the Recompression+RH+IC layout, the Double Reheated Recompression cycle is an evolution of the Recompression configuration with an enhanced reheat process. In spite of its complexity, this layout results to be very interesting given the extremely high thermal efficiency claimed by Mecheri and La Moullec [121]. The Allam,Matiant and Quasi-Combined cycles are selected as representatives for oxycombustion applications. These cycles are particularly interesting due to their high specific work which enables, along with the very high thermal efficiency, a significant footprint reduction. Moreover, it is worth noting that the Allam cycle is the only cycle that has already chieved the pre-commercial scale [133]. 64 2.8. Conclusions Finally, it must be highlighted that some cycles characterized by very high thermal efficiency ( ηth > 45%) have been excluded from the pre-selection process, mostly due to the complexity of their layouts or to the need for especial equipment what makes them less feasible than the selected configurations. In particular, the DEMO,Allam+RH and Recuperated CPOC layouts are very similar to the Allam cycle and share the same advantages but at the cost of a much more complex layout; therefore, the author has decided to consider the Allam cycle only. The same applies to the REC2,REC3 and Partial Cooling with improved recuperation cycles, which are mere evolutions of the Recompression and Partial Cooling layouts, but with a larger number of heat exchangers which is not compensated for by the resulting performance gain. 2.8 Conclusions This chapter has presented a thorough review of the state of the art of sCO 2 power cycles, covering forty two different stand-alone layouts and thirty eight combined cycle configurations. These cycles have also been categorized according to their main features, yielding twenty seven and thirty different categories respectively, Tables 2.2 and 2.3. The average thermal efficiency of the stand-alone power cycles is in the order of 40%, Table 2.4, even if values in the range from 60 to 65.5% are achieved by oxy-combustion cycles using very high turbine inlet temperatures, Figure 2.33. For combined cycle layouts, efficiencies in the range from 50 to 60% seem to be easily affordable. From a global perspective, there is no doubt that the sCO 2 power cycle has captured the attention of the energy industry either for stationary power generation, combined heat and power or waste heat recovery. Its versatility in a wide range of applications and fuels, whether fossil, nuclear or renewable, and the remarkable performance at moderate temperatures set this technology apart from the competitors that currently dominate the market. Based on this premise, the truth is that the rapid growth of the scientific and industrial communities around sCO 2 has inevitably relied on an unstructured search of more efficient and technically feasible cycles, sometimes lacking an underpinning thermodynamic rationale. This is in contrast with the seminal works by Angelino [ 38 , 6 ] and Feher [ 12 ] which put forward a systematic approach to sCO 2 technology for different operating conditions. Along the same lines as the latter authors, the author of this research has humbly tried to review and categorize the vast amount of information produced around supercritical carbon dioxide in recent years. It has indeed been shown that this can be systematically organized in cycles sharing some basic features and, therefore, performances. Such categorization will hopefully yield a sort of road-map to be used by researchers in the field to screen the cycles that meet their interests best. As a result of the this thorough literature review, twelve configurations have been selected as possible candidates for CSP power plants: Simple Recuperated,Transcritical CO 2 ,Precompression,Recompression,Recompression+RH+IC,Partial Cooling,Partial Cooling+RH,SchroderTurner,Double Reheated Recompression,Allam,Matiant and Quasi-Combined. These configurations are thoroughly presented and analyzed from a thermodynamic standpoint in the following chapter. 65 3Thermodynamic Analysis This chapter presents a thermodynamic comparison between the twelve cycles selected in the previous chapter, without further economic or technological considerations. In the first part of the analysis, no technical restrictions are considered with the aim to focus on the actual thermodynamic potential of each cycle. Then, in a second phase, restrictions are set on the maximum temperature achievable by the recuperator. In all cases, common boundary conditions are used, and various peak temperature levels are considered, theoretically corresponding to different potential applications. A brief description of the models employed to characterize the performance of heat exchangers is also provided. An adapted version of this chapter has been published in: F. Crespi, G. Gavagnin, D. Sánchez, G.S. Martínez, 2018, Analysis of the Thermodynamic Potential of Supercritical Carbon Dioxide Cycles: a Systematic Approach, Journal of Engineering for Gas Turbines and Power 140, 051701. 3.1 Introduction The objective of the present chapter is to set up and develop a systematic analysis of the different sCO 2 cycles proposed in literature in order to hopefully draw universal conclusions regarding the layouts that are most interesting. To this end, common boundary conditions must be fed into a thermodynamic model of performance along with a similar set of assumptions regarding where the technological limits (maximum pressure) lie. After the thorough review provided in Chapter 2, a total of forty two different configurations are identified, amongst which twelve layouts of interest are chosen. The corresponding layouts are presented in Figure 3.1: Simple Recuperated,Transcritical CO 2 ,Precompression,Recompression,Recompression+RH+IC,Partial Cooling,Partial Cooling+RH,Schroder-Turner,Double Reheated Recompression,Allam,Matiant and Quasi-Combined. For these configurations, the dependence of specific work and thermal efficiency on pressure ratio and turbine inlet temperature has been explored. The results are then presented in the form of standard diagrams as those already employed by Angelino in [ 6 ], Figure 3.2, and other authors for open and closed cycle gas turbines [219, 98]. Angelino’s original idea is developed a little further though and applied to the analysis of the twelve cycles at four temperature levels (550, 750, 950 and 1150 º C) and a significantly 67 Chapter 3. Thermodynamic Analysis Figure 3.1: Layouts of selected cycles. Figure 3.2: Diagrams of Thermal Efficiency vs. Specific Work, as originally proposed by Angelino [6]. larger range of pressures (in certain cases up to 600 MPa). The aim of this approach is to actually separate the thermodynamic potential of each cycle from the inherent technological constraints brought about by the very high operating pressures and temperatures. This is thought to provide a clearer insight into which cycles offer a larger margin for efficiency gain, should a parallel development of materials, manufacturing and auxiliary systems take place. 68 3.2. Simulation tools Moreover, the author decided not to consider temperatures lower than 550 º C for a twofold reason: on one hand, this is the current state-of-the-art temperature for a CSP plants with TES, and reducing this value would only lead to a reduction in terms of thermal efficiency without any evident benefit; on the other hand, even if no particular application is taken into account, Angelino [ 6 ] specifically claimed that the sCO 2 cycle is able to achieve efficiencies higher than a Rankine cycle only if its turbine inlet temperature is significantly higher than 550 º C, depending on the pressure level considered. Therefore, limiting the study to temperatures higher than 550 º C, sCO 2 power cycles are analyzed for the conditions of interest only, those for which sCO 2 technology has the potential to yield better performance than standard Rankine cycles using water/steam. Nevertheless, before starting the analysis of the selected cycles, a brief description of tools used during the simulations is provided in the next section. 