processes

Article Energy Analysis of the S-CO2 Brayton Cycle with Improved Regeneration

Muhammad Ehtisham Siddiqui * and Khalid H. Almitani Mechanical Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [email protected] * Correspondence: [email protected] or [email protected]; Tel.: +966-55-218-4681

 Received: 28 November 2018; Accepted: 17 December 2018; Published: 20 December 2018 

Abstract: Supercritical carbon dioxide (S-CO2) Brayton cycles (BC) are promising alternatives for power generation. Many variants of S-CO2 BC have already been studied to make this technology economically more viable and efficient. In comparison to other BC and Rankine cycles, S-CO2 BC is less complex and more compact, which may reduce the overall plant size, maintenance, and the cost of operation and installation. In this paper, we consider one of the configurations of S-CO2 BC called the recompression Brayton cycle with partial cooling (RBC-PC) to which some modifications are suggested with an aim to improve the overall cycle’s thermal efficiency. The type of heat source is not considered in this study; thus, any heat source may be considered that is capable of supplying ◦ ◦ temperature to the S-CO2 in the range from 500 C to 850 C, like solar heaters, or nuclear and waste heat. The commercial software Aspen HYSYS V9 (Aspen Technology, Inc., Bedford, MA, USA) is used for simulations. RBC-PC serves as a base cycle in this study; thus, the simulation results for RBC-PC are compared with the already published data in the literature. Energy analysis is done for both layouts and an efficiency comparison is made for a range of turbine operating temperatures (from 500 ◦C to 850 ◦C). The effectiveness and its influence on both layouts are also discussed.

Keywords: supercritical carbon dioxide; recompression Brayton cycle; partial cooling; improved heat regeneration; thermal efficiency; energy analysis; heat exchanger effectiveness

1. Introduction Rapid technological advancements and increasing industry all around the world have significantly increased the demand of energy. On the other side, fossil reserves are depleting rapidly, resulting in global warming and issues relating to environmental pollution. Because of this, the development of more efficient power cycles needs attention. One step towards efficiency improvement may be the utilization of industrial waste heat [1]. The supercritical carbon dioxide (S-CO2) Brayton cycle (BC) has been extensively studied in the last decade and is considered promising for exploiting low- to medium-grade heat for power generation [2]. No commercial S-CO2 power plant has yet been installed; however, some pilot small-scale units are currently present [3–5]. Carbon dioxide as a working fluid is non-toxic, stable, and non-combustible [2]. A power block utilizing S-CO2 has many benefits due to its compactness, low maintenance and running costs, and structural simplicity [6,7]. Another advantage which makes the utilization of CO2 worthy in supercritical BC is the rapid change in its thermo-physical properties near its critical point. The density of CO2 near its critical point is similar to that of its liquid form and reduces the significantly. Secondly, S-CO2 is almost twofold as dense as steam, resulting in a power block with high power density in comparison to the steam (RC). Aside from certain benefits, RC has many disadvantages over S-CO2, like poor thermal efficiency due to phase change and huge plant size.

Processes 2019, 7, 3; doi:10.3390/pr7010003 www.mdpi.com/journal/processes Processes 2018, 6, x FOR PEER REVIEW 2 of 10

