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temperature recuperator, reaching state 6. Heat rejection to the environment or for external meelecchtarinciaclael fefniceiregnycyf.rom the sCO2 stream between state 4 to state 5. The turbine exit stream preheats processing heating occurs in the pre-cooler, to return to state 1. Cooling the exhaust from the the inTcohme ienlegctCrOica2 lsetrfefiacmiesnciny othfetheigshtatnedmaprdersaCtuOre2 cryecluep(eηrSaStGoTr),grievaecnhingFsigtautree51a,isanredpirnestehneteldowin combustor and supplying thermal energy to the sCO2 turbine cycle facilitates maximizing the teEmqupaetriaotnur(e1),rwechueprerator, riesatchheitnogtalstCaOte2 m6.asHseflaotwrerajetcetinonthetocytchle.Tenhveisrpoencmifeicnetnothralfporieseoxftesrtnaatels electrical efficiency. p1r,o2c,e2ssai,n4g, 5h,eaantdin6g, aorcechu1r,sh2i,nh2tah, he4,phr5e,-acnodolhe6r,,retospreecttuivrnelyt.oTshteatceoe1f.fiCcioeonltisn0g.5t3haenedx0h.a4u7satrefrtohme mthaess The electrical efficiency of the standard sCO2 cycle (ηSSGT) given in Figure 1 is represented in cformacbtuiosntoorf CanOd2 esnutperpilnyginthgetmhearimn caol menperregssyortoantdhesescConOd2artuyrcboimneprceyscsloer,fraecsiplietacteivsemly.aTxihmeimziansgs ftlhoew is the total CO2 mass flow rate in the cycle. The specific enthalpies of states Energies2020,13,50E4n3erEgineesr2g0ie2s02,01230,,x1F3O,xRFPOERERPEREERVRIEWVIEW 5of20 3of139of1 Equation (1), where erleactetriocfalmeefftihcaiennecyre.quired to provide the necessary thermal energy is , and HHVf is the higher 1, 2, 2a, 4, 5, and 6, are h1, h2, h2a, h4, h5, and h6, respectively. The coefficients 0.53 and 0.47 are the mass heatTinhge evlaelcutericoaflmefefitchiaenec.yPoCfCtihsetshteantodtarldesleCcOtr2iccaylcpleow(ηeSSrGTr)eqguivireendinfoFriCguOr2ec1omisprreepsrseisoenntdeudring higheigrhperrespsruersesuarnedarnedacrheaeschsetastseta2t.eM2e.aMnewahniwleh, itlhee, tsheecosnecdoanrydacroymcpormespsroersscormcpormespsressthesetrheestroefsthoef th fraction of CO2 entering the main compressor and secondary compressor, respectively. The mass flow Various losses give rise to three key efficiency definitions in the FFC subsystem. Those include the Esqeuqauteiostnra(1ti)o,nw.hPerreviousliitsertahteutroetahlaCsOsh2omwansstfhloatwthraetespinectihfieccpyoclwe.eTrhreqsupierceidficfoerntchoamlpireessosfiosntaatensd CO2C, Ow2h, iwchisctharsttsaartsthaet tshaemseamprespsruerses,ubreu,tbhuigt heigrhtemr tpeemrapteurraetuarnedarnedacrheaeschsetastseta2tae. 2a. rate of methane required to provide the necessary thermal energy is , and HHVf is the higher fuel utilization efficiency (η ), the fuel cell conversion efficiency (η ), and theoverall efficiency (η ). 1r,e2f,r2igae,r4a,t5io, nanodf6C,Oar2effhou1r, hse2,qhu2ea,shtr4,ahti5o,nanadt h165, rBeasrpeisct1iv07elyk.WT/hkefgccCoeOff2ic[4ie1n],tsw0h.5ic3hanisdu0s.4ed7 ainretthoives mwaosrsk. heating value of methane. PCC is the total electrical power required for CO2 compression during Equations (5)–(7) define each efficiency, respectively. frTahcitsiopnoowf eCrOis2 keneptetrzinegrothwehmenaisnecqoumesptreastisonr aisnndosteacsosnedssaeryd.compressor, respectively. The mass flow sequestration. Previous literature has shown that the specific power required for compression and rate of methane required to provide the necessary thermal energy is , and HHVf is the higher fu Total Syngas available in exhaust ɳ = = (6) (1) (7) (1) (h −h )−0.47(h −h )−0.53(h −h )− SyngaselectrochemicallyoxidizedinFFC refrigeration of CO2 for sequestration at 15 Bar is 107 kW/kg CO2 [41], which is used in this work. ɳ= (1) heating value of methan=e. PCC is the total electrical power required for CO2 compression(d5)uring This power is kept zero when sequestration is not assessed. sequestration. Previous literature has shown that the specific