3.2 Simulation tools In order to analyze the cycles presented in the previous section, in-house Matlab models have been developed on the principal assumption that the working fluid is pure CO 2 . This assumption is however not formally correct for oxy-fired cycles (cycles j, k and l in Figure 3.1), which typically work with a mixture of CO 2 , H 2 O and residuals in the turbine and low pressure side of the recuperator. Nevertheless, the corresponding inaccuracy (i.e., the impact of the modified composition on turbine work and heat exchanger performance) is considered to not have a strong influence on cycle performance whilst, at the same time, it simplifies the calculations and enables considering these cycles for externally fired applications also. The validation presented later in this chapter confirms that this approach is correct. For the calculation of the thermodynamic properties of sCO 2 , the open-source library CoolProp has been used [ 220 ]. Fyrthermore, since the comparison developed in the present chapter is based on (on-design) thermodynamic performance only, the major equipment of the cycle can be simulated with simple thermal models, without considering their actual geometry and design. In order to carry out the thermo-economic assessment contained in the next chapters, much more elaborated models have been specifically developed by the author. 3.2.1 Heat Exchangers Heat exchangers have been modeled with a one-dimensional model whereby the equipment is divided into a suitable number of sub-heat exchangers, all with the seam heat duty, in order to consider small temperature changes and therefore constant sCO 2 properties in each of them [ 10 ]. This common expedient enables the application of simplified performance analysis methods like, for instance, the ² -NTU methodology in each division [ 221 ]. Other approaches used in literature are even simpler, assuming constant effectiveness or constant ∆Tmin (pinch-point) at one end of the heat exchanger. In the present work, an initial value of ²= 95% is assumed for all divisions and the corresponding temperature differences between hot and cold fluids ( ∆Ti ) are computed. The resulting minimum difference (pinch point of the heat exchanger ∆Tmin ) is checked to be not lower than 5 º C. If this were not the case (i.e., ∆Ti< 5 º C for any given i ), the corresponding ²i would be reduced to achieve the target pinch point. A thorough explanation of the one-dimensional model has been published by the author and co-workers in the public domain [221]. 69 Chapter 3. Thermodynamic Analysis 3.2.2 Turbomachinery Turbomachinery performance models are fairly simple given that, at this stage, the code is intended for on-design thermodynamic performance only, for which isentropic efficiencies or equivalent figures of merit of the compression/expansion process serve the purpose. Nevertheless, a survey of the isentropic compressor/turbine efficiencies reported in (or reversecalculated from) the original references yields a very large variability (the actual values are provided in a later section) so it is decided in this work to use representative polytropic efficiencies for compressors (89%), turbines (90%) and pumps (83%). These then yield different isentropic efficiencies depending on the operating conditions of each turbomachine (mostly pressure ratio). It is worth noting that the choice of a constant polytropic in lieu of isentropic efficiency is made in order to better capture the influence of the very different pressure/temperature ratios of the cycles considered1. (a) Relationship between isentropic and polytropic efficiency of an air compressor. (b) Relationship between isentropic and polytropic efficiency of an air turbine. Figure 3.3: Relationship between isentropic and polytropic efficiency in compressors and turbines (taken from [7]). 1 Boyce claims that polytropic efficiency, also called small stage or infinitesimal stage efficiency, "is the true aerodynamic efficiency exclusive of the pressure-ratio effect" [7] 70 3.2. Simulation tools Figure 3.3 shows the correlation between polytropic and isentropic efficiencies of an air compressor and turbine with varying pressure ratio [ 7 ]. It becomes clearer that, considering a constant value of polytropic efficiency, the isentropic one varies as a consequence of the specific operating conditions. 3.2.3 Split-Flow Definition As commented in the previous chapter, several sCO 2 cycles exhibit parallel streams during the compression and heat exchange processes (sometimes also during expansion) which are aimed at overcoming the known pinch point problem in low temperature heat exchangers, see Tables 2.6 and 2.7. This feature is usually referred to as a Split-Flow (or Part-Flow) compression process, and it is characterized by an additional parameter termed "Split-Flow" or "Recompression" fraction ( φ ). The latter represents the portion of fluid that, skipping the main compressor, is compressed in the recompressor without previous cooling, and then mixed with the main stream in between the low and high-T recuperators. In Figure 3.1, it is possible to see that the Recompression and Partial Cooling cycles and their respective evolutions incorporate this particular feature. Figure 3.4, taken from the work of Dyreby et al. at the University of Wisconsin-Madison [ 8 ] and showing results of a Recompression cycle operating at 550 º C and 20 MPa (TIT and cycle maximum pressure respectively) with different recuperator conductance values, shows the importance of a correct selection of φ . It is worth noting that an optimal φ, yielding the highest thermal efficiency, becomes very visible. Figure 3.4: Dependence of thermal efficiency on split-flow Fraction, considering a Recompression cycle operating at 550ºC and 20 MPa (taken from [8]). The definition of the optimum split-flow fraction, in literature, can nevertheless be defined either as the one that yields the highest thermal efficiency or, alternatively, that matches the temperatures of two streams that mix at a particular location (thus reducing thermal stresses of the components). The so defined fractions φ apply to a fixed set of boundary conditions and, when the latter change, they must change accordingly. Irrespective of this, in this dissertation, the values of φ are set to those reported in the original papers during verification of the code. Also, they do not remain constant but, on the contrary, they are continuously 71 Chapter 3. Thermodynamic Analysis there is no univocal correspondence between pressure ratio and peak cycle pressure). Also, it is worth noting that some curves present a relatively high first value, for instance 34.5 MPa for the Recompression+IC+RH layout in Figure 3.12) or 40.5 MPa the for Partial Cooling cycle in Figure 3.13. Even if this is partially due to the inherently higher compressor inlet pressures, the main reason is that the curves have been trimmed to avoid intersections between different lines. Figure 3.10: ηth vs. Wsdiagrams for the Precompression cycle. Figure 3.11: ηth vs. Wsdiagrams for the Recompression cycle. Interestingly, the shape of the ηth vs. Ws curves changes significantly depending on the configuration considered and the same happens to the maximum pressure of the. Yet, it is possible to observe several affinities between cycles characterized by similar layouts or thermodynamic features. For instance, the Recompression+IC+RH and Double Reheated Recompression layouts stem from the common root of the Recompression cycle, and this can easily be observed in the similar patterns presented in Figures 3.11, 3.12 and 3.16. The same consideration is applicable to the Partial Cooling and Partial Cooling+RH layouts, which 78 3.3. Results Figure 3.12: ηth vs. Wsdiagrams for the Recompression+RH+IC cycle. Figure 3.13: ηth vs. Wsdiagrams for the Partial Cooling cycle. are characterized by the same plateau-type trend, especially at high temperatures, or the oxy-fired Matiant and Quasi-Combined cycles, whose corresponding plots seem to fold back on themselves sharplier. Interestingly, most of these trends are in line with those already discussed by Frutschi in [ 98 ] for closed cycle hot-air turbines, demonstrating the common thermodynamic principles of both closed cycles. Finally, some common features shared by all the cycles in the comparison are worth noting. For instance, the plots corresponding to lower turbine inlet temperatures seem to have a more circular shape and they turn elliptical and flatter when temperature increases. Regarding the technological limits, it is confirmed that most cycles reach their peak thermal efficiency and specific work at pressures higher than 40 MPa when turbine inlet temperature is higher than 550 º C. On the contrary, when this temperature is lower than 550 º C, some cycles achieve peak efficiency within the feasible pressure range whilst others do not; this is shown in Figures 3.8,3.10,3.11,3.13,3.15,3.16,3.19. Remarkably, the Quasi-Combined cycle is the only configuration presenting diagrams almost fully situated within the technological limitations (black markers), mainly due the relatively low pump inlet pressure, Figure 3.19. 