Supercritical CO2 Mixtures for Advanced Brayton Power Cycles in Line-Focusing Solar Power Plants

applied sciences

Article Supercritical CO2 Mixtures for Advanced Brayton Power Cycles in Line-Focusing Solar Power Plants

Robert Valencia-Chapi 1,2,* , Luis Coco-Enríquez 1 and Javier Muñoz-Antón 1

1 Escuela Técnica Superior de Ingenieros Industriales, Universidad Politécnica de Madrid, c/José Gutiérrez Abascal, 2, 28006 Madrid, Spain; [email protected] (L.C.-E.); [email protected] (J.M.-A.) 2 Facultad de Ingeniería en Ciencias Aplicadas, Universidad Técnica del Norte, av. 17 de Julio, 5-21, 100105 Ibarra, Ecuador * Correspondence: [email protected]; Tel.: +34-9106-767-00

Received: 18 October 2019; Accepted: 17 December 2019; Published: 19 December 2019

Abstract: This work quantifies the impact of using sCO2-mixtures (s-CO2/He, s-CO2/Kr, s-CO2/H2S, s-CO2/CH4, s-CO2/C2H6, s-CO2/C3H8, s-CO2/C4H8, s-CO2/C4H10, s-CO2/C5H10, s-CO2/C5H12 and s-CO2/C6H6) as the working fluid in the supercritical CO2 recompression Brayton cycle coupled with line-focusing solar power plants (with parabolic trough collectors (PTC) or linear Fresnel (LF)). Design parameters assessed are the solar plant performance at the design point, heat exchange dimensions, solar field aperture area, and cost variations in relation with admixtures mole fraction. The adopted methodology for the plant performance calculation is setting a constant heat recuperator total conductance (UAtotal). The main conclusion of this work is that the power cycle thermodynamic efficiency improves by about 3–4%, on a scale comparable to increasing the turbine inlet temperature when the cycle utilizes the mentioned sCO2-mixtures as the working fluid. On one hand, the substances He, Kr, CH4, and C2H6 reduce the critical temperature to approximately 273.15 K; in this scenario, the thermal efficiency is improved from 49% to 53% with pure s-CO2. This solution is very suitable for concentrated solar power plants coupled to s-CO2 Brayton power cycles (CSP-sCO2) with night sky cooling. On the other hand, when adopting an air-cooled heat exchanger (dry-cooling) as the ultimate heat sink, the critical temperatures studied at compressor inlet are from 318.15 K to 333.15 K, for this scenario other substances (C3H8,C4H8,C4H10,C5H10,C5H12 and C6H6) were analyzed. Thermodynamic results confirmed that the Brayton cycle efficiency also increased by about 3–4%. Since the ambient temperature variation plays an important role in solar power plants with dry-cooling systems, a CIT sensitivity analysis was also conducted, which constitutes the first approach to defining the optimum working fluid mixture for a given operating condition.

Keywords: Brayton cycle; ﬂuid mixture; solar plant; supercritical CO2

1. Introduction The need to improve the efficiency of energy power plants emphasizes the importance of optimizing their equipment design and the inlet and operation conditions. For this reason, it is important to analyze how the use of fluid mixtures affects the operating conditions—mainly, plant efficiency [1]. There are different external conditions to the plant (environmental conditions) that mark the need to have a working fluid that adapts to these variable environments, both for low and high temperatures, with the objective that the plant works optimally. The ever-increasing necessity to reduce the environmental impact of industrial and urban energy conversion processes has led engineers to consider the use of sCO2-mixtures as working fluid for thermodynamic power and refrigeration cycles [2,3], emphasizing the mitigation of air pollution and the emission of greenhouse gases, and reducing energy production costs [4].

Appl. Sci. 2020, 10, 55; doi:10.3390/app10010055 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 55 2 of 18 Appl. Sci. 2019, 9, x FOR PEER REVIEW 2 of 18

SeveralSeveral configurations configurations of theof the Brayton Brayton cycle cycle are currently are currently under study under [5 study]. One of[5] the. O veryne of interesting the very featuresinteresting of thisfeatures cycle of is this its abilitycycle is to its achieve ability highto achieve efficiency high in efficiency a variety in of a applicationsvariety of applications operating withoperating intermediate with intermediate temperature temperature levels: concentrated levels: c solaroncentrated power (CSP)solar [p6ower,7], waste (CSP) heat [6,7] recovery, waste [8h,eat9], coal-firedrecovery [8,9] power, coal plants-fired [ 10power–12], plant ands Gen [10– IV12] nuclear, and Gen reactors IV nuclear [13– 15reactors] among [13 others.–15] among In this others. work, In thethis influence work, the of influence fluid mixtures of fluid on mixtures the recompression on the recompression Brayton cycle Brayton (cf. Figurecycle (cf.1) hasFigure been 1) studied.has been Thisstudied power. This cycle power is the cycle evolution is the evolution of the previous of the previous configuration configuration proposed proposed by Angelino by Angelino [16,17] and [16,17] has clearand hasconnections clear connections with Sulzer with and Sulzer Feher’s and work Feher’s [18,19 work]. The [18,19] cycle. is The named cycle after is named the re-compressor after the re- locatedcompressor parallel located to the parallel main compressor, to the main which compressor, means that which the flowmeans is splitthat intothe flow two foris split the compression into two for process.the compression The first amountprocess. ofThe stream first amount flows into of thestream cooler, flows where into its the temperature cooler, where is reduced its temperature to a value is closereduced to the to a critical value close temperature. to the critical The temperature. second stream The is second not cooled stream but is compressed not cooled but directly compressed in the re-compressordirectly in the [ 5 re].- Incompressor the work of[5] Al-Sulaiman. In the work [20 of], it Al was-Sulaiman determined [20], that it was the recompression determined that cycle the showedrecompression the best cycle performance showed the in best comparison performance with in other comparison configurations with other (simple, configurations pre-compression, (simple, andpre- dividedcompression expansion, and divided cycles). expansion cycles).

Figure 1. Recompression Brayton cycle layout. MC: main compressor; RC: recompressor; G: generator; Figure 1. Recompression Brayton cycle layout. MC: main compressor; RC: recompressor; G: T: turbine; PC: precooler; FS: fluid split; FM: fluid mixture; LTR: low-temperature recuperator; HTR: generator; T: turbine; PC: precooler; FS: fluid split; FM: fluid mixture; LTR: low-temperature high-temperature recuperator; PHX: primary heat exchanger; SF: solar field. recuperator; HTR: high-temperature recuperator; PHX: primary heat exchanger; SF: solar field. The novelty of this work over the state of the art is new mixtures with mixing ratio and new fluids,The in thenovelty recompression of this work Brayton over the cycle. state In of Section the art2, theis new methodology mixtures with whichmixing this ratio work and was new fluids, in the recompression Brayton cycle. In Section 2, the methodology with which this work was developed is explained. The obtained results of the recompression Brayton cycle using sCO2-mixtures aredeveloped discussed is explained in Section. 3The. Conclusions obtained results and futureof the r workecompression are discussed Brayton in Sectioncycle using4. An sCO increase2-mixtures in are discussed in Section 3. Conclusions and future work are discussed in Section 4. An increase in the the thermal efficiency of the recompression Brayton power cycle using sCO2-mixtures is the main conclusionthermal efficiency of this manuscript. of the recompression Brayton power cycle using sCO2-mixtures is the main conclusion of this manuscript. 2. Assumptions and Methods 2. Assumptions and Methods This work proposes a comparison between the performance of the cycles operating with pure s-CO2Thisand work the cycles proposes of admixtures a comparison of s-CO between2 with He,the Kr,perf Hormance2S, CH4,C of2 Hthe6,C cycles3H8,C operating4H8,C4H with10,C5 pureH10, s-CO2 and the cycles of admixtures of s-CO2 with He, Kr, H2S, CH4, C2H6, C3H8, C4H8, C4H10, C5H10, C5H12, and C6H6. These mixtures have been used because their physical properties stimulate the betterC5H12, behavior and C6H6 of. T thehese plant mixtures cycle. have been used because their physical properties stimulate the better behaviorThe computerof the plant program cycle. SCSP (Supercritical Concentrated Solar Power Plant) is used for the simulationsThe computer of the performance program SCSPof the recompression (Supercritical BraytonConcentrated cycle using Solar pure Power s-CO Plant)2 and sCOis used2-mixtures. for the Thissimulations program ohasf the been performance developed by of members the recompression of the Energy Engineering Brayton cycle Department using pure at the s- TechnicalCO2 and UniversitysCO2-mixtures. of Madrid This [21 program] and it ishas based been on developed the software by core members developed of by the Dyreby Energy in his Engineering doctoral thesisDepartment [22]. SCSP at the sets Technical a constant University heat recuperator of Madrid total [21] conductanceand it is based for on the the performance software core calculation developed methodologyby Dyreby in andhis doctoral uses optimization thesis [22] algorithms. SCSP sets (SUBPLEXa constant [heat23], NEWUOArecuperator [24 total] and conductance BOBYQA [ 25for]) the to calculateperformance the optimal calculation cycle methodology performance. and Figure uses2 illustratesoptimization the algorithms iteration process (SUBPLEX for the [23] cycle, NEWUOA models integrated[24] and BOBYQA into theSCSP [25]) software.to calculate the optimal cycle performance. Figure 2 illustrates the iteration process for the cycle models integrated into the SCSP software. Appl. Sci. 2020, 10, 55 3 of 18 Appl. Sci. 2019, 9, x FOR PEER REVIEW 3 of 18

FigureFigure 2. Iteration 2. Iteration process process for for the the cycle cycle modelsmodels integrated integrated into into the the SCSP SCSP software software..