RC has many disadvantages over S-CO2, like poor due to phase change and huge Processesplant size.2019 , 7, 3 2 of 10 Feher [8] and Angelino [9] proposed the supercritical carbon dioxide cycle in the 1960s. They achieved a cycle thermal efficiency of close to 55% under ideal conditions. However, this cycle came Feher [8] and Angelino [9] proposed the supercritical carbon dioxide cycle in the 1960s. back into the limelight in 2004 after the refined version was proposed by Dostal [10] with its They achieved a cycle thermal efficiency of close to 55% under ideal conditions. However, this cycle application to next-generation nuclear reactors. Since then, different configurations for the S-CO2 came back into the limelight in 2004 after the refined version was proposed by Dostal [10] with its Brayton cycle have been reported in the literature, including the simple cycle, the pre-compression application to next-generation nuclear reactors. Since then, different configurations for the S-CO cycle, the re-compression cycle with a partial cooling cycle, the intercooling cycle, and the split2 Brayton cycle have been reported in the literature, including the simple cycle, the pre-compression expansion cycle [11,12]. cycle, the re-compression cycle with a partial cooling cycle, the intercooling cycle, and the split The integration of various types of heat sources into S-CO2 BC has been studied in the last expansion cycle [11,12]. decade. Sarkar [13] performed an energy and exergy analysis of the S-CO2 recompression Brayton cycleThe (RBC) integration utilizingof nuclear various waste types heat of heat and sources performed into S-COa sensitivity2 BC has analysis. been studied He concluded in the last that decade. the irreversibilitiesSarkar [13] performed of heat an exchangers energy and exergyare considerably analysis of thegreater S-CO 2inrecompression comparison Braytonto those cycle of turbo- (RBC) machineries.utilizing nuclear Sarkar waste and heat Bhattacharyya and performed [14] a performed sensitivity analysis.an exergy He analysis concluded for the that RBC the irreversibilitiesand optimized itsof heatperformance. exchangers They are found considerably that the greater differences in comparison in specific to heat those capacities of turbo-machineries. at the compressor Sarkar outlet and andBhattacharyya the turbine [14outlet] performed play an important an exergy role analysis in the foroptimization the RBC andof the optimized cycle’s its performance. ratio and They found that the differences in specific heat capacities at the compressor outlet and the turbine intermediate pressure. Ahn et al. [15] investigated various configurations of the S-CO2 BC for applicationoutlet play an to importantnuclear reactors role in theand optimization identified an of RBC the cycle’s layout pressure more efficient ratio and for intermediate a mild turbine pressure. inlet Ahntemperature et al. [15 range] investigated (450 °C to various 600 °C). configurations of the S-CO2 BC for application to nuclear reactors and identified an RBC layout more efficient for a mild turbine inlet temperature range (450 ◦C to 600 ◦C). The integration of concentrating solar power (CSP) with S-CO2 Brayton cycles has also been The integration of concentrating solar power (CSP) with S-CO2 Brayton cycles has also been investigated. Turchi [16] studied an S-CO2 RBC integrated with CSP and found that it could offer efficienciesinvestigated. higher Turchi than [16 ]those studied of ansupercritical S-CO2 RBC or integrated superheated with steam CSP andRank foundine cycles. that it Padilla could offer[17] efficiencies higher than those of supercritical or superheated steam Rankine cycles. Padilla [17] performed an energy and exergy analysis of eight different configurations of S-CO2 with the heat performedsource being an a energy solar andreceiver. exergy He analysis concluded of eight that different the recompression configurations Brayton of S-CO cycle2 with with the main heat compressorsource being intercooling a solar receiver. has He the concluded best thermal that the and recompression exergetic performance. Brayton cycle This with was main achieved compressor by introducingintercooling hasan intercooling the best thermal stage and in exergetic the main performance. compressor, This which was is achieved claimed by to introducing decrease the an compressorintercooling work stage and, in the eventually, main compressor, the net power which outp is claimedut of the to cycle. decrease The theliterature compressor also reports work and, the utilizationeventually, theof cold net power energy output of liquefied of the cycle. natural The literaturegas (LNG) also as reports a heat the sink utilization in proposing of cold energy new of liquefied natural gas (LNG) as a heat sink in proposing new configurations for the CO2 power cycle configurations for the CO2 power cycle with an ultimate goal of improving the thermodynamic withperformance an ultimate of the goal cycle of improving[18–21]. the thermodynamic performance of the cycle [18–21]. The literature reports numerous thermodynamic analyses carried out for S-CO power cycles The literature reports numerous thermodynamic analyses carried out for S-CO22 power cycles utilizing either either waste waste heat, heat, nuclear, nuclear, or or CSP CSP system systems.s. Various Various configurations configurations have have been been proposed proposed to achieveto achieve the the maximum maximum possible possible therma thermall efficiencies. efficiencies. In this In thispaper, paper, we wepropose propose modifications modifications to the to standardthe standard recompression recompression Brayton Brayton cycle cycle with with pa partialrtial cooling cooling (RBC-PC) (RBC-PC) which which target target maximum recovery of heat from within the cycle to minimize external heat input, thus maximizing the overall cycle’s thermal efficiency. efficiency. No specificspecific type of heat input to the cycle is cons considered;idered; thus, the proposed configurationconfiguration maymay be be integrated integrated with with any any suitable suitable heat heat source source working working within within the range the ofrange the turbineof the turbineinlet temperature inlet temperature of interest. of The interest. effect ofThe heat effect exchanger of heat effectiveness exchanger oneffectiveness the cycle’s performanceon the cycle’s is performancealso examined is foralso both examined configurations. for both configurations.

2 2 Figure 1. Supercritical CO2 (S-CO(S-CO2)) power power cycle cycle layouts: layouts: ( (aa)) recompression recompression Brayton Brayton cycle cycle (RBC) with partial coolingcooling and and (b )( RBCb) RBC with with partial partial cooling cooling and improved and improved heat regeneration. heat regeneration. LTR: low-temperature LTR: low- temperaturerecuperator; HTR:recuperator; high-temperature HTR: high-t recuperator.emperature Layoutsrecuperator. (a) adapted Layouts from (a) adapted [17]. from [17].