79 Chapter 3. Thermodynamic Analysis Figure 3.14: ηth vs. Wsdiagrams for the Partial Cooling + RH cycle. Figure 3.15: ηth vs. Wsdiagrams for the Schroder-Turner cycle. 3.3.2 Compared Analysis A global assessment of the individual plots shown in the foregoing section suggests that some of the cycles still hold a non-negligible potential for further efficiency increase (should higher pressures be attainable) whereas others seem to have already achieved the best performance possible for a given turbine inlet temperature (no further gains for higher pressures), all this for the current limits of technology. For instance, the Transcritical CO 2 cycle operating at 750 º C turbine inlet temperature would be able to attain efficiencies higher than 50% with a very high specific work, hence fuel and footprint savings simultaneously; such performance would set the thermodynamic road-map for further cycle development, notwithstanding the very high pressures that would be required ( ∼ 75 MPa). At the same time, cycles acknowledged to be most efficient, like the Recompression layout, seem to have already achieved the highest efficiency for the current turbine inlet temperatures, thus holding no further gains coming from higher operating pressures. 80 3.3. Results Figure 3.16: ηth vs. Wsdiagrams for the Double Reheated Recompression cycle. Figure 3.17: ηth vs. Wsdiagrams for the Allam cycle. Another interesting, not obvious question to answer is which the most efficient or most compact cycle is for a given turbine inlet temperature (energy source). In order to provide a sensible answer to this question, this section presents a comparison amongst the various layouts discussed earlier which are overlaid on one single chart for each temperature level. This is shown in Figures 3.20 to 3.21 where some plots have been trimmed to simplify the reading. The increasing ranges of the horizontal and vertical scales for increasing inlet temperature must be noted. Let the chart corresponding to 550 º C be considered, Figure 3.20. Those cycles conceived for oxy-fired applications (if stable oxy-combustion at such temperature is possible at all) like the Allam and, especially, Matiant cycles are not of much interest as they exhibit fairly low thermal efficiency in spite of a very high specific work (small footprint). For this peak temperature, the highest specific work corresponds to the Allam cycle if mechanical limits are set on the operating pressure, and the Transcritical CO 2 if higher pressures are allowed. 81 Chapter 3. Thermodynamic Analysis Figure 3.18: ηth vs. Wsdiagrams for the Matiant cycle. Figure 3.19: ηth vs. Wsdiagrams for the Quasi-Combined cycle. With respect to efficiency, the Partial Cooling + RH and Recompression+IC+RH layouts attain highest efficiencies (46.5 and 47.6% respectively) when pressure is limited to 40 MPa whereas efficiency rises to a higher value (48%) for the Recompression+IC+RH cycle if this limit is released. Moreover, from a global standpoint, the Partial Cooling+RH and Transcritical CO 2 cycles provide a good compromise between thermal efficiency and specific work. In summary, Figure 3.20 confirms that the most interesting cycles are the Recompression,Double Reheated Recompression,Recompression+IC+RH,Partial Cooling+RH,Transcritical CO2 and, in terms of specific work only, Allam cycles. Increasing turbine inlet temperature brings about changes in the absolute thermal efficiency and specific work achieved by each cycle and also in their relative position in the ηth vs. Ws diagram. This is easily observed by comparing the two graphs in Figure 3.20. In the plot on the right, corresponding to 750 º C, the Matiant cycle exhibits highest specific work but this feature is offset by a very low thermal efficiency. The Allam cycle follows behind with a slightly lower specific work but higher thermal efficiency. Nevertheless, both oxy-fired cycles are still 82 3.3. Results burdened by a low turbine inlet temperature and cannot compete against most of the cycles in the comparison. Considering thermal efficiency only, the scenario remains the same as for 550 º C. The Recompression+IC+RH cycle achieves highest ηth , 54.5 or 55.8% depending on whether or not pressure limits are in place. The Double Reheated Recompression and Partial Cooling + RH layouts follow close behind, enabling efficiencies of almost 54%. Overall, the cycles indicated in the previous paragraph remain the most interesting options. A turbine inlet temperature of 550 º C would be typical of a WHR application, or even a state-ofthe-art CSP plant using molten salts, whereas 750 º C would represent nuclear applications in Gen IV High Temperature Gas Reactors. 950 º C is a very interesting temperature level as this is currently foreseen for next generation CSP applications using central receiver technology. The resulting performances at this temperature are shown in Figure 3.21 where the corresponding plots for each cycle are observed to concentrate on a smaller region of the ηth vs. Ws diagram. Regarding oxy-fired cycles, the Matiant cycle shifts rightwards to attain very high specific work even if still with the lowest efficiency amongst the cycles considered. When pressure is limited to 40 MPa, the Partial cooling+RH layout stems as the most efficient although with moderate specific work, being later matched in efficiency by the Recompression+IC+RH cycle when no pressure limit exists; it is noteworthy that the latter cycles can achieve almost 60% efficiency at 950 º C only. Globally, the cycles of interest at this temperature are the Recompression,Double Reheated Recompression,Recompression+IC+RH,Partial Cooling+RH,Transcritical CO2 , Quasi-Combined and, again only in terms of specific work, Allam cycles. The last chart is shown in Figure 3.21 and corresponds to 1150 º C turbine inlet temperature. It shows similar patterns to Figure 3.21 but with higher efficiency and specific work, in particular the latter. The are two main takeaways in this chart. The first is that whilst the achievable efficiency for the given pressure limit of 40 MPa is just over 62%, some of the cycles have the potential to raise this value to almost 65%, which is remarkable for a somewhat moderate inlet temperature. The second is related to the Quasi-Combined cycle which shifts "north-east" from its initial position in Figure 3.20 to a relative position in Figure 3.21 where it begins to outperform all the other configurations. This modifies the overall scenario, as a result of which the most interesting cycles turn out to be the Precompression,Recompression+IC+RH,Partial Cooling+RH,Transcritical CO2 ,Allam and Quasi-Combined layouts. Actually, the latter yields the best combination of thermal efficiency (63%) and specific work ( ∼ 475 kJ/kg), amongst the portfolio of cycles in this work. This is a very interesting finding as one could have overlooked the true potential of this layout if having the information in Figure 3.20 only, which comes to highlight the interest of the parametric analysis shown in this chapter. 