The fluidThe fluid properties properties were were obtained obtained from from thethe REFPROP REFPROP (Reference (Reference fluid fluid Properties) Properties) database database developeddeveloped by NISTby NIST (National (National Institute Institute of of Standards Standards and Technology) Technology) in inthe the USA USA [26] [.26 Figure]. Figure 3a,b3 a,b show, respectively, the critical pressure and temperature of the mixture when the mole fraction of show, respectively, the critical pressure and temperature of the mixture when the mole fraction the additive fluid changes. Figure 3a specifies that the tendency of the pressure lines is very different of the additive fluid changes. Figure3a specifies that the tendency of the pressure lines is very among the different binary mixtures based on s-CO2, as there a non-linearity between the critical differentpressure among and thethe dimolefferent fraction binary. Figure mixtures 3b shows based that the on critical s-CO2 temperature, as there a distributions non-linearity of mixtures between the criticalfollow pressure a monotonous, and the molenearly fraction. linear trend. Figure The3 criticalb shows temperatures that the critical of s-CO temperature2/He, s-CO2/Kr, distributions s-CO2/CH4, of mixturesand s follow-CO2/C2 aH monotonous,6 have a downward nearly slope linear, while trend. the critical The critical temperatures temperatures of s-CO2 of/H s-CO2S, s-CO2/He,2/C3H s-CO8, s- 2/Kr, s-CO2/CH4, and s-CO2/C2H6 have a downward slope, while the critical temperatures of s-CO2/H2S, s-CO2/C3H8, s-CO2/C4H10, s-CO2/C5H10, s-CO2/C5H12, s-CO2/C4H8, and s-CO2/C6H6 have an upward slope. Therefore, based on the critical temperature distribution trends, the s-CO2 binary mixtures can Appl. Sci. 2019, 9, x FOR PEER REVIEW 4 of 18

Appl. Sci. 2020, 10, 55 4 of 18 CO2/C4H10, s-CO2/C5H10, s-CO2/C5H12, s-CO2/C4H8, and s-CO2/C6H6 have an upward slope. Therefore, based on the critical temperature distribution trends, the s-CO2 binary mixtures can be divided into two begroups: divided ‘group into twoA’ mixtures groups: ‘group(substances A’ mixtures for reduci (substancesng the critical for reducing temperature) the critical and ‘group temperature) B’ mixtures and ‘group(substances B’ mixtures for increasing (substances the critical for increasing temperature). the critical temperature).

He Kr H2S He Kr H2S CH4 C2H6 C3H8 CH4 C2H6 C3H8 C4H8 C4H10 C5H10 C4H8 C4H10 C5H10 C5H12 C6H6 C5H12 C6H6

14 500 12 400 10 8 300 6 200 4 100

Critical Pressure (MPa) Critical Temperature (K) 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Mole fraction Mole fraction

(a) (b)

FigureFigure 3.3. PropertiesProperties ofof mixtures:mixtures: ((aa)) variationvariation ofof thethe criticalcritical pressurepressure vs.vs. thethe molemole fractionfraction ofof addedadded ﬂuid;fluid; ((bb)) variationvariation ofof thethe criticalcritical temperaturetemperature vs.vs. thethe molemole fractionfraction ofof addedadded ﬂuid.fluid.

The performances of the pure s-CO2 and sCO2-mixtures’ recompression Brayton cycle have been The performances of the pure s-CO2 and sCO2-mixtures’ recompression Brayton cycle have been analyzed. The input parameters for the simulation are shown in Table1. The results obtained were analyzed. The input parameters for the simulation are shown in Table 1. The results obtained were validated with the Thermoflex 27 software [27], UniSim Design R451 software [28] (UniSim uses validated with the Thermoflex 27 software [27], UniSim Design R451 software [28] (UniSim uses Peng-Robinson equation of state for thermodynamic property estimations), and scientific articles about Peng-Robinson equation of state for thermodynamic property estimations), and scientific articles the effect of gaseous admixtures on cycles with s-CO2 [1,29,30]. about the effect of gaseous admixtures on cycles with s-CO2 [1,29,30].

TableTable 1.1. MainMain assumptionsassumptions forfor thethe powerpower cyclescycles calculations.calculations.

Nomenclature ValueValue UnitUnit NetNet power power output output WW 50.0050.00 MWMW 1 Optimized1 // Compressor inlet temperature T1 Optimized // K Compressor inlet temperature T 2 K 1 [318.15[318.15///323.15/323.15///328.15/328.15///333.15]/333.152 ] 3 Optimized3 // 4 CompressorCompressor inlet inlet pressure pressure PP11 Optimized //critical pressure MPaMPa critical pressure4 Turbine inlet temperature T6 823.15 K Turbine inlet temperature T6 823.15 K TurbineTurbine inlet inlet pressure pressure PP66 25.0025.00 MPaMPa MainMain compressor compressor efficiency eﬃciency [31,32] [31,32] ηηmcmc 0.890.89 - -

Re-Re-compressorcompressor efficiency eﬃciency [31,32] [31,32] ηηrcrc 0.890.89 - - Turbine efficiency [31,32] ηt 0.93 - Turbine eﬃciency [31,32] ηt 0.93 - Heat exchanger conductance for Heat exchanger conductance for low UALT 2500 // 5000 // 7500 kW/K UA 2500//5000//7500 kW/K low temperaturetemperature recuperator recuperator LT Heat exchanger conductance for Heat exchanger conductance for UAHT 2500 // 5000 // 7500 kW/K UA 2500//5000//7500 kW/K highhigh temperature temperature recuperator recuperator HT Split fraction γ Optimized - Split fraction γ Optimized - 1 CIT optimized for group A mixtures. 2 CIT’s range for group B mixtures. 3 CIP optimized for group A 1 CIT optimized for group A mixtures. 2 CIT’s range for group B mixtures. 3 CIP optimized for group A mixtures. 4 4 CIP just above themixtures critical pressure. CIP j forust group above B the mixtures. critical pressure for group B mixtures. Appl.Appl. Sci. Sci. 20192020, 9, 10x FOR, 55 PEER REVIEW 5 of5 of1818

3. Results and Discussion 3. Results and Discussion The results for group A and group B of the binary mixtures are calculated for a total heat exchangerThe results conductance for group (UA A andtotal) group of 5000, B of the 10000 binary, and mixtures 15000 are kW/K calculated (combining for a total low heat and exchanger high temperatureconductance heat (UA exchangerstotal) of 5000,, i.e. 10,000,, UAtotal and is the 15,000 sum kWof UA/KLT (combining and UAHT). low and high temperature heat exchangers,The optimal i.e., efficiency UAtotal is theof the sum s-CO of UA2 recompressionLT and UAHT). Brayton cycle using pure s-CO2 is for a CIT (CompressorThe optimal Inlet e Temperature)ﬃciency of the equal s-CO to2 recompression the critical temperature Brayton cycle and using a CIP pure (Compressor s-CO2 is for Inlet a CIT Pressure)(Compressor above Inlet the Temperature) critical pressure equal to the[22] critical. These temperature values are and 45.4% a CIP (Compressor (CIP = 7.41 Inlet MPa Pressure) and UAabovetotal = the5000 critical kW/K), pressure 48.4% [(CIP22]. These= 7.43 MPa values and are UA 45.4%total = (CIP 10000= 7.41 kW/K), MPa and and 49.4% UAtotal (CIP= 5000 = 7.44 kW MPa/K), 48.4%and UA(CIPtotal = 150007.43 MPa kW/K). and UAtotal = 10,000 kW/K), and 49.4% (CIP = 7.44 MPa and UAtotal = 15,000 kW/K). AsAs mentioned mentioned above, above, the the s-CO s-CO2 binary2 binary mixtures mixtures are aredivided divided into intotwo twogroups: groups: substances substances for reducingfor reducing the critical the critical temperature, temperature, group group A, which A, which include include s-CO2 s-CO/He, 2 s/-He,CO2/Kr, s-CO s2-/COKr,2/CH s-CO4, 2 and/CH 4, s-andCO2/C s-CO2H6;2 /C and2H 6 substances; and substances for increasing for increasing the critical the critical temperature, temperature, group group B, B, which which include include s-s-COCO2/H2/H2S,2 S,s-CO s-CO2/C23/HC38,H s8-CO, s-CO2/C24H/C104,H s10-CO, s-CO2/C5H2/C10,5 Hs-CO10, s-CO2/C5H212/C, 5sH-CO12,2 s-CO/C4H82 /andC4H s8-COand2/C s-CO6H6.2 / C6H6. InIn the the case case of of group group A A,, sCO sCO2-mixtures,2-mixtures, the the recompression recompression Brayton Brayton cycle cycle efficiency eﬃciency is ismaximum maximum whenwhen the the cycle cycle works works with with a CIT a CIT and and CIP CIP nearly nearly the the critical critical point point.. To To avoid avoid the the phase phase changing changing zone zone,, thethe condition condition of of working working just just above above the the critical critical point point was was appointed appointed.. InIn the the case case of of group group B BsCO sCO2-mixture,2-mixture, a CIT a CIT range range of of318.15 318.15 to to 333.15 333.15 K Kand and CIP CIP just just above above critical critical pressurepressure were were considered considered in in this this study. study.