Processes 2019, 7, 3 3 of 10 Processes 2018, 6, x FOR PEER REVIEW 3 of 10 2. Cycle Configurations 2. Cycle Configurations In this paper, we investigate two variants of S-CO2 Brayton cycles. One is the recompression In this paper, we investigate two variants of S-CO2 Brayton cycles. One is the recompression Brayton cycle with partial cooling (RBC-PC), and the second is the modified version of RBC-PC with Brayton cycle with partial cooling (RBC-PC), and the second is the modified version of RBC-PC with improved heat regeneration (RBC-PC-IHR). Many researchers have already studied the RBC-PC [11,16,17]; improved heat regeneration (RBC-PC-IHR). Many researchers have already studied the RBC-PC thus, it can serve as a basis for comparison of the proposed layout performance. Figure1 presents the [11,16,17]; thus, it can serve as a basis for comparison of the proposed layout performance. Figure 1 configurations of both cycles. presents the configurations of both cycles. Figure1a presents the layout of the RBC with partial cooling. In this configuration, the stream Figure 1a presents the layout of the RBC with partial cooling. In this configuration, the stream leaving low-temperature recuperator (State 4), denoted by LTR, is cooled and compressed (State 6) leaving low-temperature recuperator (State 4), denoted by LTR, is cooled and compressed (State 6) to the intermediate pressure of the cycle using main compressor C1. The stream is then divided into to the intermediate pressure of the cycle using main compressor C1. The stream is then divided into two; one is cooled and compressed to the high pressure of the cycle (State 8) which later recovers two; one is cooled and compressed to the high pressure of the cycle (State 8) which later recovers heat heat in LTR, whereas the second stream is compressed to the high pressure of the cycle (State 10) in LTR, whereas the second stream is compressed to the high pressure of the cycle (State 10) and and mixed with the first stream leaving LTR (State 9). The mixed stream (State 11) recovers heat mixed with the first stream leaving LTR (State 9). The mixed stream (State 11) recovers heat in high- in high-temperature recuperator (HTR) and then flows to the heat source, where it is heated to the temperature recuperator (HTR) and then flows to the heat source, where it is heated to the cycle’s cycle’s high temperature. The high-temperature and high-pressure stream (State 1) is expanded in the high temperature. The high-temperature and high-pressure stream (State 1) is expanded in the expander (T1). expander (T1). Figure1b presents the proposed configuration (RBC-PC-IHR); it is very similar to the RBC-PC but Figure 1b presents the proposed configuration (RBC-PC-IHR); it is very similar to the RBC-PC with a third heat recuperator for improved heat regeneration. In this configuration, the stream leaving but with a third heat recuperator for improved heat regeneration. In this configuration, the stream the LTR (State 5) is cooled (State 6) and compressed (State 7) to the intermediate pressure of the cycle. leaving the LTR (State 5) is cooled (State 6) and compressed (State 7) to the intermediate pressure of The stream is then divided into two; one stream (stream 7b) is cooled and compressed to the cycle’s the cycle. The stream is then divided into two; one stream (stream 7b) is cooled and compressed to high pressure, then flows to a medium-temperature recuperator (MTR) to recover the heat, whereas the cycle’s high pressure, then flows to a medium-temperature recuperator (MTR) to recover the heat, the other stream (stream 7a) receives heat in LTR before it is compressed to the high pressure of the whereas the other stream (stream 7a) receives heat in LTR before it is compressed to the high pressure cycle in C2. The streams leaving the compressor C2 and MTR are mixed and flow to HTR to recover of the cycle in C2. The streams leaving the compressor C2 and MTR are mixed and flow to HTR to heat before heating in the Heater. recover heat before heating in the Heater. Figure2a,b display the temperature– plots for the RBC-PC and RPC-PC-IHR, respectively, Figures 2a and 2b display the ◦temperature–entropy plots for the RBC-PC and RPC-PC-IHR, at a turbine inlet temperature of 500 C. In the proposed layout (RBC-PC-HR), the S-CO2 stream after respectively, at a turbine inlet temperature of 500 °C. In the proposed layout (RBC-PC-HR), the S-CO2 the compression process between States 6 and 7 splits into two; one is cooled down to State 8, and the stream after the compression process between States 6 and 7 splits into two; one is cooled down to second recovers heat in LTR and reaches State 11 prior to compression between States 11 and 12. State 8, and the second recovers heat in LTR and reaches State 11 prior to compression between States Because of the heat recuperation in LTR (between States 7 and 11), the temperature of the S-CO prior 11 and 12. Because of the heat recuperation in LTR (between States 7 and 11), the temperature2 of the to HTR (between States 13 and 14) is higher than that which could be achieved at the same location in S-CO2 prior to HTR (between States 13 and 14) is higher than that which could be achieved at the RBC-PC. Eventually, due to higher heat recuperation with the RBC-PC-IHR layout, the temperature of same location in RBC-PC. Eventually, due to higher heat recuperation with the RBC-PC-IHR layout, the S-CO2 before the heat source is higher in RBC-PC-IHR, which requires less heat input in the Heater the temperature of the S-CO2 before the heat source is higher in RBC-PC-IHR, which requires less in comparison to the RBC-PC layout. heat input in the Heater in comparison to the RBC-PC layout.

Figure 2. AA temperature–entropy temperature–entropy diagram diagram for for different different S-CO S-CO2 Brayton2 Brayton cycle cycle layouts: layouts: (a) RBC-PC, (a) RBC-PC, and and(b) RBC-PC (b) RBC-PC with with improved improved heat heat regeneration regeneration (RBC-P (RBC-PC-IHR).C-IHR). The The highest highest temperature temperature of ofthe the cycle cycle is is500 500 °C.◦ C.

3. Energy Model

The first-law efficiency, the thermal efficiency (η), of the cycle is calculated as η =(W − W ,)/(Q ) (1)

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3. Energy Model

The first-law efficiency, the thermal efficiency (ηth), of the cycle is calculated as . . . ηth = (Wturbine − Wnet, compressor)/(Qheater) (1)

. . where Wturbine is the work output of the turbine and Wnet, compressor is the net compression work . input to the cycle. Qheater is the heat input given to the cycle via the heat source. The heat exchanger effectiveness, ηHEX, is considered for the total hot stream [17,22] and is defined as

ηHEX = (hHTR_HI − hLTR_HO)/(hHTR_HI − hLTR_HO@Tc) (2) where hHTR_HI and hLTR_HO are the of the hot streams at the inlet of the high-temperature recuperator and the outlet of the low-temperature recuperator, respectively. hLTR_HO@Tc is the of the hot stream at the outlet of the low-temperature recuperator calculated based on the minimum temperature that it could achieve [23] (T8 for RBC-PC and T7 for RBC-PC-IHR). Since in both configurations the flow stream splits into two, another important parameter called the split ratio (SR) is introduced, which is defined as the ratio of mass flow rate of the cold stream entering LTR to . . . . the total mass flow rate of the cycle. It is equal to m6a/mt for RBC-PC and m7a/mt for RBC-PC-IHR, . where mt is the cycle’s total mass flow rate.