83 Chapter 3. Thermodynamic Analysis (a) Comparison of cycles operating at TIT=550ºC. (b) Comparison of cycles operating at TIT=750ºC. Figure 3.20: Comparison of cycles operating at TIT=550 ºC and TIT=750ºC. 3.3.3 Further Mechanical Limitations An interesting analysis from a practical standpoint is to consider another mechanical constraint with regards to the hot inlet temperature of the high temperature recuperator. To assess this effect, the operating temperature of this equipment is limited to 800 º C which is higher than for state-of-the-art equipment made of stainless steel (675 º C) but still compatible with 84 3.3. Results (a) Comparison of cycles operating at TIT=950ºC. (b) Comparison of cycles operating at TIT=1150ºC. Figure 3.21: Comparison of cycles operating at TIT=950ºC and TIT=1150ºC. more advanced materials such as Inconel 625 [227]. When this restriction is applied to a turbine inlet temperature of 950 º C, Figure 3.21(a) transforms into Figure 3.22 where some of the formerly feasible pressure ratios are not feasible anymore. For instance, the Recompression+IC+RH and Double Reheated Recompression cycles 85 Chapter 3. Thermodynamic Analysis cannot satisfy the new requirement for any pressure ratio, due to the reduced expansion ratio of the last turbine, caused by the reheating process; therefore, the corresponding curves are removed from the chart. Also, the Partial Cooling+RH layout complies with the new constraint for pressures higher than 40.5 MPa only, which means that they are at the very end of what is considered technically feasible today (and most likely economically unfeasible). Considering 1150 º C, Figure 3.23 represents the new scenario and the dramatic difference is immediately observed by comparing the latter chart with Figure 3.21(b). At this high turbine inlet temperature, only three cycles comply with the new mechanical constraint: Quasi-Combined, Transcritical CO2and Allam. These observations confirm the conclusion obtained in the previous section; i.e., that the Quasi-Combined and Partial Cooling+RH cycles are the most interesting cycles at intermediate to high turbine inlet temperature levels. The interest and versatility of the approach presented in this chapter is also highlighted further. Figure 3.22: Comparison of cycles operating at TIT=950 º C. Operating conditions yielding recuperators with hot inlet temperatures higher than 800ºC have been removed. 3.3.4 Second Law Analysis Table 3.2 showed earlier that the boundary conditions applied to each cycle were not completely homogeneous. Such differences come from the need to model dissimilar cycles and become particularly evident for the compressor/pump inlet conditions in the Transcritical CO 2 and the Quasi-Combined layouts. Although this is inevitable to model the particular features of these cycles properly (condensation and cryogenic cooling respectively), it can also be misleading when the comparison relies on the First Law of Thermodynamics only, as in Figures 3.20 to 3.23. 86 3.3. Results Figure 3.23: Comparison of cycles operating at TIT=1150 º C. Operating conditions yielding recuperators with hot inlet temperatures higher than 800ºC have been removed. Such limitation is easily overcome if the Second Law is also used, as it is the case in this section where the Carnot Factor (CF) is used as a metric of cycle performance. This factor is the ratio from the thermal efficiency of the cycle ( ηth ) to the thermal efficiency of the Carnot cycle operated between the same extreme temperatures (ηC), Eq. (3.1). ηC=1−TL TH ,CF =ηth ηC (3.1) Based on this figure of merit representing Second Law performance, a new plot of efficiency vs. specific work is presented in Figures 3.24 and 3.25. These new charts account for the dissimilar cold cycle temperatures, and they introduce significant changes in the results with respect to the previous analysis. It is immediately observed, in fact, that the QuasiCombined layout, which stood out as one of the most promising cycles in Figure 3.22 and the best in Figure 3.23, is no longer interesting in Figure 3.25(a) and does not seem the most promising in Figure 3.25(b) either. Actually, the apparently very high thermal efficiency was due to an extremely low temperature at compressor inlet and not to a layout with unmatched thermodynamic potential. On the contrary, the Partial Cooling + RH configuration exhibits better performance than any other cycle in the comparison, which confirms the results based on First Law presented in earlier sections. In this case, the cycle has some inherent advantages over the alternative layouts whereas no significant changes are produced in the 550 º C and 750ºC scenarios. 87 Chapter 4. Economic Analysis 229 ], with the ultimate objective to estimate the Overnight Capital Costs (OCC) of the resulting sCO 2 -based CSP plants employing the different cycle layouts presented in the foregoing chapter. Ten layouts are selected amongst the twelve cycles considered originally, with the boundary conditions and specifications presented in Table 4.1. In this selection, both the Matiant and Quasi combined cycles have been discarded, the former due to its poor thermal performance at 750 º C (see Figure 3.20(b)) and the latter due to its low Second Law efficiency brought about by cryogenic cooling (see Figure 3.24(b)). Additionally, these two configurations present further complexity due to the presence of three-flow heat exchangers and cryogenic cooling system, whose higher costs are not compensated for by a high thermal performance. Power Output Pmax,sCO2TIT Ts,min Ts,max TEScapaci t y SM [MWel ] [MPa] [ºC] [ºC] [ºC] [hour] [-] 50 30 750 480 770 10 2.4 Table 4.1: Specifications of the reference power plant. 4.2 Cost Estimation techniques and models Estimating the cost of a Concentrated Solar Power plant can become an extremely complex task, depending on the level of detail required [ 230 ]. The difficulty lies on the lack of reliable data since these are mostly proprietary of the EPC companies acting in the CSP industry, especially when an emergent technology like sCO 2 in this work is involved. The only publication that is worth mentioning is the work developed by Weiland et al. [ 74 ], providing cost estimation correlations for all the major components of a sCO 2 power cycle, employing vendor component costs collected by U.S. DOE and presented in ASME Turbo Expo 2019, only a few weeks before the present manuscript was deposited. In this section, cost estimation models developed for the entire power plant are reported and discussed. At this stage, the various equipment are considered are modeled individually since the chapter is meant only to assess the installation costs of the plant, for which transient and partial load conditions of the power plant (i.e., system integration) are not necessary. 4.2.1 Solar Subsystem With the expression Solar Subsystem, the author refers to all the equipment, not included in the power block, that collect and concentrate solar radiation, transforming it into the final heat power input for the power block itself. Therefore, the Solar Subsystem is constituted by the field of heliostats, solar tower and receiver and thermal energy storage system. The intermediate heat exchanger that links the solar heat transfer fluid with the sCO 2 working fluid is not hereby considered but it is, instead, included in the Power Block section. Before analyzing each one of these equipment though, the following assumption concerning the entire solar subsystem must be discussed. The high temperatures considered in this work are unattainable by the molten salts used in contemporary CSP plants, whose degradation temperature is in the order of 600 º C [ 231 ]. Therefore, salts with a different composition and capable of enabling the turbine inlet temperature demanded by the present study needs to be taken into account. Amongst the different candidates, FLiNaK seems to be the most interesting 94 4.2. Cost Estimation techniques and models one, thanks to its good thermo-physical properties and its wide range of operability in terms of maximum and minim temperature allowed [ 232 ]. This fluid has been studied several times in literature, in particular for thermal and mechanical design of Printed Circuit Heat Exchanger [13, 73] and as coolant for nuclear reactor applications [233]. FLiNaK is a ternary eutectic alkaline metal fluoride salt mixture of Lithium, Sodium and Potassium (46.5% LiF, 11.5% NaF and 42% KF). It has a melting point of 454 º C and a boiling point of 1570 º C, yielding an operating temperature range that is compatible with the sCO 2 power blocks considered. A comparison between FLiNaK and the standard solar salt, along with their thermodynamic properties, is provided in Table 4.2 where a constant temperature difference of 20 º C between the hot (salt) and cold (carbon dioxide) fluids is adopted to model the heat transfer rate between FLiNaK and sCO 2 (note that CO 2 behaves close to ideally in this temperature and pressure region far from the critical point). This assumption considers that the heat transfer process between FLiNaK and sCO 2 is not far from ideal (constant, low temperature difference between hot and cold fluid) and yields a standard approach