3.1.3.1. Results Results of of‘G ‘Grouproup A’ A’ M Mixturesixtures (S (Substancesubstances for for R Reducingeducing the the Critical Critical Temperature Temperature))

ForFor ‘group ‘group A’ A’ mixtures, mixtures, the the maximum maximum molar molar fractions fractions for for the the s- s-COCO2/He,2/He, s- s-COCO2/Kr2/Kr and and s- s-COCO2/CH2/CH4 4 mixturesmixtures have have been been fixed fixed at at90.0/10.0, 90.0/10.0, 68.0/32.0 68.0/32.0 and and 67.0/33.0 67.0/33.0 respectively respectively because because in in these these conditions conditions theirtheir critical critical temperatures temperatures are are close close to to 273.15 273.15 K. The K. The molar molar fraction fraction span for span the for s-CO the2/ C s-2COH6 2was/C2H 100.06 was/0.0 100.0/0.0to 0.0/100.0 to 0.0/100.0 because because its critical its temperature critical temperatu rangere is approximatelyrange is approximately 304.13 K to304.13 290.21 K K.to 290.21 This means K. This that meansthe CIT’s that rangethe CIT’s studied range is studied approximately is approximately 304.13 K to 304.13 273.15 K K, to except 273.15 forK, theexcept s-CO for2/ Cthe2H s6-.CO The2/C power2H6. Thecycle power diagrams cycle fordiagrams pressure for with pressure respect with to therespect enthalpy to the are enthalpy shown inare Figure shown4, in where Figure it is 4, possible where it to is seepossible the cycle to see has the a dicyclefferent has behavior a different when behavior it uses when sCO2 it-mixture uses sCO as2 working-mixture fluid.as working fluid.

s-CO2_Pure s-CO2 / He (90/10) s-CO2 / CH4 (67/33) s-CO2 / Kr (68/32) s-CO2 / C2H6 (68/32) 2 3 4 5 6 25 10

15 Pressure(MPa) 10 1 9 8 7

5 150 350 550 750 950 1150 1350 Enthalpy (kJ/kg)

Figure 4. Real gas cycles with sCO2-mixtures as working ﬂuid in the thermodynamic plane P-h. Figure 4. Real gas cycles with sCO2-mixtures as working fluid in the thermodynamic plane P-h. Group Group A mixtures with UAtotal = 15,000 kW/K. A mixtures with UAtotal = 15000 kW/K. For the study of the Brayton cycle performance, optimal values of CIT and CIP at the main For the study of the Brayton cycle performance, optimal values of CIT and CIP at the main compressor and recompressor inlet has been considered; it has been observed that the sCO2-mixtures compressor and recompressor inlet has been considered; it has been observed that the sCO2-mixtures produce a gain in cycle eﬃciency over pure s-CO2 cycles of approximately 4%. Also, a linear trend is produce a gain in cycle efficiency over pure s-CO2 cycles of approximately 4%. Also, a linear trend is observed for s-CO2/Kr and s-CO2/CH4 (cf. Figure5). observed for s-CO2/Kr and s-CO2/CH4 (cf. Figure 5). Appl.Appl. Sci. Sci. 20192020, 9,,10 x ,FOR 55 PEER REVIEW 6 6of of 18 18

UAtotal = 5,000 kW/K He Kr CH4 C2H6 UAtotal = 10,000 kW/K He Kr CH4 C2H6 UAtotal = 15,000 kW/K He Kr CH4 C2H6 0.53

0.51

0.49

0.47 Cycle efficiency 0.45

0.43 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Mole fraction

Figure 5. Cycle thermal efficiency versus mole fraction. Group A mixtures with UAtotal of 5000, 10,000 Figureand 15,000 5. Cycle kW thermal/K. efficiency versus mole fraction. Group A mixtures with UAtotal of 5000, 10000 and 15000 kW/K. Table2 shows the results summary (cycle thermal e fficiency and working fluid properties using Table 2 shows the results summary (cycle thermal efficiency and working fluid properties using group A sCO2-mixtures) for the Brayton cycle working with UAtotal = 15,000 kW/K, CIT and CIP groupoptimized. A sCO To2-mixtures) summarize for the the results Brayton obtained, cycle work someing working with UA fluidtotal properties= 15000 kW/K which, CIT have and a direct CIP optimizeimpactd on. To the summarize cycle performance the results and obtained, on the some power working cycle equipment fluid properties detail designwhich have are showna direct in impactthis table. on the cycle performance and on the power cycle equipment detail design are shown in this table. TheTable turbomachine 2. Results summary dimensions for ‘group are A’constrained mixtures with to the UA workingtotal = 15,000 fluid kW density/K, CIT and[33,34] CIP. optimized.If the density is increased, the compressorMolar and turbine sizesIsobaric will Heat be minimized.Kinetic TheThermal addition of krypton provides Density Prandtl Plant higher density values; hence,Mass the turbomachines3 Capacity would haveViscosity a minimizedConductivity size. However, the isobaric (kg/m ) 2 Number Efficiency heat capacity (Cp), kinetic(kg/ kmol)viscosity and thermal(kJ/kg*K) conductivity(cm /s) must also(W/m*K) be considered in the heat s-CO pure 44.01 565.43 49.62 7.19 10 4 1.03 10 1 19.61 0.49 exchangers 2design. The heat exchanger’s heat transfer coefficients× − are closely× − related to the viscosity s-CO /He (90.0/10.0) 40.01 386.23 378.95 6.68 10 4 5.52 10 2 177.08 0.53 2 × − × − (dynamics-CO /Kr and (68.0 kinetic/32.0)), thermal 56.74 conductivity, 740.15 density 7.95 and6.20 isobaric10 4 heat5.94 capacity10 2 [35]6.13. The highest 0.53 Cp 2 × − × − ands-CO density/CH values(67.0/33.0) and the 34.78 lowest kinetic 414.49 viscosity 6.59 value 7.42minimize10 4 the6.52 recuperator10 2 (low3.11-temperature 0.52 2 4 × − × − s-CO /C H (68.0/32.0) 39.55 371.85 1830.20 7.91 10 4 9.13 10 2 597.86 0.52 recuperator2 2 6(LTR) and high-temperature recuperator (HTR)×) dimensions.− × The− ethane mixture is the solution for maximizing the isobaric heat capacity. Moreover, the helium mixture and krypton mixtureThe are turbomachine the solution dimensionsfor minimizing are constrainedthe kinetic viscosity. to the working fluid density [33,34]. If the density is increased,Another theimportant compressor issue and to be turbine considered sizes will is the be minimized. Ultimate Heat The Sink addition (UHS) of krypton thermal provides storage systemhigher, densitythis system values; design hence, depends the turbomachines on the mixture would critical have temperature. a minimized Here size., two However, possible the technical isobaric solutionsheat capacity are going (Cp), to kinetic be studied viscosity. The andnigh thermalt cooling conductivity radiative panels must could also bebe consideredproposed as in the the first heat technicalexchangers solution design., and The this heat proposal exchanger’s has been heat transferdiscussed coe byffi cientsAna Dyreson are closely [36] related. The cooling to the viscosity fluid’s lowest(dynamic temperature and kinetic), for thermalthis proposal conductivity, could be density between and 278 isobaric.15 and heat 298 capacity.15 K; for [35 this]. The scenario highest, the Cp ethaneand density mixture, values with and a critical the lowest temperature kinetic viscosity around value290.82 minimize K, is the theoptimal recuperator solution (low-temperature, as stated by J. Muñozrecuperator-Antón (LTR) [37] and and Steven high-temperature A. Wright [38] recuperator. (HTR)) dimensions. The ethane mixture is the solutionIn the for future, maximizing alternative the isobaric refrigerants heat capacity.could also Moreover, be utilized the to helium vary the mixture UHS andtemperature krypton mixturerange. Coolingare the solution with cold for storage minimizing system the b kineticased on viscosity. water ice could be proposed as the second technical solutionAnother. In this important case, the h issueelium to mixture be considered, with a critical is the Ultimate temperature Heat around Sink (UHS) 274.24 thermal K, is the storage most suitablesystem, option. this system design depends on the mixture critical temperature. Here, two possible technical solutionsIn conclusion are going, maximizing to be studied. the Theworking night cooling fluid density radiative in panels turbomachines could be proposedminimizes as the the equipmentfirst technical dimensions, solution, but and also this has proposal to be warrantied has been the discussed equipment by Anamanufacturability. Dyreson [36]. M Theaximizing cooling thefluid’s Cp and lowest density temperature values and for minimizing this proposal the couldkinetic be viscosity between value 278.15 reduce and298.15 the heat K; exchangers for this scenario, size, andthe finally ethane, selecting mixture, witha mixture a critical with temperature a critical temperature around 290.82 compatible K, is the with optimal the UHS solution, storage as statedsystem by. TheJ. Muñoz-Ant optimum só-COn [372 mixtures] and Steven could A. be Wright obtained [38]. with helium or ethane. However, another constraint, which was not cited before, is the added substance’s maximum operating temperature. Helium has a maximum working temperature of around 2000 K, and the maximum working temperature of ethane is around 675 K. Accordingly, for the purposes in this work, the optimum mixture is s-CO2/He Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 18