4. Simulation Environment The commercial software Aspen HYSYS V9 (Aspen Technology, Inc., Bedford, MA, USA) was used to configure and simulate the S-CO2 Brayton cycles. We used the Peng–Robinson model for the state properties calculation. The investigation assumes the following conditions:

1. The cycle operates under steady-state conditions [11,16,17]; 2. Energy losses in the pipelines are negligible [11,16,17]; 3. The compression and expansion processes are adiabatic [11,16,17]; 4. The turbine and compressor efficiencies are 93% and 89%, respectively [11,16,17]; 5. The heat exchanger effectiveness is 95% (except in Section 7.2, where we investigate its effect ◦ on cycle performance) with a minimum pinch point temperature (∆Tmin) of 5 C for all heat exchangers [11,16,17]; 6. The cycle maximum pressure is 25 MPa [11,16,17]; 7. The turbine inlet temperature varies from 500 ◦C to 850 ◦C; 8. The cycle intermediate pressure is 7.5 MPa; 9. The split ratio (SR) is 0.5.

5. Parametric Adjustments

The thermodynamic performance of S-CO2 recompression Brayton cycles is greatly influenced by a number of parameters, such as the turbine inlet temperature, cycle pressure ratio, split ratio, heat exchanger effectiveness, and the minimum allowed temperature in the heat exchangers [8–10,24,25]. To compare our results with the published data, we kept some of the parameters constant, as mentioned in Section4. Some parameters were adjusted to operate the cycle at near-optimal conditions. We investigated the performance of each configuration, shown in Figure1, against the cycle’s minimum pressure, pmin, (p5 for RBC-PC and p6 for RBC-PC-IHR). The turbine inlet pressure (TIP) values considered were 16 MPa and 25 MPa (which is the maximum allowable in this study). Figure3 presents the cycle’s thermal efficiency and minimum pinch temperature plotted against the cycle’s minimum pressure for RBC-PC and RCB-PC-IHR. Considering RBC-PC (Figure3a) with a turbine inlet temperature of 850 ◦C, the cycle’s thermal efficiency decreases continuously with the increase of pmin for a turbine inlet pressure of 16 MPa or 25 MPa, whereas the minimum allowable Processes 2019, 7, 3 5 of 10

◦ pinch temperature (∆Tmin), i.e., 5 C, occurs at pmin close to 3.8 MPa for a TIP of 25 MPa. For a turbine inlet temperature of 500 ◦C with a TIP of 25 MPa, the temperature remains crossed in the heat ◦ exchanger. However, with a TIP of 16 MPa, the minimum pinch temperature of 5 C occurs for pmin approximately equal to 4.3. Thus, the cycle’s minimum pressure (p5) was set to 4.5 MPa for RBC-PC. Similarly, the near-optimal value of the cycle’s minimum pressure was set to 5.5 MPa for RBC-PC-IHC. Processes 2018, 6, x FOR PEER REVIEW 5 of 10

(a) (b)

FigureFigure 3. 3. CycleCycle thermal thermal efficiency efficiency (solid (solid lines) lines) and and minimum minimum pinch pinch temperature temperature in in the the heat heat exchanger exchanger

(dashed(dashed lines) lines) plotted plotted as as a a function function of of the the cycle’s cycle’s minimum minimum pressure pressure ( (ppmin) )for for ( (aa)) RBC-PC RBC-PC and and ( (bb)) RBC-PC-IHR.RBC-PC-IHR. TheThe turbineturbine inlet inlet pressure pressure (TIP) (TIP) was setwas to 25set MPa to 25 or 16MPa MPa or for 16 turbine MPa inletfor turbine temperatures inlet temperatures(TIT) of 850 ◦C (TIT) and 500of 850◦C. °C The and red 500 dot shows°C. The the red near-optimal dot shows valuethe near-optimal for the cycle’s value minimum for the pressure. cycle’s minimum pressure. 6. Model Validation 6. ModelThe simulationValidation results for the base cycle, i.e., RBC-PC, were validated using data already published by KulhThe ásimulationnek and Dost resultsál [11 ],for Turchi the base et al. cycle, [16], and i.e., Padilla RBC-PC, et al.were [17]. validated Figure4 presents using data the effectalready of publishedthe turbine by inlet Kulhánek pressure and on Dostál the efficiency [11], Turchi and minimumet al. [16], and pinch Padilla temperature et al. [17]. at differentFigure 4 presents turbine inlet the ◦ ◦ effecttemperatures of the turbine from 500 inletC pressure to 850 C. on The the thermal efficiency efficiency and minimum increases pinch monotonically temperature with at increasing different turbineturbine inlet inlet temperatures pressure and from temperature, 500 °C to as 850 shown °C. The in Figurethermal4a. efficiency For a given incr turbineeases monotonically inlet temperature, with increasingthe minimum turbine pinch inlet temperature pressure decreasesand temperature, linearly for as ashown turbine in inlet Figure pressure 4a. For above a given 16 MPa, turbine as shown inlet temperature,in Figure4b. Thus,the minimum for a given pinch turbine temperature inlet temperature, decreases the linearly maximum for a cycle turbine efficiency inlet pressure is restricted above by 16the MPa, condition as shown of the in minimum Figure 4b. allowable Thus, for pinch a given temperature. turbine Ininlet the temperature, current study, the the maximum minimum pinchcycle ◦ efficiencytemperature is restricted is 5 C; thus, by the the condition red dots of in the Figure minimum4b represent allowable the near-optimalpinch temperature. operating In the current study,for each the turbine minimum inlet pinch temperature, temperature and is their 5 °C; values thus, arethe listedred dots in Tablein Figure1. Figure 4b represent5 presents the a near- plot optimalof the thermal operating efficiency pressures of for the each cycle turbine versus inlet turbine temperature, inlet temperatures. and their values Data are points listed takenin Table from 1. Figurereferences 5 presents [11,16 ,a17 plot] are of also the thermal plotted forefficiency comparison. of the cycle It is versus evident turbine from theinlet plots temperatures. that the results Data pointsproduced taken by from the current references model [11,16,17] agree well are withalso thoseplotted in for the comparison. literature. Slight It is differencesevident from between the plots our thatdata the and results published produced data could by the be acurrent result of model differences agree in well the thermodynamicwith those in the properties literature. databases Slight differencesused in this simulationbetween our and data in published and published models. data could be a result of differences in the thermodynamic properties databases used in this simulation and in published models. Table 1. Turbine inlet pressures at different turbine inlet temperatures for maximum thermal efficiency of the recompression Brayton cycle with partial cooling (RBC-PC).