linking the temperature change of molten salts to the temperature change of sCO 2 without loss of generality. Accordingly, the fact that the ∆T experienced by both fluids are linked, implies that the inventory (or mass flow rate) of molten salts needed in the solar subsystem is a function of the inlet temperature of carbon dioxide to the heat addition process, which depends itself on cycle layout, turbine inlet temperature and pressure ratio. Salt Composition Freezing Point [ºC] Boiling Point [ºC] Density [kg/m3] Specific heat J/kgK] Price [$/kg] Solar Salt NaNO3-KNO3220 [231] 600 [231] −0.636·T+2090 [75] 0.172·T+1443 [75] 1.1 [234] FLiNaK LiF-NaF-KF 454 [235] 1570 [235] 2408.9−0.624·T[13] 1267.2+1.0634·T[13] 8.6 Table 4.2: Comparison between a standard molten salt and FLiNaK. Price of FLiNaK calculated from data available in [13]. Solar Power Towers are fully-developed commercially nowadays [ 19 ], as shown by the significant number of operating commercial-scale plants [ 230 ], and as such several software have added the capability to provide a design for all the major equipment of the plant, along with their cost estimations. Amongst these tools, the author decided to use SAM, an open-source software developed by NREL and used frequently by various works in literature, for instance Ho et al [ 236 , 237 ] and Schmitt et al. [ 76 ]. This software provides a wide range of different CSP plant design and of their corresponding financial models, with default commercial values that can easily be customized. Moreover, a significant set of interesting locations worldwide is available, for which the solar subsystem equipment can automatically be optimized according to geographical coordinates. Using these features, a conventional 50 MW Solar Power Tower with Thermal Energy storage based on molten salts is modeled, considering the reference location in Seville and employing the specifications provided in Table 4.1 1 . The resulting costs of the solar subsystem are stored in a database to be used later in the power plants based on sCO 2 technology. This latter information is used in later sections. 1 With the exception of minimum and maximum temperatures of the salts, which must be 290 and 574 º C given that standard solar salts are employed. 95 Chapter 4. Economic Analysis Of course, the change in composition of the heat transfer fluid affects the final cost of the solar subsystem in several ways. First of all, FLiNaK is significantly more expensive than the standard solar salts. Secondly, the higher temperature rise of molten salts enabled by FLiNak poses larger challenges to the design of the solar receiver and thermal energy storage. This is all discussed in the next section. Solar Field The cost of the solar field ( CSF ) is very sensitive to the efficiency of the power block as this figure drastically affects the heat input required for the given power output. This is shown in Figure 4.1 where the inverse, non-linear dependence of CSF upon ηth is observed. These results are obtained with SAM, considering a surrounding field composed by square heliostats with a unit surface of 144.4m 2 . The total amount of mirrors, and therefore the total reflecting surface, obviously changes inversely to the thermal efficiency, and it is obtained by an automatic optimization process carried out by the software. Figure 4.1: Solar Field Cost function as produced by SAM. Solar Receiver and Tower The cost of these components is again obtained with SAM based on the values given for a reference power plant using steam turbine technology. For the tower, the cost depends on height, which is itself dependent on the thermal efficiency of the power block through heat input [ 230 ], Figure 4.2. This is the only dependence of the solar tower cost function as no differences are expected between towers in power plants based on steam turbines or sCO 2 cycles. With respect to the receiver, a cylindrical one similar to Gemasolar Power Plant [ 22 ] is taken into account, and two correction factors are then applied to the reference values calculated with SAM for state-of-the-art molten salts used in contemporary CSP plants. The first correction accounts for the different operating temperature of the receiver, which in this work is increased to 770 º C with respect to standard steam technology. In accordance to this, and in order to account for the higher technical risk, 30% higher costs are considered regardless of the size of the receiver. The second correction factor takes into account that the working 96 4.2. Cost Estimation techniques and models Figure 4.2: Solar Tower Cost function as produced by SAM. fluid in a CSP plant based on steam turbines and in a plant based on sCO 2 technology are likely to exhibit a very different temperature rise across the receiver. This translates into an inversely proportional variation of molten salt flow rate and, therefore, receiver volume. The factor takes into account the different energy absorption capacity of state-of-the-art salts used in contemporary CSP plants with respect to a high temperature salt like FLiNaK, which is the working fluid of choice in this work. The resulting global correction factor is shown in Eq.(4.1) where subscripts FLiNaK and re f refer to the said high temperature salt and the solar salt used by default in commercial CSP plants. The cost function of the reference receiver CR,re f is shown in Figure 4.3. CR,FLi NaK =frec ·CR,re f =1.3· ¯ cp,re f ·∆Tre f ¯ cp,FLi NaK ·∆TFLi NaK ·CR,re f (4.1) Figure 4.3: Solar Receiver Cost function as produced by SAM. 97 Chapter 4. Economic Analysis Thermal Energy Storage The Thermal Energy Storage system is perhaps the equipment which is affected the most by the change in molten salts, due to the huge amount of HTF contained in it and for the greater temperature rise enabled by FLiNak. Its cost ( CT ES ) is calculated with an in-house code previously developed at the University of Seville. Originally, this model considered an 1 MWe parabolic trough plant based on steam turbines operating at 550 º C, with Delcoterm thermal oil employed in the TES system.The model, which was initially intended for small plants, was modified by Rodríguez to fit to larger scales and then modified again by the author of this thesis to incorporate FLiNak as HTF, both from the thermodynamic and economic standpoints. A complete description and validation of Rodriguez’s model is provided in [ 238 ], including the cost of purchasing the major equipment as well as other costs related to installation, insulation, foundations and all the auxiliary equipment required for system operation. The costs employed by the model are corrected with cost indexes available in the International Journal of Production Economics to account for the time value of money [ 239 ], and with exponential cost scaling factors taken from literature [ 240 ]. The cost of the individual components of the storage system are adapted from the detailed project budget reported in [ 234 ], which provides cost estimates of every single component of a real storage project. Additional information, like wages, labor hours and productivity is taken from [241]. In the present study, the maximum operating temperature of molten salts is set to 770 º C whereas the minimum temperature is dictated by the working sCO 2 cycle, meaning that it has a different value for each configuration. The gap between these two temperatures is the temperature rise across the solar receiver ( ∆Tsol ar ) which is found to affect the size and cost of the TES largely; this was also the case for the receiver in the previous section. It is to note that estimating the effect of this parameter combined with the one caused by thermal efficiency is not trivial, especially because the relation between the two is not known a priori. To this end, a sensitivity analysis of CT ES to variations of ηth and ∆Tsol ar is done by varying these parameters in the ranges 30-60 % and 90-300 º C respectively. The results of this study are presented in Figure 4.4, where it becomes evident that the size of the storage system is inversely proportional to ∆Tsol ar . Indeed, when ∆Tsol ar increases, the specific energy storage capacity (kJ/kg) of the storage material increases, thus reducing the inventory of molten salts for the same specifications (hours of extended operation at full load). On the other hand, ηth also contributes to reducing the size of the storage system since the heat input required for a given electric output is reduced proportionally to ηth. Therefore, knowing the pattern of ∆Tsol ar for each cycle configuration turns out indispensable to complete the thermo-economic comparison, since the TES system is undoubtedly one of the most expensive equipment of a CSP plant. These trends are successively presented and discussed in Section 4.3 of this Chapter. 