(90.0/10.0). However, for future works, it would be advisable to continue researching on a mixture based on adding both helium and ethane, as this last fluid has a very beneficial impact on the heat exchanger and also simplifies the UHS storage system’s economical and technical design, opening future research paths for studying diverse refrigeration thermodynamic cycles coupled with the main Appl.s-CO Sci.2 Brayton2020, 10, 55power cycle. 7 of 18

Table 2. Results summary for ‘group A’ mixtures with UAtotal = 15000 kW/K, CIT and CIP optimized. In the future, alternative refrigerants could also be utilized to vary the UHS temperature range. Cooling with cold storage system based onIsobaric water ice could be proposed as the second technical solution. Molar Kinetic Thermal In this case, the helium mixture,Density with a criticalheat temperature around 274.24 K, is the mostPrandtl suitable Plant option. mass viscosity conductivity In conclusion, maximizing(kg/m the3) workingcapacity fluid density in turbomachines minimizesnumber the equipmentefficiency (kg/kmol) (cm2/s) (W/m*K) dimensions, but also has to be warrantied(kJ/kg*K) the equipment manufacturability. Maximizing the Cp and density values and minimizing the kinetic viscosity value reduce the heat exchangers size, and finally, s-CO2 pure 44.01 565.43 49.62 7.19 x 10-4 1.03 x 10-1 19.61 0.49 selecting a mixture with a critical temperature compatible with the UHS storage system. The optimum s-COs-CO2 /mixtures He could be obtained with helium or ethane. However, another constraint, which was 2 40.01 386.23 378.95 6.68 x 10-4 5.52 x 10-2 177.08 0.53 not(90.0 cited/10.0 before,) is the added substance’s maximum operating temperature. Helium has a maximum workings-CO2 / Kr temperature of around 2000 K, and the maximum working temperature of ethane is around 56.74 740.15 7.95 6.20 x 10-4 5.94 x 10-2 6.13 0.53 675(68.0 K./32 Accordingly,.0) for the purposes in this work, the optimum mixture is s-CO2/He (90.0/10.0). sHowever,-CO2/CH4 for future works, it would be advisable to continue researching on a mixture based on 34.78 414.49 6.59 7.42 x 10-4 6.52 x 10-2 3.11 0.52 adding(67.0/33 both.0) helium and ethane, as this last fluid has a very beneficial impact on the heat exchanger and also simplifies the UHS storage system’s economical and technical design, opening future research s-CO2/C2H6 paths for studying39.55 diverse refrigeration371.85 1830.20 thermodynamic 7.91 cyclesx 10-4 coupled9.13 x with 10-2 the main597.86 s-CO Brayton0.52 (68.0/32.0) 2 power cycle. A schematic diagram of the pressure vs. enthalpy for the s-CO Recompression Brayton cycle is A schematic diagram of the pressure vs. enthalpy for the s-CO22 Recompression Brayton cycle is shown in Figure6, this cycle works with CIP and CIT optimal values, pure s-CO as working fluid and shown in Figure 6, this cycle works with CIP and CIT optimal values, pure s-2CO2 as working fluid UAandtotal UA=total15,000 = 15000 kW/ K.kW/K. The specific The specific heat contributing heat contributing to the cycle to the through cycle the through primary the heat primary exchanger heat is represented by q . The specific work of the main compressor is w , the specific work of the exchanger is representedPHX by qPHX. The specific work of the main compressormc is wmc, the specific work w w recompressorof the recompressor is rc, is the wrc specific, the specific work work of the of turbine the turbine is tis,the wt, maximumthe maximum achievable achievable temperature temperature in the high-pressure side from the low-pressure side is T , and ∆h is the specific enthalpy increment in the high-pressure side from the low-pressure side is tTt, and Δha a is the specific enthalpy increment betweenbetween thethe entranceentrance ofof thethe primaryprimary heatheat exchangerexchanger andand thethe exitexit ofof thethe turbine.turbine.

Figure 6. Pressure vs enthalpy. Recompression Brayton cycle using pure s-CO2 and UAtotal = 15,000 kW/K. Figure 6. Pressure vs enthalpy. Recompression Brayton cycle using pure s-CO2 and UAtotal = 15000 kW/K. The thermal efficiency of the recompression Brayton cycle is properly defined as the net specific workThe divided thermal by theefficiency net supply of the of recompression heat [19]. The thermalBrayton ecyclefficiency is properly can be expresseddefined as as the net specific work divided by the net supply of heat [19]. The thermal efficiency can be expressed as wmc wrc 1 (1 γ) w γ w η = − − · t − · t (1) th ∆h 1 + rg wt where γ is the split fraction of the flow of the plant. The thermal efficiency depends on three dimensionless variables: the dimensionless main compression work, wmc/wt, the dimensionless recompression work, wrc/wt, and the dimensionless additional enthalpy supplied due to real gas conditions, ∆hrg/wt. These terms depend on the thermodynamic properties of the working fluid in the Appl. Sci. 2020, 10, 55 8 of 18

recompression cycle. Further, ∆hrg is the diﬀerence between the heat needed in a cycle working at real gas conditions and the heat needed in an ideal cycle [39]. It can be expressed by:

∆hrg = ∆ha + ∆hTt (2) where ∆hTt is the enthalpy variation of the isothermal Tt; this variable tends to zero when the turbine works at high temperatures. Thus, in these cases, Equation (1) can be approximated to:

1 (1 γ) wmc γ wrc wt wt ηth = − − · − · (3) 1 + ∆ha wt

The dimensionless variables wmc/wt, wrc/wt and ∆ha/wt play an important role in the cycle eﬃciency. For this reason, the ﬂuctuation of wmc/wt, wrc/wt and ∆ha/wt of the s-CO2 mixtures with respect to the pure s-CO2 have been obtained using the next equations:

(wmc/wt ) (wmc/wt ) sCO2pure − sCO2mixture δwmc/wt = (4) (wmc/wt )sCO2pure

(wrc/wt ) (wrc/wt ) sCO2pure − sCO2mixture δwrc/wt = (5) (wrc/wt )sCO2pure

(∆ha/wt ) (∆ha/wt ) sCO2pure − sCO2mixture δ∆ha/wt = (6) (∆ha/wt )sCO2pure X δtotal = δi = δwmc/wt + δwrc/wt + δ∆ha/wt (7) i where δwmc/wt is the variation of the dimensionless main compression work of the sCO2-mixtures respect to the pure s-CO2, δwrc/wt is the variation of the dimensionless recompression work of the sCO2-mixtures respect to the pure s-CO2, δ∆ha/wt is the variation of the dimensionless additional enthalpy of the sCO2-mixtures respect to the pure s-CO2, and δtotal is the total variation of the dimensionless cycle work of the sCO2-mixtures respect to the pure s-CO2. It has been observed that the cycle efficiency increases when δtotal increases [40]. Therefore, the influence of the dimensionless Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 18 variables wmc/wt, wrc/wt and ∆ha/wt on the cycle efficiency can be displayed in Figure7.

Figure 7. Variation of the parameters wmc/wt, wrc/wt and ∆ha/wt of the s-CO2 mixtures with respect to Figure 7. Variation of the parameters wmc/wt, wrc/wt and Δha/wt of the s-CO2 mixtures with respect to the pure s-CO2. Recompression Brayton cycle with UAtotal = 15,000 kW/K for Group A. the pure s-CO2. Recompression Brayton cycle with UAtotal = 15000 kW/K for Group A.

The adoption of s-CO2 cycles is particularly promising for large-scale, high-temperature CSP The adoption of s-CO2 cycles is particularly promising for large-scale, high-temperature CSP plants [2]. Four factors are important for incorporating s-CO2 into CSP plants: superior performance vs.plants steam [2]. Rankine Four factors cycles, are the important ability to for integrate incorporating thermal s-CO energy2 into storage, CSP plants: ultimate superior heat sinkperformance thermal vs. steam Rankine cycles, the ability to integrate thermal energy storage, ultimate heat sink thermal energy storage [36–38], and dry cooling [41]. This work presents air-cooled s-CO2 cycle configurations specifically selected for a CSP application. The estimated cost calculation of the PTC (parabolic trough collector) and LF (linear Fresnel) systems were developed with the following equation [42]:

SF퐶푂푆푇 = SF퐸퐴 · C푈퐶 · 퐶퐹 (8)

where SF퐶푂푆푇 is the cost of the solar field, SF퐸퐴 is the effective area of the solar field, C푈퐶 is the linear collector unitary costs, and 퐶퐹 is the construction factor of the solar field. The linear collector unitary costs and construction factor (cf. Table 3) have been obtained from Thermoflex 27 software [27].