Turbine inlet temperature (◦C) 500 550 600 650 700 750 800 850 Turbine inlet pressure (MPa) 20.0 21.5 23.0 24.9 25.0 25.0 25.0 25.0 Thermal efficiency (%) 43.2 45.7 48.0 50.0 51.7 53.2 54.5 55.8

Figure 4. (a) Thermal efficiencies of RBC-PC plotted versus turbine inlet pressure for TIT from 500 °C to 850 °C. (b) Minimum pinch temperature versus turbine inlet pressure; red dots represent the minimum pinch temperature of 5 °C.

Table 1. Turbine inlet pressures at different turbine inlet temperatures for maximum thermal efficiency of the recompression Brayton cycle with partial cooling (RBC-PC).

Processes 2018, 6, x FOR PEER REVIEW 5 of 10

(a) (b)

Figure 3. Cycle thermal efficiency (solid lines) and minimum pinch temperature in the heat exchanger

(dashed lines) plotted as a function of the cycle’s minimum pressure (p) for (a) RBC-PC and (b) RBC-PC-IHR. The turbine inlet pressure (TIP) was set to 25 MPa or 16 MPa for turbine inlet temperatures (TIT) of 850 °C and 500 °C. The red dot shows the near-optimal value for the cycle’s minimum pressure.

6. Model Validation The simulation results for the base cycle, i.e., RBC-PC, were validated using data already published by Kulhánek and Dostál [11], Turchi et al. [16], and Padilla et al. [17]. Figure 4 presents the effect of the turbine inlet pressure on the efficiency and minimum pinch temperature at different turbine inlet temperatures from 500 °C to 850 °C. The thermal efficiency increases monotonically with increasing turbine inlet pressure and temperature, as shown in Figure 4a. For a given turbine inlet temperature, the minimum pinch temperature decreases linearly for a turbine inlet pressure above 16 MPa, as shown in Figure 4b. Thus, for a given turbine inlet temperature, the maximum cycle efficiency is restricted by the condition of the minimum allowable pinch temperature. In the current study, the minimum pinch temperature is 5 °C; thus, the red dots in Figure 4b represent the near- optimal operating pressures for each turbine inlet temperature, and their values are listed in Table 1. Figure 5 presents a plot of the thermal efficiency of the cycle versus turbine inlet temperatures. Data points taken from references [11,16,17] are also plotted for comparison. It is evident from the plots that the results produced by the current model agree well with those in the literature. Slight Processesdifferences2019, 7,between 3 our data and published data could be a result of differences in6 ofthe 10 thermodynamic properties databases used in this simulation and in published models.

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Turbine inlet temperature (°C) 500 550 600 650 700 750 800 850 FigureFigure 4.4. ((aa)) Thermal efficiencies efficiencies of of RBC-PC RBC-PC plotted plotted vers versusus turbine turbine inlet inlet pressure pressure for for TIT TIT from from 500 500 °C Turbine inlet pressure (MPa) 20.0 21.5 23.0 24.9 25.0 25.0 25.0 25.0 ◦toC to850 850 °C.◦ C.(b ()b Minimum) Minimum pinch pinch temperature temperature versus versus turbin turbinee inlet inlet pressure; pressure; red dotsdots representrepresent thethe Thermal efficiency (%) 43.2 45.7 48.0 50.0 51.7 53.2 54.5 55.8 minimumminimum pinchpinch temperaturetemperature of of 5 5◦ °C.C.

Table 1. Turbine inlet pressures at different turbine inlet temperatures for maximum thermal efficiency of the recompression Brayton cycle with partial cooling (RBC-PC).