4.2.2 Heat Exchangers Following the most usual approach, and even if the author acknowledges that it might not be the best option for a large scale-commercial power plant, Printed Circuit Heat Exchangers have been considered the technology of choice in this analysis, for their common acceptance and proven capability [ 67 , 78 , 242 ]. The name of this HXs derives from the procedure used to 98 4.2. Cost Estimation techniques and models Figure 4.4: Cost of Thermal Energy Storage system. manufacture the flat metal plates that form the core of the heat exchanger, done by chemical milling. The plates are then stacked, diffusion bonded and finally converted into a solid metal block, as shown in Figure 4.5 from [ 9 ]. This model of compact heat exchangers is particularly indicated for high pressure fluids, due to the fact that the plates are alternately joined by diffusion bonding, yielding a compact, extremely strong, all-metal heat exchanger core [ 242 ]. On the negative side, the resulting equipment is bulky and heavy and the manufacturing cost is very high. The main manufacturers of PCHEs today are Heatric [ 243 ], Vacuum Process Engineering VPE [ 244 ] and Alfa Laval [ 245 ], which declare different maximum design pressures and temperatures in the range from 650 to 1000 bar and from 800 to 900 º C. Any of these manufacturers provide equipment suitable for the operating conditions considered in the feasible range of the present study, Table 4.1. Figure 4.5: Section of a counter-flow PCHE. Taken from [9]. The thermal performance of the PCHE has been modeled with an in-house code whose description and validation are available in a series of joint publications by the author of this thesis and Kevin Hoopes, from Southwest Research Institute, TX [ 221 , 246 ]. These works were originally presented at the 5 th International sCO 2 Power Cycles Symposium held in San Antonio in 2016 and the ASME Turbo Expo conference held in Charlotte, NC, in 2017. Reference to the second work is made in Chapter 5. 99 Chapter 4. Economic Analysis The model is based on the standard approach considering the heat exchanger as divided in N divisions with equal heat duty and with a low enough temperature rise/drop on each side so as to enable the application of the ² -NTU method in each division 2 [ 10 ]. In addition to this, as published in [ 221 , 246 ], the code has recently been improved with new thermal correlations for wavy channels PCHE [ 73 ] and a mechanical stress analysis based on the work by Yoon [ 13 ]. To this latter aim, a maximum allowable mechanical stress must be set, which in this case corresponds to a maximum pressure difference between the hot and cold sides after which the geometry of the PCHE (channel pitch and wall thickness) is modified to ensure mechanical integrity at the working pressure and temperature of interest. This approach links the working pressure and void fraction of the equipment, yielding bulkier PCHEs at higher pressures. A complete description of the in-house model, along with the thermodynamic correlations employed, is provided in Annex A. The default geometry of the PCHE design code is presented in Figure 4.6. This geometry makes use of a counter-flow layout with semi-cylindrical, zigzag channels whose dimensions take values usually employed in the industry [ 67 ]. In particular, the channel pitch and plate thickness take approximate values which must later be varied according to the pressure levels in order to ensure mechanical integrity (see Annex A). Figure 4.6: Section of the counter-flow PCHE taken into account in the in-house model. Dc , Pcand tcare channel diameter, pitch and plate thickness. The cost of the PCHEs is estimated with a methodology based on the works by Dostal [ 67 ] and Kim [ 73 ]. In these, the mass of the heat exchanger M is obtained from its volume V and void fraction -or porosity- ( ²HX = 1 −fm ) which is given a reference value taken from literature. The latter parameter represents a sort of "density" of the HX, as defined in Eq.(4.2) where Dc , Pc and tc are the channel diameter, pitch and plate thickness. The former is set to 3 mm whilst the other two parameters result from the mechanical analysis (typical values are 3.5 and 2 mm respectively). The total mass is finally obtained by merely multiplying V , fm and ρm (density of the raw material considered). The cost of the PCHE is then calculated from the cost of the raw material (Cr aw ), expressed in $/kg, Eq.(4.3). 2 The ² -NTU method is based on the assumption that the fluid’s properties are constant. Hence, it cannot be applied in a flange to flange simulation or with too few internal divisions, due to the strong real-gas-behavior of sCO2. 100 4.2. Cost Estimation techniques and models fm=1−π·Dc2 8·Pc·tc ;M=ρm·V·fm(4.2) CHX [$] =M·Craw (4.3) Two different alloys are considered depending on the operating temperature. Stainless Steel 316L is used for the coolers, which do not have to withstand high temperatures, and the recuperators whose maximum temperature does not exceed 475 º C. Inconel 617 is employed in those HXs operating at higher temperatures, including the heaters. The maximum allowable mechanical stresses of these alloys, taken from [ 247 , 248 ], are represented as a function of temperature in Figure 4.7. (a) Allowable stress for Stainless Steel 316L. [247] (b) Allowable stress for Inconel617 [248]. Figure 4.7: Maximum allowable mechanical stresses of materials employed in HX design, as a function of temperature. Estimating the manufacturing/processing cost to be added to the raw material (usually supplied in bars) to calculate Craw in PCHEs is a challenging task, inasmuch as this information is proprietary of the original equipment manufacturers. This is why the approach presented by Kim et al. to produce a correction factor that could be applied to the un-processed (raw material) cost is used, in the absence of a better approach [ 73 ]. These authors consider a cost of 150 $/kg for the processed Alloy 800 HT, which is six times higher than the cost of the un-processed material in the market (ca. 25 $/kg). Applying this correction factor to the afore-listed alloys yields the following cost ranges: Stainless Steel 316L from 20 to 25 $/kg, Inconel 617 from 120 to 180 $/kg. 4.2.3 Turbomachinery Turbomachinery components are simulated with simple lumped volume models given that these are intended for on-design performance only, the same way already discussed in Chapter 3. Then, due to the lack of reliable cost data for sCO 2 turbomachinery, standard cost estimates for air compressors and centrifugal pumps are employed, as presented in [ 249 ]. The cost of centrifugal compressors is obtained as a function of the required electric power in Horse Power, Eq.(4.4), whereas the cost of the pumps is calculated as a function of their volumetric 101 Chapter 4. Economic Analysis flow Qand head Hin gal/min and ft, Eq.(4.5). Ccompr [k$] =7.90·˙ Wel 0.62, 200 <˙ Wel [HP]<30000 (4.4)        Cpump[$] =2·FT·Cb FT=exp(9.8849−1.6164·ln(Q·pH)+0.083·(ln(Q·pH))2) Cb=3·exp(8.833−0.6019·ln(Q·pH)+0.0519(ln(Q·pH))2) (4.5) Supercritical CO 2 turbines are expected to be less costly than steam turbines of similar output due to the lower footprint brought about by the lower specific volume of the working fluid and the lower pressure ratio of the working cycle (fewer stages) [ 67 ]. Based on this rationale, the cost of sCO 2 turbines is extrapolated from the cost of supercritical steam turbines without steam bleeds, as produced by Thermoflex software [ 250 ]. Two correction factors are then applied, the first of which is the ratio of volume flow rate between the reference and sCO 2 turbines. The second correction factor is based on the assumption that, due to material strength limitations, stage loading in a sCO2turbine is roughly 25-30% lower than in a steam turbine, Eq.