Table 3. Linear collector unitary costs. PTC: parabolic trough collector; LF: linear Fresnel; HTF: Heat Transfer Fluid.

Value Unit PTC with AISI 347 stainless steel receiver for Solar Salt as HTF 432 $/m2 LF with AISI 347 stainless steel receiver for Solar Salt as HTF 300 $/m2 Construction factor 1.16 - The better performance of the plant implies a smaller solar field effective area; this, in turn, reduces the cost of the 50 MW plant. In view of this, Figure 8 shows that the savings with the installation of PTC could reach up to 8 million USD for the mixture of s-CO2/He with a 10% molar fraction.

UAtotal = 5,000 kW/K He Kr CH4 C2H6 UAtotal = 10,000 kW/K He Kr CH4 C2H6 UAtotal = 15,000 kW/K He Kr CH4 C2H6 91 89 87 85 83 81 79 77 75

PTC Solar PTC Field cost (Millon USD) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Mole fraction

Figure 8. PTC Solar Field cost vs. a concentration of s-CO2 for group A mixtures. Appl. Sci. 2019, 9, x FOR PEER REVIEW 9 of 18

Figure 7. Variation of the parameters wmc/wt, wrc/wt and Δha/wt of the s-CO2 mixtures with respect to the pure s-CO2. Recompression Brayton cycle with UAtotal = 15000 kW/K for Group A.

Appl. Sci. 2020, 10, 55 9 of 18 The adoption of s-CO2 cycles is particularly promising for large-scale, high-temperature CSP plants [2]. Four factors are important for incorporating s-CO2 into CSP plants: superior performance vs. steam Rankine cycles, the ability to integrate thermal energy storage, ultimate heat sink thermal energy storage [36–38], and dry cooling [41]. This work presents air-cooled s-CO2 cycle conﬁgurations energyspeciﬁcally storage selected [36–38] for, and a CSP dry application. cooling [41] The. This estimated work presents cost calculation air-cooled of s the-CO PTC2 cycle (parabolic configurations trough specificallycollector) and selected LF (linear for a Fresnel)CSP application. systems wereThe estimated developed cost with calculation the following of the equation PTC (parabolic [42]: trough collector) and LF (linear Fresnel) systems were developed with the following equation [42]:

SFCOST = SFEA CUC CF (8) SF퐶푂푆푇 = SF퐸퐴· · C푈퐶 ·· 퐶퐹 (8) where SFCOST is the cost of the solar field, SFEA is the effective area of the solar field, CUC is the linear where SF퐶푂푆푇 is the cost of the solar field, SF퐸퐴 is the effective area of the solar field, C푈퐶 is the linear collector unitary costs, and CF is the construction factor of the solar field. The linear collector unitary collector unitary costs, and 퐶퐹 is the construction factor of the solar field. The linear collector unitary costs and construction factor (cf. Table3) have been obtained from Thermoflex 27 software [27]. costs and construction factor (cf. Table 3) have been obtained from Thermoflex 27 software [27].

Table 3. Linear collector unitary costs. PTC: parabolic trough collector; LF: linear Fresnel; HTF: Heat Table 3. Linear collector unitary costs. PTC: parabolic trough collector; LF: linear Fresnel; HTF: Heat Transfer Fluid. Transfer Fluid. Value Unit Value Unit PTC with AISI 347 stainless steel receiver for Solar Salt as HTF 432 $/m2 PTC with AISI 347 stainless steel receiver for Solar Salt as HTF 432 $/m2 LF with AISI 347 stainless steel receiver for Solar Salt as HTF 300 $/m2 LF with AISI 347 stainlessConstruction steel receiver factor for Solar Salt as HTF 300 1.16 $/m - 2 Construction factor 1.16 - TheThe betterbetter performance performance of of the the plant plant implies implies a smaller a smaller solar solar ﬁeld efieldﬀective effective area;this, area in; this, turn, in reduces turn, reducesthe cost ofthe the cost 50 of MW the plant. 50 MW In view plant. of In this, view Figure of 8 this, shows Figure that 8 the shows savings that with the the saving installations with the of installationPTC could reachof PTC up could to 8 million reach up USD to for8 million the mixture USD for of s-CO the mixture2/He with of as 10%-CO2 molar/He with fraction. a 10% molar fraction.

UAtotal = 5,000 kW/K He Kr CH4 C2H6 UAtotal = 10,000 kW/K He Kr CH4 C2H6 UAtotal = 15,000 kW/K He Kr CH4 C2H6 91 89 87 85 83 81 79 77 75

PTC Solar PTC Field cost (Millon USD) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Mole fraction

Figure 8. PTCPTC Solar Solar Field Field cost cost vs vs.. a a concentration concentration of of s s-CO-CO22 forfor g grouproup A A mixtures mixtures..

The solar field’s effective area with linear Fresnel is larger than the solar field’s effective area with the parabolic trough collector (approximately 12%). Nevertheless, the estimated cost of the solar field with LF is lower than the solar field with PTC, because the price per square meter of the solar field with LF is lower than that of the PTC. Thermodynamic results show that savings, when the Brayton cycle coupled with LF’s solar field uses s-CO2 mixtures, could reach 6 million USD compared to using pure s-CO2 (cf. Figure9). Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 18

Appl. Sci.The 2019 solar, 9, x FOR field PEER’s effective REVIEW area with linear Fresnel is larger than the solar field’s effective10 of area 18 with the parabolic trough collector (approximately 12%). Nevertheless, the estimated cost of the solar fieldThe with solar LF fieldis lower’s effective than the area solar with field linear with Fresnel PTC, because is larger the than price the per solar square field meter’s effective of the area solar withfield the with parabolic LF is lowertrough than collector that of(approximately the PTC. Thermodynamic 12%). Nevertheless results, the show estimated that savings, cost of thewhen solar the fieldBrayton with cycleLF is coupledlower than with the LF's solar solar field field with uses PTC s-CO, because2 mixtures the, couldprice perreach square 6 million meter USD of thecompared solar fieldto using with pureLF is s -lowerCO2 (cf. than Figure that 9of). the PTC. Thermodynamic results show that savings, when the

BraytonAppl. Sci. cycle2020, 10 coupled, 55 with LF's solar field uses s-CO2 mixtures, could reach 6 million USD compared10 of 18 UA = 5,000 kW/K to using puretotal s-CO2 (cf. Figure 9). He Kr CH4 C2H6 UAtotal = 10,000 kW/K He Kr CH4 C2H6 UAtotal = 15,000 kW/K He Kr CH4 C2H6

UAtotal = 5,000 kW/K He Kr CH4 C2H6 71 UAtotal = 10,000 kW/K He Kr CH4 C2H6 UAtotal = 15,000 kW/K He Kr CH4 C2H6

7168

6865

6562

6259 LF LF SolarField cost (Millon USD) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Mole fraction

59 LF LF SolarField cost (Millon USD) 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 Figure 9. LF Solar Field cost vs. a concentration of s-CO2 for ‘group A’ mixtures. Mole fraction