Figure 5. ValidationValidation of simulation results for the RBC-PC with [[11,16,17].11,16,17]. 7. Results and Discussions 7. Results and Discussions 7.1. Cycle Thermal Efficiency 7.1. Cycle Thermal Efficiency The performance of the proposed cycle, RBC-PC-IHR, was studied by comparing its thermal efficiencyThe performance with that of RBC-PC. of the proposed Figure6 shows cycle, theRBC-PC-IHR, variation in was the proposedstudied by cycle’s comparing thermal its efficiency thermal andefficiency minimum with pinchthat of temperatureRBC-PC. Figure in the 6 shows heat exchanger the variation with in respectthe proposed to the turbinecycle’s thermal inlet pressure efficiency for aand range minimum of turbine pinch inlet temperature temperatures. in the The heat cycle exchange efficiencyr with increases respect to monotonically the turbine inlet with pressure increasing for turbinea range inletof turbine pressure inlet and temperatures. temperature, The as cycle expected. efficiency The minimumincreases monoto pinch temperaturenically with inincreasing the heat exchangersturbine inlet also pressure drops and with temperature, increasing turbine as expe inletcted. pressure, The minimum thus limiting pinch temperature the maximum in possiblethe heat operatingexchangers pressure also drops of the with cycle. increasing Table2 lists turbine the near-optimal inlet pressure, values thus of limiting turbine the operating maximum pressures possible at differentoperating turbine pressure inlet of temperaturesthe cycle. Table with 2 lists a minimum the near-optimal pinch temperature values of ofturbine 5 ◦C. operating pressures at different turbine inlet temperatures with a minimum pinch temperature of 5 °C. Table 2. Turbine inlet pressures at different turbine inlet temperatures for maximum thermal efficiency of the RBC-PC with improved heat regeneration (RBC-PC-IHR).

Turbine inlet temperature (◦C) 500 550 600 650 700 750 800 850 Turbine inlet pressure (MPa) 17.2 17.9 18.6 19.3 20 20.7 21.4 22.1 Thermal efficiency (%) 44.1 46.8 49.2 51.4 53.3 55.0 56.7 58.2

Figure 6. (a) Thermal efficiencies of the RBC-PC-IHR plotted versus turbine inlet pressure for TIT from 500 °C to 850 °C. (b) Minimum pinch temperature versus turbine inlet pressure; red dots represent the minimum pinch temperature of 5 °C.

Table 2. Turbine inlet pressures at different turbine inlet temperatures for maximum thermal efficiency of the RBC-PC with improved heat regeneration (RBC-PC-IHR).

Turbine inlet temperature (°C) 500 550 600 650 700 750 800 850 Turbine inlet pressure (MPa) 17.2 17.9 18.6 19.3 20 20.7 21.4 22.1 Thermal efficiency (%) 44.1 46.8 49.2 51.4 53.3 55.0 56.7 58.2 The thermal efficiency of the RBC-PC-IHR configuration is plotted in Figure 7a along with the efficiency of the RBC-PC at different turbine inlet temperatures. A significant increase in thermal

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Turbine inlet temperature (°C) 500 550 600 650 700 750 800 850 Turbine inlet pressure (MPa) 20.0 21.5 23.0 24.9 25.0 25.0 25.0 25.0 Thermal efficiency (%) 43.2 45.7 48.0 50.0 51.7 53.2 54.5 55.8

Figure 5. Validation of simulation results for the RBC-PC with [11,16,17].

7. Results and Discussions

7.1. Cycle Thermal Efficiency The performance of the proposed cycle, RBC-PC-IHR, was studied by comparing its thermal efficiency with that of RBC-PC. Figure 6 shows the variation in the proposed cycle’s thermal efficiency and minimum pinch temperature in the heat exchanger with respect to the turbine inlet pressure for a range of turbine inlet temperatures. The cycle efficiency increases monotonically with increasing turbine inlet pressure and temperature, as expected. The minimum pinch temperature in the heat exchangers also drops with increasing turbine inlet pressure, thus limiting the maximum possible Processesoperating2019 pressure, 7, 3 of the cycle. Table 2 lists the near-optimal values of turbine operating pressures7 of 10 at different turbine inlet temperatures with a minimum pinch temperature of 5 °C.

Figure 6.6. ((aa)) ThermalThermal efficiencies efficiencies of of the the RBC-PC-IHR RBC-PC-IHR plotted plotted versus versus turbine turbine inlet inlet pressure pressure for TIT for from TIT 500from◦ C500 to 850°C ◦toC. 850 (b) Minimum°C. (b) Minimum pinch temperature pinch temperat versusure turbine versus inlet turbine pressure; inlet red pressure; dots represent red dots the minimumrepresent the pinch minimum temperature pinch of temperature 5 ◦C. of 5 °C.