(4.6), ΨsCO2= Wstage,sCO2 u2 sCO2=0.75·Ψsteam =0.75· Wstage,steam u2 steam (4.6) where Ψ is the stage loading coefficient, Wstage,steam is the expansion work and u is the peripheral blade speed at mean turbine radius. Such a statement can be easily deduced from the following expression of the forces exerted by turbine blades on an incompressible, inviscid flow expanding across a bi-dimensional cascade, given by mass and momentum conservation: (Fx=(p1−p2)·b Fy=ρ·b·c2 x·(tanα1−tanα2)(4.7) where ρ is density, b is pitch of the cascade, cx is axial velocity and α is flow angle with respect to the axial direction. The boundary conditions and forces are illustrated in Figure 4.8. Should the steam and carbon dioxide flows turn a similar angle across the cascade (deflection) in Figure 4.8, the tangential force Fy exerted on the blade would increase proportionally to the change in density and axial velocity squared, Eq.(4.7). With this in mind, the following observations are noteworthy: • Turbine inlet density almost doubles when using supercritical carbon dioxide in a CSP application at 750 ° C versus a similar plant using supercritical steam turbines at the standard temperature of 560°C3. 3 The approximate density of steam at 250 bar and 560 ° C is 75 kg/m 3 whilst carbon dioxide at 300 bar and 750 º C has a density of 145 kg/m3. 102 4.2. Cost Estimation techniques and models Figure 4.8: Forces on a cascade of turbine blades. • In addition, the density drop along the expansion line in a supercritical steam cycle is much larger than in a supercritical CO 2 cycle due to (i) the much larger expansion ratio of the former cycle and (ii) the higher isentropic exponent of steam. As a result, the average densities of steam and carbon dioxide in these turbines are 40 and 90 kg/m 3,4 . The cumulative effect on tangential force, based on these average densities, would be a double Fyfor CO2. • On the other hand, the change in axial velocity can be correlated to the change in speed of sound, which is in the order of 20% (525 m/s for CO 2 and 650 m/s for steam at turbine inlet). This means a 35% lower axial velocity squared, hence tangential force, for CO2. Nevertheless, this last contribution is not able to counteract the significant increase in Fy produced by the difference in fluid density, and the tangential force in the sCO 2 case can be roughly considered as 165% higher than the supercritical steam one. In the light of these results, F y in a sCO 2 turbine could be reduced by simply reducing the pitch/chord ratio of the blade row. Nevertheless, it is unrealistic to think that the twofold difference between Fy,CO2 and Fy,H2O can completely be offset through this effect as this would drastically increase profile losses (friction on the blade passage walls). This is why a 15-25% lower load coefficient for sCO 2 is assumed in Eq.(4.6), the remainder reduction of Fy,CO2 (if any) relying on a higher solidity. The resulting difference in tangential force Fy between sCO 2 and supercritical steam turbines turns out to be in the order of 150%, as indicated in Eq. 4.8 later. If expansion work in the Rankine steam cycle and in each sCO 2 cycle is then expressed as a function of expansion ratio, turbine inlet conditions and properties of the working fluid, the following correction factor can be devised under the assumption that all stages in the turbine exchange equal work NsCO2 Nsteam =1.5· ¯ cp,sCO2·T IT ·(1−PR 1−γ γ) ∆hsteam (4.8) where N is the number of stages, T IT and PR are the turbine inlet temperature and pressure ratio of the sCO 2 cycle and ∆hsteam is the isentropic enthalpy change across the steam turbine. 4 These densities are based on isentropic expansions from the conditions in footnote 1 to 0.080 and 75 bar for steam and carbon dioxide respectively. 103 Chapter 4. Economic Analysis component. Figure 4.11: Cumulative probability distribution of Overnight Capital Costs per kilowatt. All cycles (see Figure 3.1 to identify labels). The physical explanation of the foregoing discussion has to do with the fact that these cycles with higher costs are extremely recuperative, leading to significantly smaller values of ∆Tsol ar (smaller temperature rise in the heaters) and an exponential rise of the size of receiver and TES; this confirms what was already observed in Section 4.2.1. On the other end, heat recovery in the Transcritical CO 2 layout is not particularly enhanced, yielding a larger ∆Tsol ar and a more vertical slope in Figure 4.11. This is also observed in the close-up of those cycles with lowest capital cost presented in Figure 4.12. In the light of these results, it is easily concluded that the Transcritical CO 2 cycle is the only layout likely to yield an OCC lower than 6000 $/kW whilst the Partial Cooling and Allam cycles yield the same value but with 90% confidence only. 110 4.5. Economic Results Figure 4.12: Cumulative probability distribution of Overnight Capital Costs per kilowatt. Closeup of Figure 4.11. 4.5.2 Cost Breakdown Upon evaluation of the impact of uncertainty, the 85% percentiles are used to perform a capital cost comparison of the ten cycles considered in the analysis. The comparison is presented in Figure 4.13 with the labels already presented in Figure 3.1. Figure 4.13: Breakdown of Capital Costs. Labels refer to Figure 3.1. At first glance, the Recompression+IC+RH and Double Reheated layouts ( e and h in Figure 4.13) exhibit unusual results. Indeed, the costs of thermal energy storage and tower/receiver are significantly higher than that of the solar field, which is usually the most expensive subsystem in a CSP plant. A similar though slightly attenuated pattern is presented by other layouts: 111 Chapter 4. Economic Analysis Recompression,Schroder-Turner and Partial Cooling+RH ( d , i and g respectively). This is due to the very low ∆Tsol ar , which is actually much lower than ∆Tre f and leads to a dramatic increase in the size of these components. In particular, the Double Reheated layout presents a ∆Tsol ar of 80 º C, a value three times lower than ∆Tre f (284 º C) and the maximum ∆Tsol ar achieved by some of the configurations considered (290 º C, see Table 4.4). The conclusion already reported in [ 253 ] with regards to the capital importance of ∆Tsol ar is confirmed here again. Another interesting observation in Figure 4.13 is the share of the solar field in those cycles with more complex layouts ( e , g , h , i ) which is indeed lower thanks to a higher efficiency ηth . Unfortunately, this lower cost is outweighed by the much higher cost of the remaining components in the plant. And for the same reasons, the cost of the power block is significantly lower than that of the solar subsystem in those cycles characterized by simpler configurations (band j, for instance). Also due to this relationship between efficiency and size of solar field, the costs of power block and solar field are comparable in those cycles incorporating reheating and intercooling (e,g), due to the higher thermal efficiencies achieved. Nevertheless, on the negative side, these cycles typically exhibit low ∆Tsol ar , see Table 4.4, which leads to extremely high CT ES , CR and Ctower . This can be better observed in Figure 4.14 where a breakdown of the power block cost is provided. Figure 4.14: Breakdown of Power Block Costs. Labels refer to Figure 3.1. The Recompression+IC+RH,Partial Cooling + RH,Double Reheated and Schroder-Turner layouts in Figure 4.14 ( e , g , h and i ) show a high turbine cost, due to the larger number of turbomachineries required by the reheating configuration. Yet, the costliest items turn out to be the heaters, owing to the more expensive materials that must be used to withstand the extremely high temperatures at the inlet. Furthermore, the cost of the heaters is directly affected by ∆Tsol ar given that, for a given output, a larger temperature rise across the heater implies a lower ∆T across the solar receiver, which also implies a smaller temperature difference between the hot and cold tanks of the thermal energy storage system. This can be inferred from the parallel trends of TES and heaters costs, yellow bars in Figures 4.13 and 4.14 112 4.5. Economic Results respectively. The thermodynamic information presented in Chapter 3 and the cost analysis in the previous section are integrated in Figure 4.15. This chart presents a comparison between the ten cycles considered in terms of First and Second Law efficiencies and OCC , allowing to better understand the foregoing discussion. It is easily observed that the Transcritical