Figure 9. LF Solar Field cost vs. a concentration of s-CO2 for ‘group A’ mixtures. 3.2. Results ofFigure Group 9. B LF M ixturesSolar Field (Substances cost vs. a forconcentration increasing theof s -CriticalCO2 for T‘gemperatureroup A’ mixtures). . 3.2. ResultsFor group of Group B mixtures, B Mixtures the (Substancescycle works for with Increasing a CIP just the Criticalabove critical Temperature) pressure and a CIT’s range 3.2. Results of Group B Mixtures (Substances for increasing the Critical Temperature). fromFor 318.15 group K to B mixtures,333.15 K. This the cycle CIT’s works range withhas been a CIP studied just above in this critical work pressure because and most a CIT’sof CSPs range are fromlocatedFor 318.15 group in sites K B to mixtures, 333.15 where K. the the This ambientcycle CIT’s works range temperature with has a been CIP is studiedjust above abovein the thiscritical s work-CO pressure2 becausecritical and temperature most a CIT’s of CSPs range, arei.e. , fromlocatedCIT 318.15= 318.15, in sites K to323.15, where 333.15 328.15 the K. ambient This, and CIT’s 333.15 temperature range K [43,44] has is been above. studied the s-CO in2 thiscritical work temperature, because most i.e., of CIT CSPs= 318.15, are located323.15,In 328.15, inthe sites case and of where CIT 333.15 equal the K [ ambient43 to, 44318.15]. temperature K and UAtotal is= 15000 above kW/K the , s t-heCO maximum2 critical temperaturemolar fractions, i.e. for, CITthe = sIn318.15,-CO the2/H case 323.15,2S, of s- CITCO 328.152 equal/C3H, and8, to s- 318.15333.15CO2/C K4KH and[43,44]10, s UA-CO. total2/C=5H15,00010, s-CO kW2/C/K,5H the12, maximum s-CO2/C4H molar8 and fractions s-CO2/C6 forH6 themixtures s-COIn the2 /case haveH2S, of s-CO been CIT2 / fixedequalC3H8 , atto s-CO 318.1566.0/34.0,2/C 4KH and 10 72.5/27.5,, s-CO UAtotal2/C = 90.0/10.0,5 H1500010, s-CO kW/K 97.5/2.5,2/C,5 tHhe12 maximum, 97.5/2.5, s-CO2/C 92.5/7.54 Hmolar8 and ,fractions s-COand 92.5/7.52/C for6H 6 themixturesrespectively s-CO2/H have2S,, because sbeen-CO2/C fixed the3H 8critical,at s- 66.0CO 2/temperatures/C34.0,4H10 72.5, s-CO/27.5, 2/Cin 90.05theseH10/, 10.0, sconditions-CO 97.52/C5/H2.5,12 ,are 97.5 s- COjust/2.5,2/C below4 92.5H8 and/ 7.5,to 318.15 sand-CO 92.52 /CK.6 H/The7.56 mixturesrespectively,power cycle have becausediagrams been fixed the for critical atpressure 66.0/34.0, temperatures with 72.5/27.5, respect in these to 90.0/10.0, the conditions enthalpy 97.5/2.5, are are just 97.5/2.5,shown below in 92.5/7.5 to Figure 318.15, 10and K., Thewhere 92.5/7.5 power it i s respectivelycyclepossible diagrams to, seebecause forthe pressurecycle the hascritical with a different respecttemperatures behavior to the enthalpyin whenthese it areconditions uses shown sCO in2are-mixture Figure just below10 as, whereworking to 318.15 it isfluid. possible K . The to power cycle diagrams for pressure with respect to the enthalpy are shown in Figure 10, where it is see the cycle has a different behavior when it uses sCO2-mixture as working fluid. possible to see the cycle has a different behavior when it uses sCO2-mixture as working fluid. s-CO2_Pure 66.0% CO2 + 34.0% H2S 92.5% CO2 + 7.5% C4H8 72.5% CO2 + 27.5% C3H8 97.5% CO2 + 2.5% C5H10 92.5% CO2 + 7.5% C6H6 90.0% CO2 + 10.0% C4H10 97.5% CO2 + 2.5% C5H12 s-CO2_Pure 3 66.0% CO25 + 34.0% H2S 6 92.5% CO2 + 7.5% C4H8 25 2 4 72.5% CO2 + 27.5% C3H8 10 97.5% CO2 + 2.5% C5H10 92.5% CO2 + 7.5% C6H6 90.0% CO2 + 10.0% C4H10 97.5% CO2 + 2.5% C5H12 3 5 6 2520 2 4 10

2015 Pressure(MPa) 1510

1 9 8 7 Pressure(MPa) 10 5 1 300 500 9 8700 7 900 1100 1300 Enthalpy (kJ/kg) 5 Figure300 10. Real gas cycles500 with mixtures700 as working ﬂuid900 in the thermodynamic1100 plane P-h. Group1300 B Figure 10. Real gas cycles with mixtures Enthalpyas working (kJ/kg) fluid in the thermodynamic plane P-h. Group B mixtures with a CIT = 318.15 K and UAtotal = 15,000 kW/K. mixtures with a CIT = 318.15 K and UAtotal = 15,000 kW/K.

FigureComparing 10. Real the gas recompression cycles with mixtures Brayton as working cycle using fluid pure in the s-CO thermodynamic2 and the same plane cycle P-h using. Group ‘group B B’ mixtures with a CIT = 318.15 K and UAtotal = 15,000 kW/K. sCO2-mixtures, it can be observed that the cycle efficiency with group B mixtures decreases when it works with CIT and CIP just above the critical point. In contrast, a better efficiency has been obtained if the cycle works with sCO2-mixtures and higher compressor inlet temperatures, i.e., 318.15, 323.15, 328.15 and 333.15 K. Most series of cycle efficiency versus molar fraction have a linear trend, with a minority of lines following an exponential trend, such as the mixtures s-CO2/H2S and s-CO2/C3H8. Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 18 Appl. Sci. 2019, 9, x FOR PEER REVIEW 11 of 18 Comparing the recompression Brayton cycle using pure s-CO2 and the same cycle using

‘groupComparing B’ sCO2-mixtures, the recompression it can be observed Brayton that cycle the cycleusing efficiency pure s- COwith2 andgroup the B mixtures same cycle decrease usings when‘group it B work’ sCOs2 -withmixtures, CIT and it can CIP be just observed above thethat critical the cycle point. efficiency In contrast, with groupa better B mixturesefficiency decrease has beens obtainedwhen it work if thes cyclewith CITwork ands with CIP sCO just2 -abovemixtures the andcritical higher point. compressor In contrast, inlet a better temperatures efficiency, i.e. has 318.15, been 323.15,obtained 328.15 if the and cycle 333 work.15 Ks with. Most sCO series2-mixtures of cycle and efficiency higher compressorversus molar inlet fraction temperatures have a linear, i.e. 318.15, trend, Appl. Sci. 2020, 10, 55 11 of 18 with323.15, a 328.15 minority and of333 lines.15 K following. Most series an of exponential cycle efficiency trend versus, such molar as the fraction mixtures have s -aCO linear2/H2 Strend, and swith-CO 2/C a minority3H8. The cycle of lines efficiency following improve an exponentials by about 3trend to 4%,, such when as thethe cycle mixtures works s -withCO2/H group2S and B ThesCOs-CO cycle2-2mixtures/C3H e8ﬃ. Theciency, CIP cycle just improves efficiency above bycritical aboutimprove pressure 3 tos by 4%, and about when CIT 3 the to= 318.15 cycle4%, when worksK, as theshown with cycle group in worksFigure B sCO with112. -mixtures, group B CIPsCO just2-mixtures above, critical CIP just pressure above critical and CIT pressure= 318.15 and K, asCIT shown = 318.15 in FigureK, as shown 11. in Figure 11.

UAtotal = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 10,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 15,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 10,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 15,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S

0.45 0.45

0.43

0.43 Cycle efficiency

0.41 Cycle efficiency 0.41

0.39 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.39 0.00 0.05 0.10 Mole0.15 fraction 0.20 0.25 0.30 Mole fraction Figure 11. Cycle efficiency vs. a concentration of s-CO2. Group B mixtures with a CIT = 318.15 K.

FigureFigure 11.11. CycleCycle eefficiencyfficiency vs.vs. aa concentrationconcentration ofof s-COs-CO22. Group B mixtures with a CIT = 318.15318.15 K K.. The same analysis of ‘group A’ mixtures (substances added for decreasing the critical temperature)The samesame has analysis analysis been of developed ‘groupof ‘group A’ mixtures with A’ ‘mixturesgroup (substances B ’ (substancesmixtures added ( forsubstances added decreasing for added decreasingthe critical for increasing temperature) the critical the hascriticaltemperature) been temperature developed has been with). As developed ‘group a result B’ mixtures of with this ‘ group analysis, (substances B’ mixtures it has added been ( forsubstances observed increasing added that the critical the for cycle increasing temperature). efficiency the As a result of this analysis, it has been observed that the cycle efficiency increases when δ increases. increasescritical temperature when 훿푡표푡푎푙). Asincreases a result. T herefore, of this analysis, the influence it has of beenthe parameters observed w thatmc/w thet, w cyclerc/wtotalt and efficiency Δha/wt Therefore, the influence of the parameters wmc/wt, wrc/wt and ∆ha/wt on the cycle efficiency that works onincreases the cycle when efficiency 훿푡표푡푎푙 thatincreases works. Twithherefore, UAtotal the = 15000influence kW/K of theand parameters CIT = 318.15 w mcK /wcant, wberc /wseent and in ΔhFigurea/wt with UAtotal = 15,000 kW/K and CIT = 318.15 K can be seen in Figure 12. 1on2. the cycle efficiency that works with UAtotal = 15000 kW/K and CIT = 318.15 K can be seen in Figure 12.