TheTable thermal 2. Turbine efficiency inlet pressures of the RBC-PC-IHR at different configurationturbine inlet temperatures is plotted in for Figure maximum7a along thermal with the Processes 2018, 6, x FOR PEER REVIEW 7 of 10 efficiencyefficiency of the of the RBC-PC RBC-PC at with different improv turbineed heat regeneration inlet temperatures. (RBC-PC-IHR). A significant increase in thermal efficiency for the RBC-RC-IHR configuration is noted, especially at high turbine inlet temperatures. efficiencyTurbine for the inlet RBC-RC-IHR temperature configuration (°C) 500 is note550d, especially600 650 at high700 tu rbine750 inlet800 temperatures. 850 Figure7b is plotted to compare the efficiency improvement (in percentage points) offered by the Figure 7bTurbine is plotted inlet to pressurecompare (MPa)the efficiency 17.2 im provement17.9 18.6 (in percentage19.3 20 points) 20.7 offered21.4 by22.1 the RBC- RBC-PC-IHR layout in comparison to the RBC-PC. A minimum efficiency increase of 2% occurs at a PC-IHR layoutThermal in comparison efficiency to (%) the RBC-PC. 44.1 A minimum46.8 49.2 efficiency 51.4 increase53.3 of55.0 2% occurs56.7 at58.2 a turbine turbine inlet temperature of 500 ◦C, and this increases to nearly 4.5% by 800 ◦C. inlet Thetemperature thermal efficiencyof 500 °C, andof the this RBC-PC-IHR increases to configurnearly 4.5%ation by is 800 plotted °C. in Figure 7a along with the Besides being more efficient, the RBC-PC-IHR operating pressure is much lower than that for the efficiencyBesides of beingthe RBC-PC more efficient, at different the RBC-PC-IHRturbine inlet temperatures.operating pressure A significant is much increaselower than in thermalthat for theRBC-PC RBC-PC configuration configuration (refer (refer to Tables to Table1 and 1 and2). For Tabl bothe 2). cycles, For both the cycles, operating the operating turbine inlet turbine pressure inlet pressureincreases increases with increasing with increasing turbine inletturbine temperature inlet temperature with a minimum with a minimum of 20 MPa of 20 and MPa 17.2 and MPa 17.2 at ◦ MPaa turbine at a inletturbine temperature inlet temperature of 500 C of for 500 RBC-PC °C for and RBC-PC RBC-PC-IHR, and RBC-PC-IHR, respectively. respectively. The maximum The maximumpressure is pressure restricted is to restricted 25 MPa into this 25 MPa investigation, in this investigation, which is attained which by is RBC-PCattained atby the RBC-PC turbine at inlet the ◦ turbinetemperature inlet oftemperature 700 C; however, of 700for °C; the however, RBC-PC-IHR for the configuration, RBC-PC-IHR the configuration, turbine inlet pressurethe turbine is raised inlet ◦ pressureup to 22.1 is MPa raised by up the to turbine 22.1 MPa inlet by temperature the turbine ofinlet 850 temperatureC. of 850 °C.

Figure 7. ((aa)) The The thermal thermal efficiencies efficiencies of of RBC-PC-IHR RBC-PC-IHR and and RBC-PC RBC-PC plotted versus turbine inlet temperaturestemperatures from from 500 500 °C◦C to 850 °C.◦C. ( b)) The improvement in thermal efficiency efficiency from RBC-PC-IHR compared to RBC-PC in percentage points.

7.2. Heat Heat Exchanger Exchanger Effectiveness An investigation investigation was was carried carried out out to toevaluate evaluate the theperformance performance of both of bothcycles cycles (RBC-PC (RBC-PC and RBC- and RBC-PC-IHR) with respect to heat exchanger effectiveness (η ). The heat exchanger effectiveness PC-IHR) with respect to heat exchanger effectiveness (ηHEX). TheHEX heat exchanger effectiveness varies betweenvaries between 85% and 85% 95%. and For 95%. each For value each of valueheat exch of heatanger exchanger effectiveness, effectiveness, the cycle theminimum cycle minimum pressure (ppressure5 for RBC-PC (p5 for and RBC-PC p6 for and RBC-PC-IHR) p6 for RBC-PC-IHR) was adjusted was following adjusted followingthe procedure the procedure mentioned mentioned earlier in Sectionearlier in 5. Section Figure5 .8a Figure presents8a presents the cycle the thermal cycle thermal efficiency efficiency at different at different turbine turbine inlet inlet temperatures temperatures for heatfor heat exchanger exchanger effectiveness effectiveness values values of of85% 85% and and 95%. 95%. Decreasing Decreasing the the heat heat exchange exchange effectiveness decreases the cycle efficiency efficiency due to a decrease in heat recuperation. The thermal efficiency efficiency of the proposed layout (RBC-PC-IHR) at low values of heat exchanger effectiveness is significantly better than that of RBC-PC, especially at low turbine inlet temperatures. Figure 8b presents an estimate of the efficiency improvement offered by the RBC-PC-IHR configuration in comparison to the RBC-PC at different values of heat exchanger effectiveness. The RBC-PC-IHR configuration was found to be nearly 14% more efficient than the RBC-PC at a turbine inlet temperature of 500 °C. Except for a heat exchanger effectiveness of 95%, with increasing turbine inlet temperature, a fall in efficiency improvement is noticed with a minimum of nearly 5% at a turbine inlet temperature of 850 °C.

Processes 2018, 6, x FOR PEER REVIEW 7 of 10

efficiency for the RBC-RC-IHR configuration is noted, especially at high turbine inlet temperatures. Figure 7b is plotted to compare the efficiency improvement (in percentage points) offered by the RBC- PC-IHR layout in comparison to the RBC-PC. A minimum efficiency increase of 2% occurs at a turbine inlet temperature of 500 °C, and this increases to nearly 4.5% by 800 °C. Besides being more efficient, the RBC-PC-IHR operating pressure is much lower than that for the RBC-PC configuration (refer to Table 1 and Table 2). For both cycles, the operating turbine inlet pressure increases with increasing turbine inlet temperature with a minimum of 20 MPa and 17.2 MPa at a turbine inlet temperature of 500 °C for RBC-PC and RBC-PC-IHR, respectively. The maximum pressure is restricted to 25 MPa in this investigation, which is attained by RBC-PC at the turbine inlet temperature of 700 °C; however, for the RBC-PC-IHR configuration, the turbine inlet pressure is raised up to 22.1 MPa by the turbine inlet temperature of 850 °C.