CO 2 ( b ), Allam ( j ) and Partial Cooling ( f ) cycles are the least expensive options. Nevertheless, while the first two configurations do not exhibit particularly good thermodynamic features, the Partial Cooling system seems to provide a better compromise. This is further assessed in Figure 4.16, where the trade-offs between the key figures of merit of each cycle are presented. These metrics are thermal efficiency ηth , Carnot Factor CF , temperature rise across the receiver ∆Tsol ar and installed cost (expressed as 1-$/kW). Thermal efficiency has a direct impact on the size of the solar field and, accordingly, the tower and receiver. The Carnot Factor is a measure of the overall irreversibility of the cycle, hence the temperature gap (between the hot and cold reservoirs) needed to achieve a given thermal efficiency; i.e., a combination of thermal efficiency and compressor inlet temperature for cycles operating at constant turbine inlet temperature. The temperature rise is an indirect measure of the inventory of molten salts that is needed to run the cycle and store thermal energy in the Thermal Energy Storage system. Finally, the complementary relative cost 1-$/kW is self-explanatory. Figure 4.15: Thermo-economic comparison of supercritical CO2cycles. The aim of Figure 4.16 is to provide a graphical comparison of the overall performance of the cycles, both thermally and economically. Accordingly, the layout achieving highest value in each axis (note that each metric is expressed in relative terms for the sake of the comparison) stems as the best option since it provides highest production of energy at the minimum cost. With this in mind, it becomes clear that the Double Reheated layout cannot be considered the best choice because it exhibits an extremely high OCC (1-$/kW → 0) in spite of its high thermal efficiency. The other three cycles, on the other hand, present very similar areas. 113 Chapter 4. Economic Analysis Figure 4.16: Thermo-economic comparison of supercritical CO 2 cycles. Trade-offs between key figures of merit. The economic results of the uncertainty analysis, Figure 4.12, suggest that whilst the Transcritical CO 2 cycle could be the layout of choice for the CSP application considered, the Partial Cooling cycle also presents significantly higher thermal efficiency and Carnot factor, Figure 4.15, even if with slightly higher $/kW, Figure 4.16. For these reasons, the Partial Cooling cycle would potentially step forth as a shorter-term, slightly more feasible option whereby a balanced techno-economic performance would be attained with less demanding design constraints for the solar receiver. On the negative side, this would be at the cost of a larger inventory of salts as shown in Figure 4.16. 4.6 Conclusions This chapter presented an assessment of the Overnight Capital Cost of a 50 MW e CSP power plant with a 10 hour Thermal Energy Storage system, operating at high temperature and employing a sCO 2 power cycle. The major equipment of the plant have been modeled either with validated in-house codes (Thermal Energy Storage, heat exchangers) or using software accepted by the industry (SAM for the solar field, tower and receiver, and Thermoflex for the turbomachinery and cooling tower). The commercial software has also been employed to calculate reference costs of a steam-based CSP plant with a TES of similar capacity using state-of-the-art molten salts. Then, a series of correction factors have been developed in order to account for the difference between the high temperature salt FLiNaK and the reference salt, thus adapting the cost estimates to plants based on sCO2technology. The integral thermo-economic analysis applied to the cycles explored in Chapter 3 has been based on the Overnight Capital Cost per kilowatt and on efficiency according to the First and Second Laws of Thermodynamics. A first conclusion is that only the Transcritical CO 2 cycle seems to be likely to enable installation costs lower than 6000 $/kW with a 100% probability. If the 85% confidence interval is considered, the capital cost of this cycle is 5657 $/kW, 114 4.6. Conclusions which seems to be competitive against some 3800 $/kW for a coal power plant [ 254 ] or 5800 $/kW for a state-of-the-art CSP plant using tower technology [ 255 ]. Interestingly, this configuration does not present a remarkably high ηth (lower than 48.5%) or a very high Carnot Factor. The Partial Cooling and the Allam layouts follow close behind with 5907 and 5943 $/kW respectively. Considering the former cycle, the relatively low OCC is combined with very good thermodynamic features. This cycle provides a thermal efficiency higher than 51%, and apparently the best compromise between thermodynamic and economic features. Finally, very complex layouts seem to be not advisable, even if they are characterized by really high thermal efficiencies ηth . The Double Reheating,Recompression+IC+RH and Partial Cooling+RH cycles are actually able to exceed 53% thermal efficiency but suffer from a much larger number of components, some of them operating at high temperature. As a consequence, their capital costs per kilowatt increase to 12538, 9096 and 8130 $/kW respectively. The work in this chapter suggests that sCO 2 can potentially be installed at a cost that is comparable with current steam turbine technology. Bearing in mind that the latter technology does not hold the potential to become much more efficient than it currently is, this is a promising result that has now to be confirmed by the calculation of the corresponding Levelized Cost of Electricity in the next Chapter. 115 5Partial Load Analysis and LCoE Assessment This chapter is going to be embargoed during the next six months in order to ensure publication confidentiality. 117 6Conclusions This thesis has presented a systematic approach, based on a thorough thermo-economic analysis, to selecting sCO 2 power cycles for Concentrated Solar Power applications with the aim to assess their actual potential to yield lower cost of electricity than state-of-the-art CSP plants based on steam turbines. This final chapter provides a closure to this work by presenting a critical review of the various assumptions and the methodology applied in the research, and by summarizing the main findings of it. 6.1 Critical review of assumptions and methodology Assessing a trustworthy and thorough feasibility analysis of CSP plants employing sCO 2 power blocks is very challenging, mostly due to the low TRL of sCO 2 technology and to the scarcity of reliable cost-related information, especially for turbomachines. Furthermore, the comparison between several cycle configurations, characterized by different thermodynamic features and required boundary conditions, brings in additional complexity to the problem under analysis. In consequence, a series of assumptions have been made throughout the present dissertation, in order to reduce the complexity of the problem down to a manageable level. In this section, these assumptions are revisited with the aim to assess the reliability of the results provided by the thesis, highlighting both the principal positive features and also the main flaws. First of all, considering a single value of compressor inlet temperature may be regarded as an oversimplification. The value of 32 º C taken into account results to be only slightly higher than the supercritical point, and it could be argued that higher temperatures would be preferred in order to avoid strongly variable sCO 2 thermophysical properties. Nevertheless, the choice was pondered and considered reliable for the next reasons. On the one hand, 32 º C is well-established value in specific sCO 2 power cycle literature and does not undermine the validity of the results. Property databases like Refprop and Coolprop provide good approximations at temperatures 1 º C above the supercritical value, and considering higher temperatures would only lead to worse cycle thermal performances. On the other hand, looking into the future, 32 º C results would be suitable if sCO 2 blends were used in lieu of pure sCO 2 as this temperature would enable condensation of the working fluid and, hence, better thermal performance of the cycle. This is currently under research in the SCARABEUS project, funded by the European Commission under the H2020 programme and developed by an European consortium participated by the University of Seville. 119