Figure 12. Variation of the parameters wmc/wt, wrc/wt and ∆ha/wt of the s-CO2 mixtures with respect to Figure 12. Variation of the parameters wmc/wt, wrc/wt and Δha/wt of the s-CO2 mixtures with respect the pure s-CO2. Recompression Brayton cycle with UAtotal = 15,000 kW/K, CIP = just above the critical toFigure the pure 12. Variations-CO2. Recompression of the parameters Brayton wmc cycle/wt, wwithrc/w UAt andtotal Δh = 15000a/wt of k W/Kthe s,- CIPCO2 =mixtures just above with the respectcritical pressure of the working ﬂuid and CIT = 318.15 K for group B mixtures. pressureto the pure of sthe-CO working2. Recompression fluid and BraytonCIT = 318.15 cycle K with for UAgrouptotal =B 15000mixtures kW/K. , CIP = just above the critical Duepressure to the of the mixtures working used fluid in and the CIT recompression = 318.15 K forBrayton group B mixtures cycle, savings. in PTC installations could Due to the mixtures used in the recompression Brayton cycle, savings in PTC installations could reach up to 7 million USD for CIT = 318.15 K (cf. Figure 13). The maximum saving was obtained reachDue up toto 7the million mixtures USD used for CIT in the = 318.15 recompression K (cf. Figure Brayton 13). The cycle, maximum savings insaving PTC wasinstallations obtained could with with the s-CO2/H2S mixture (66.0/34.0), and the minimum saving was obtained with s-CO2/C5H12 the s-CO2/H2S mixture (66.0/34.0), and the minimum saving was obtained with s-CO2/C5H12 mixture mixturereach up (97.5 to 7 /million2.5). USD for CIT = 318.15 K (cf. Figure 13). The maximum saving was obtained with (97.5/2.5). the s-Alternatively,CO2/H2S mixture in the (66.0/34.0 case of) linear, and the Fresnel minimum installations, saving was savings obtained could with reach s-CO 6 million2/C5H12 USDmixture for CIT(97.5/2.5)= 318.15. K (cf. Figure 14). In the same way as for the PTC installations, the maximum saving for LF installations was obtained with the s-CO2/H2S mixture (66.0/34.0). Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 18

UAtotal = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 10,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 15,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S

100 Appl. Sci. Sci. 20192020,, 910, x, 55FOR PEER REVIEW 1212 of of 18 18

UAtotal94 = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 10,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 15,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S 91

100 88

97 85 PTC Solar Field cost (Millon USD) (Millon cost SolarField PTC 0.00 0.05 0.10 0.15 0.20 0.25 0.30 94 Mole fraction 91 Figure 13. PTC’s solar field estimated cost vs concentration of s-CO2. Group B mixtures with a CIT88 = 318.15 K and CIP = just above the critical pressure of the working fluid.

PTC Solar Field cost (Millon USD) (Millon cost SolarField PTC Alternatively, in the case of linear Fresnel installations, savings could reach 6 million USD for 0.00 0.05 0.10 0.15 0.20 0.25 0.30 CIT = 318.15 K (cf. Figure 14). In the same wayMole as forfraction the PTC installations, the maximum saving for LF installations was obtained with the s-CO2/H2S mixture (66.0/34.0). Figure 13. PTC’s solar ﬁeld estimated cost vs concentration of s-CO2. Group B mixtures with a Figure 13. PTC’s solar field estimated cost vs concentration of s-CO2. Group B mixtures with a CIT = 318.15 K and CIP = just above the critical pressure of the working ﬂuid. CIT = 318.15 K and CIP = just above the critical pressure of the working fluid.

UAtotal = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAAlternatively,total = 10,000 kW/K in theC6H6 case of linearC5H12 Fresnel C5H10installationsC3H8, savings couldC4H8 reach 6 C4H10million USDH2S for UA = 15,000 kW/K CIT =total 318.15 K (cf. FigureC6H6 14). In theC5H12 same way asC5H10 for the PTCC3H8 installations,C4H8 the maximumC4H10 savingH2S for LF installations was obtained with the s-CO2/H2S mixture (66.0/34.0). 79

UAtotal = 5,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UA = 10,000 kW/K 73total C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S UAtotal = 15,000 kW/K C6H6 C5H12 C5H10 C3H8 C4H8 C4H10 H2S

70 79

67 LF Solar Field cost (Millon USD) (Millon cost SolarField LF 76 0.00 0.05 0.10 0.15 0.20 0.25 0.30 Mole fraction 73 Figure 14. LF’s solar ﬁeld estimated cost vs concentration of s-CO2. Group B mixtures with a Figure 14. LF’s solar field estimated cost vs concentration of s-CO2. Group B mixtures with a CIT = 318.15 K and CIP = just above the critical pressure of the working ﬂuid. CIT70 = 318.15 K and CIP = just above the critical pressure of the working fluid.

67There are different issues to be considered when selecting the optimum sCO2-mixture. The first LF Solar Field cost (Millon USD) (Millon cost SolarField LF There are different issues to be considered when selecting the optimum sCO2-mixture. The first one is the0.00 mixture density;0.05 as already0.10 explained0.15 in this work,0.20 the density0.25 has a direct impact0.30 on the one is the mixture density; as already explained in this work, the density has a direct impact on the turbomachine’s final dimension. It has been seenMole benzenefraction mixtures provide the maximum density at turbomachine’s final dimension. It has been seen benzene mixtures provide the maximum density at the compressor inlet (Table4). Other important considerations to be assessed are related to the isobaric the compressorFigure 14. LF inlet’s s olar(Table field 4) estimated. Other important cost vs concentration considerations of s -CO to be2. Group assessed B mixtures are related with to a the heat capacity and kinetic viscosity. As mentioned before in this study, the highest Cp and density values isobaricCIT heat = 318.15 capacity K and andCIP =kinetic just above viscosity the critical. As pressurementioned of the before working in thisfluid. study, the highest Cp and and the lowest kinetic viscosity value minimize the recuperator (low-temperature recuperator (LTR) density values and the lowest kinetic viscosity value minimize the recuperator (low-temperature and high-temperature recuperator (HTR)) dimensions. The s-CO2/H2S and s-CO2/C4H10 mixtures recuperatorThere are (LTR) different and issues high- temperatureto be considered recuperator when selecting (HTR)) the dimensions optimum sCO. The2-mixture. s-CO2/H The2S andfirst have higher Cp values, and the s-CO2/C6H6 mixture has a higher density value. The s-CO2/C4H8 and sone-CO is2/ Cthe4H 10mixture mixtures density have; highas alreadyer Cp value explaineds, and inthe this s-CO work,2/C6 Hthe6 mixture density has has a a higher direct densityimpact value.on the s-CO2/C4H10 mixtures have lower kinetic viscosity value. Theturbomachine’s s-CO2/C4H8 andfinal s -dimension.CO2/C4H10 mixturesIt has been have seen lower benzene kinetic mixtures viscosity provide value. the maximum density at Another important factor impacting in the power cycle performance is the mixture maximum the compressor inlet (Table 4). Other important considerations to be assessed are related to the operating temperature. At an operating temperature of around 823.15 K at the turbine inlet, isobaric heat capacity and kinetic viscosity. As mentioned before in this study, the highest Cp and hydrocarbons pyrolysis or chemical decomposition could occur. Also, air infiltration in the power cycle density values and the lowest kinetic viscosity value minimize the recuperator (low-temperature working fluid due to leakages could provoke added substance auto-ignition. The mixture substances recuperator (LTR) and high-temperature recuperator (HTR)) dimensions. The s-CO2/H2S and which are more stable in these scenarios are the cyclic hydrocarbons, short-string hydrocarbons, s-CO2/C4H10 mixtures have higher Cp values, and the s-CO2/C6H6 mixture has a higher density value. and hydrocarbons with double links. Based on the REFPROP fluid property library information [26], The s-CO2/C4H8 and s-CO2/C4H10 mixtures have lower kinetic viscosity value. the maximum operating temperature for benzene and hydrogen sulfide is 725 K and 760 K, respectively.

The advantage of benzene is that it has a lower mole fraction than hydrogen sulﬁde.

Appl. Sci. 2020, 10, 55 13 of 18

Table 4. Results summary for ‘group B’ mixtures with CIT = 318.15 K, CIP = critical pressure 1 and

UAtotal = 15,000 kW/K.

Molar Isobaric Heat Kinetic Thermal Density Prandtl Plant Mass Capacity Viscosity Conductivity (kg/m3) Number Eﬃciency (kg/kmol) (kJ/kg*K) (cm2/s) (W/m*K) s-CO pure 44.01 202.44 2.45 9.62 10 4 3.17 10 2 1.50 0.42 2 × − × − s-CO /H S (64.0/34.0) 40.78 323.24 17.12 7.95 10 4 9.23 10 2 14.20 0.46 2 2 × − × − s-CO /C H (92.5/7.5) 44.02 195.79 2.64 9.71 10 4 3.29 10 2 1.52 0.46 2 3 8 × − × − s-CO /C H (92.5/7.5) 44.92 368.04 12.54 7.49 10 4 6.34 10 2 5.46 0.46 2 4 8 × − × − s-CO /C H (97.5/2.5) 44.66 311.47 6.46 7.64 10 4 5.06 10 2 3.04 0.45 2 5 10 × − × − s-CO /C H (92.5/7.5) 46.57 613.85 7.30 8.28 10 4 7.26 10 2 5.11 0.46 2 6 6 × − × − s-CO /C H (90.0/10.0) 45.42 401.36 12.98 7.50 10 4 6.64 10 2 5.61 0.46 2 4 10 × − × − s-CO /C H (97.5/2.5) 44.71 287.34 5.27 8.30 10 4 4.06 10 2 2.16 0.45 2 5 12 × − × − 1 Just above the critical pressure of the working ﬂuid.