Figure 7. (a) The thermal efficiencies of RBC-PC-IHR and RBC-PC plotted versus turbine inlet temperatures from 500 °C to 850 °C. (b) The improvement in thermal efficiency from RBC-PC-IHR compared to RBC-PC in percentage points.

7.2. Heat Exchanger Effectiveness An investigation was carried out to evaluate the performance of both cycles (RBC-PC and RBC- PC-IHR) with respect to heat exchanger effectiveness (ηHEX). The heat exchanger effectiveness varies between 85% and 95%. For each value of heat exchanger effectiveness, the cycle minimum pressure (p5 for RBC-PC and p6 for RBC-PC-IHR) was adjusted following the procedure mentioned earlier in ProcessesSection2019 5. Figure, 7, 3 8a presents the cycle thermal efficiency at different turbine inlet temperatures8 of for 10 heat exchanger effectiveness values of 85% and 95%. Decreasing the heat exchange effectiveness decreases the cycle efficiency due to a decrease in heat recuperation. The thermal efficiency of the proposed layout (RBC-PC-IHR) at low values of heatheat exchangerexchanger effectivenesseffectiveness is significantlysignificantly better than thatthat ofof RBC-PC,RBC-PC, especiallyespecially atat lowlow turbineturbine inletinlet temperatures.temperatures. Figure8 8bb presentspresents anan estimateestimate ofofthe theefficiency efficiency improvement improvementoffered offeredby by the the RBC-PC-IHR RBC-PC-IHR configurationconfiguration in in comparison comparison to to the the RBC-PC RBC-PC at atdiff differenterent values values of heat of heat exchanger exchanger effectiveness. effectiveness. The The RBC-PC-IHR configuration was found to be nearly 14% more efficient than the RBC-PC at a RBC-PC-IHR configuration was ◦found to be nearly 14% more efficient than the RBC-PC at a turbine turbineinlet temperature inlet temperature of 500 °C. of Except 500 C. for Except a heat for exchanger a heat exchanger effectiveness effectiveness of 95%, with of 95%, increasing with increasing turbine turbine inlet temperature, a fall in efficiency improvement is noticed with a minimum of nearly 5% at inlet temperature, a fall in efficiency◦ improvement is noticed with a minimum of nearly 5% at a aturbine turbine inlet inlet temperature temperature of of 850 850 °C.C.

Figure 8. (a) Cycle thermal efficiencies versus turbine inlet pressure with heat exchanger effectiveness values of 85% and 95%. (b) Improvement in thermal efficiency from the RBC-PC-IHR compared to the RBC-PC in percentage points at different values of heat exchanger effectiveness between 85% and 95%.

8. Conclusions In this work, we proposed a modified version of a recompression Brayton cycle with partial cooling (RBC-PC). We called this configuration a recompression Brayton cycle with partial cooling and improved heat regeneration (RBC-PC-IHR). Energy analysis was performed to investigate the thermal efficiency of the proposed cycle configuration over that of RBC-PC. The key outcomes of the investigation are as follows:

• For a given turbine inlet temperature, the thermal efficiency increased with increasing turbine inlet pressure for both configurations (RBC-PC and RBC-PC-IHR); however, the pinch temperature in the heat exchanger maintained a decreasing trend. • For a given heat exchanger effectiveness and minimum allowable pinch temperature, the maximum turbine inlet pressure increased with increasing turbine inlet temperature for both layouts. • The RBC-PC-IHR configuration was significantly efficient in comparison with the RBC-PC. The magnitude of its efficiency would be determined by a number of factors, like turbine inlet temperature, minimum pinch temperature in the heat exchanger, and its effectiveness. • For a heat exchanger effectiveness of 95% and a minimum pinch of 5 ◦C, the RBC-PC-IHR was found to be 2% and 4.5% more efficient than the RBC-PC at turbine inlet temperatures of 500 ◦C and 850 ◦C, respectively. • Decreasing the heat exchanger effectiveness and keeping the minimum pinch at a given value at 5 ◦C resulted in decreased cycle efficiency for both layouts. However, the RBC-PC lost cycle efficiency drastically, especially at low turbine inlet temperatures (between 500 ◦C to 700 ◦C). On the other side, the RBC-PC-IHR performed much better between the turbine inlet temperatures of 500 ◦C and 700 ◦C. With a heat exchanger effectiveness of 85%, the RBC-PC-IHR was found to be nearly 14% more efficient than the RBC-PC at 500 ◦C. • For any given turbine inlet temperature, the operating turbine inlet pressure for the RBC-PC-IHR was found to be much lower than that for the RBC-PC, as seen from Tables1 and2. This would result in a more economical piping system for the RBC-PC-IHR configuration. Processes 2019, 7, 3 9 of 10

Author Contributions: M.E.S. conceived and set up the simulation in Aspen HYSYS V9; M.E.S. and K.H.A. analyzed the simulation results; M.E.S. wrote the article. K.H.A. managed research financials, wherever required. Both authors proofread the final submission. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest.

Nomenclature

TIT turbine inlet temperature, ◦C TIP turbine inlet pressure, MPa LTR low-temperature recuperator MTR medium-temperature recuperator HTR high-temperature recuperator SR split ratio

ηth thermal efficiency, % ηHEX heat exchanger effectiveness ◦ ∆Tmin minimum pinch temperature, C pmin cycle’s minimum pressure, MPa hHTR_HI enthalpy of hot stream at the inlet of high-temperature recuperator, kJ/kg hHTR_HO enthalpy of hot stream at the outlet of low-temperature recuperator, kJ/kg

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