This study paves the way for future works which should achieve a detailed equipment design and cost assessments. The final recommendation extracted from this analysis is to compare the cycle performance and detailed equipment design with benzene and hydrogen sulfide mixtures. Subsequent analyses should be focused on comparing the results with the other mixtures in Table4. Another complementary power cycle design work will be focused on adding two or more substances to the sCO2-mixtures, considering the benefits provided by each individual substance, and balancing the required critical temperature according to the CSP-sCO2 location ambient conditions. For the case where CIT equal to 323.15, 328.15 and 333.15 K, the maximum molar fractions for the s-CO2/H2S, s-CO2/C3H8, s-CO2/C4H10, s-CO2/C5H10, s-CO2/C5H12, s-CO2/C4H8 and s-CO2/C6H6 mixtures are shown in Table5. Bearing in mind that in these conditions the critical temperatures are below to CIT’s range studied, i.e., if the additives molar fraction exceeds these values, the mixture critical temperature will be greater than CIT’s range studied. A power cycle efficiency improvement from 3% to 4% has been obtained for group B sCO2-mixtures. Thermodynamic results show savings in PTC’s installations could reach up to 11 million USD for CIT = 323.15 K, 9 million USD for CIT = 328.15 K, and 10 million USD for CIT = 333.15 K. Alternatively, in the case LF’s installations, the savings could reach 8 million USD for CIT = 323.15 K, 7 million USD for CIT = 328.15 K, and 7 million USD for CIT = 333.15 K. As discussed previously for Table4, there are several factors when selecting the optimum s-CO 2 mixture, namely power cycle efficiency impact, critical temperature, the plant location’s ambient temperature, equipment, performance, and cost, etc. When increasing the CIT (cf. Table5), the first conclusion is the requirement to increase the substance’s mole fraction to reach critical temperature values just below of the CIT’s range (323.15, 328.15 and 333.15 K). The substance’s addition influences in the sCO2-mixtures properties. The higher impact on the plant’s equipment design has been gained by density, isobaric heat capacity and kinetic viscosity, similar to working with CIT = 318.15 K. Therefore, the recommendations for the power cycle detail design are the same as cited in Table4. The dry-cooling technical solution is usually adopted in deserts, where water is a scarce resource and the ambient temperature is high. A typical temperature selected for CSP design is 318.15 K, hence, the CIT = 333.15 K is a solution in these places because the difference between the plant location’s ambient temperature and CIT is around 15.00 K. To summarize the conclusions obtained from Table5, it is important to highlight that the substance addition mole fraction has an important impact on sCO2-mixture decomposition. The target should be aligned with the mole fraction minimization. For example, the benzene mole fraction is 12.50%, which is much lower than hydrogen sulfide at 50.00% when the cycle works with CIT = 333.15 K. Finally, it is important to remark that the plant results showed in Tables4 and5 were obtained with a CIP just above the critical pressures. A future study will focus on optimizing the CIP in order to make a comparison with the work developed by J. Dyreby [22] wherein plant efficiency improvement has been demonstrated to increase the CIP above the critical pressure. Appl. Sci. 2020, 10, 55 14 of 18

1 Table 5. Results summary for group B mixtures with CIP = critical pressure and UAtotal = 15,000 kW/K.

Mole Fraction Plant PTC Cost LF Cost CIT (K) (%) Eﬃciency (Million USD) (Million USD)

s-CO2 pure 100.0 323.15 0.42 97.23 76.65 s-CO2/H2S 60.0/40.0 323.15 0.45 86.66 68.37 s-CO2/C3H8 65.0/35.0 323.15 0.45 89.80 70.56 s-CO2/C4H8 90.0/10.0 323.15 0.45 90.00 70.81 s-CO2/C5H10 95.0/5.0 323.15 0.45 89.13 70.12 s-CO2/C6H6 90.0/10.0 323.15 0.44 90.28 71.72 s-CO2/C4H10 87.5/12.5 323.15 0.45 90.12 70.87 s-CO2/C5H12 95.0/5.0 323.15 0.45 90.32 71.05 s-CO2 pure 100.0 328.15 0.40 99.91 78.76 s-CO2/H2S 55.0/45.0 328.15 0.44 90.77 71.56 s-CO2/C3H8 60.0/40.0 328.15 0.44 91.88 72.15 s-CO2/C4H8 87.5/12.5 328.15 0.44 92.10 72.41 s-CO2/C5H10 95.0/5.0 328.15 0.44 92.70 72.90 s-CO2/C6H6 90.0/10.0 328.15 0.43 92.87 73.09 s-CO2/C4H10 85.0/15.0 328.15 0.44 92.47 72.67 s-CO2/C5H12 82.5/7.5 328.15 0.44 91.75 72.12 s-CO2 pure 100.0 333.15 0.39 102.59 80.87 s-CO2/H2S 50.0/50.0 333.15 0.43 92.73 73.09 s-CO2/C3H8 55.0/45.0 333.15 0.43 93.90 73.72 s-CO2/C4H8 85.0/15.0 333.15 0.43 94.22 74.04 s-CO2/C5H10 92.5/7.5 333.15 0.43 93.97 73.85 s-CO2/C6H6 87.5/12.5 333.15 0.42 95.21 74.87 s-CO2/C4H10 82.5/17.5 333.15 0.43 94.75 74.43 s-CO2/C5H12 92.5/7.5 333.15 0.43 94.91 74.58 1 Just above the critical pressure of the working ﬂuid.

4. Conclusions

This study was mainly focused on quantifying the impact of CSP-sCO2 thermal efficiency due to the mixing of the substances (He, Kr, CH4 C2H6,C3H8,C4H8,C4H10,C5H10,C5H12, and C6H6) with pure s-CO2. The obtained results confirmed that the variations in working fluid properties directly impact in the cycle thermodynamic efficiency. On one hand, it is confirmed that He, Kr, CH4 and C2H6 addition reduces the critical temperature, and hence it increases the power cycle thermal efficiency. Detailed results are summarized in Table2. The working fluids mixtures s-CO2/He (90.0/10.0) and s-CO2/Kr (68.0/32.0) increase the power cycle efficiency from 49.0% to 53.0%. Further, krypton and helium are inert gases and the addition of them to the pure s-CO2 is very beneficial for avoiding the equipment materials corrosion. The group sCO2-mixtures, for reducing the sCO2 critical temperature, are very suitable for the CSP-sCO2 night sky cooling technology. On the other hand, another CSP ultimate heat sink technical solution is the dry-cooling system with air-cooled heat exchangers. Most CSPs are located in sites where the ambient temperature is above the s-CO2 critical temperature (CIT = 318.15, 323.15, 328.15, and 333.15 K). In this scenario, the target is setting the CIT near the working fluid’s critical temperature, hence, it is required to increase the working fluid critical temperature by adding H2S, C3H8,C4H8,C4H10,C5H10,C5H12 or C6H6 to the cycle’s working fluid. In Tables4 and5 the results obtained for the CSP with dry-cooling scenario are summarized. As a result of this work, it is concluded that the solar power plant design-point efficiency is improved by about 3–4% when adding the mentioned substances in comparison with the reference pure s-CO2. In works developed by Dyreby [22] and Marchionni [45], it was observed that an increase in the turbine inlet temperature (TIT) implies an improvement in the performance of the recompression Brayton cycle. As a result of this study, it is concluded that this effect of increasing the TIT is equivalent to the use of mixtures of supercritical fluids in the Brayton cycles. Appl. Sci. 2020, 10, 55 15 of 18

Future works should align with the working fluid chemical composition customization according to the ambient conditions where the solar power plant will be located. The environmental impact should also play an important role, and the substances added should be environmentally friendly. For this reason, inert gases in combination with other substances are advisable in future CSP-sCO2 conceptual designs. Additional simulations are required to analyze more complex Brayton cycle configurations: the recompression with partial cooling cycle (RCPC) and recompression with main compressor intercooling cycle (RCMCI), both with reheating. In addition, it will be necessary to analyze the variation of increasing the CIP for compensating the CIT increment in hot locations. Also, detailed experimental analysis is required to verify that the possible reactions and chemical decomposition of mixtures do not affect the plant’s performance.

Author Contributions: R.V.-C. and L.C.-E. developed the computer program SCSP (Supercritical Concentrated Solar Power Plant); All authors wrote the paper. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Community of Madrid’s Industrial Doctorates program (IND2018/IND-9952). Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

CO2 Carbon Dioxide CH4 Methane C2H6 Ethane C3H8 Propane C4H8 1-Butene C4H10 Butane C5H10 Cyclopentane C5H12 Isopentane C6H6 Benzene CIP Compressor Inlet Pressure CIT Compressor Inlet Temperature CSP-sCO2 Concentrated Solar Power Plant coupled to s-CO2 Brayton power cycles FM Flow Mixture FS Flow Split G Generator H2S Hydrogen Sulﬁde He Helium HTF Heat Transfer Fluid HTR High Temperature Recuperator Kr Krypton LF Linear Fresnel LTR Low Temperature Recuperator MC Main Compressor NIST National Institute of Standards and Technology PC Precooler PHX Primary Heat Exchanger PTC Parabolic Trough Solar Collector RC Recompressor RCMCI Recompression with Main Compression and Intercooling Cycle REFPROP Reference Fluid Thermodynamic and Transport Properties Database s-CO2 Supercritical Carbon Dioxide SF Solar Field T Turbine TIT Turbine Inlet Temperature TIP Turbine Inlet Pressure UA Heat Exchanger Conductance Appl. Sci. 2020, 10, 55 16 of 18

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