power required for compression and refrigerationofCO2 forsequestra(thion−aht1)5−B0a.4r7is(h107−khW)/k−g0C.5O32(h[41−],hwh)ic−hisusedinthiswork. Electrical power generated by FFC This power is kept zero when sequestration is not as sessed. Total Chemical energy of the available syngas (h −h )−0.47(h −h )−0.53(h −h )− ɳ==Electricalpowergeneratedbyfuelcell ov Chemical energy from the hydrocarbon fuel fc FFC electrochemically oxidized both H2 and CO to generate electric power. Equation (8) shows the effective fuel cell reaction), in which the coefficients a1, b1, and γ1 depend upon the a and b stoichiometric coefficients from Equation (3) and the fuel utilization efficiency of the FFC (Equation (5)). a1CO+b1H2+γ1O2 →a1CO2+b1H2O Writing the reaction Equation (8) per mole of syngas leads to Equation (9). a1 CO+ b1 H2+ γ1 O2→ a1 CO2+ b1 H2O a1 + b1 a1 + b1 a1 + b1 a1 + b1 a1 + b1 (8) FiguFriegu1.reSc1h. eSmchaetmic aotficaosftansdtanrdasrCdOs2CBOra2 yBtroanytcoynclceywcliethwriethcurpeecurapteiornataionndarnedcormecpormespsrioesnssiohnowshinowg ing (10). In Equation (10), R is the universal gas constant, T is absolute temperature (in Kelvin), and K is the equilibrium constant of reaction in Equation (8). The mole specific enthalpy of reaction (8) (∆hFC) is used to calculate the thermo-neutral potential (Vth) as shown in Equation (11) where n is the number of TheTihneitianlitCiaOl 2CfOro2mfrosmtatseta2teis2pirsehpereahtedatiendthinetlhoewlotewmtpeemrapteurraeturreecurepceurapteorrataonrdarnedacrheaeschsetastsetat electrons released per mole of fuel in the fuel cell reaction (two electrons per mole of syngas) and F is 2a w2ahewrehethretthweotwCoO2CsOtr2esatmresamcosmcboimneb.inTeh.eTchoemcpolmetpelesteresatmreaismthisenthfeunrtfhuerrthperrehpereahtedatiendthinethieghig Faraday’s constant. t e m t p e e m r a p t e u r r a e t u r r e e c u r e p c e u r a p t e o r r a t a o n r d a n r de a c r h e a e s c h s e t s a t s e t a 3 t . e F 3 u . r F t h u e r r t h h e e r a h t e a a d t d a i t d i do n i t i o f r n o mf r o e m x t e e r x n t a e l r n s a o l u s r o c e u s r c l e i s k e l i k −∆goFC RT comcboumsbtiuosntiofnaofuaelfVuoerelvao=croancoentcreantti−rnagtisnoglalsnro(tlKhare)rtmhearlmhaelaht etraatntsrfaenrsfleurifdluviida vaiaheaa(ht1e0ea)xtchexacnhgaenrgberrinbgrsing of partial pressures in the subsystem is equal to the mole fraction of the components, assuming ideal gas behavior. propcersosciensgsinhgeahtienagtinogccuorcscuirns tihne thpere-pcroeo-cleoro, letor, rteoturrentutron sttoatseta1t.e C1o. oClionoglinthge thexeheaxuhsat ufsrtomfrotmhe th comcboumsbtourstaonrdansdupspulypipnlgyinthgertmhearlmeanleergnyergtoy thoethsCeOs2COtu2rbtuinrebincyeclceycflaeciflaitcaitleitsatmesaxmimaxiziminigzinthgeth elecetlreicatrliecaffliceifefnicciyen. cy. K = i ysyn (12) P EquEaqtiuoanti(o1n),(w1)h,ewrehere isthisethoetatloCtaOl2CmOa2smsaflsoswflorawteraintethinetchyeclcey.cTleh.eTshpecspifeiciefnictheanltphiaelspoiefssotaftsetsate y N P i TheTehlecetlreicatrliceaffliceifefnicciyenocfytohfetshteansdtanrdasrCdOs2CcOy2clceyc(ηleSS(GηT)SSgGTi)vegnivienFiinguFrigeu1reis1reisprespernetsedntiend i i=1 For the fuel cell reaction, Equation (13) shows how to determine the equilibrium constant, where Xi 1, 2,12, a2, 42,a5, ,4a, n5,da6n,dar6e, ahr1e, h21,,h22a, h24a,,h54,,ahn5,dahn6d, rhe6s,precsptievcetliyv.eTlyh.eTchoefcfoiceifefnictisen0.t5s30a.5n3da0n.d470a.4r7e athre tmheasms as is the mole fraction of species ‘i’. fracftriaocntiofnCoOf2CeOn2ternintegritnhgetmheai−mnb acoinmc−poγrmespsroe−rassaonrdasnedcosnecdoanrydacroymcpormespsroers,sroers,precsptievcetliyv.eTlyh.eTmheasmsaflsoswflow K = X( a+b )X( a+b )X( a+b ) (13) rateraotfemofetmhaenthearneequreirqeudirteodptoropvirdoevitdhetnhecensescaersysatrhyertmhearlmeanleergnyerigsyis ,a n,danHdHHVHf iVs fthisethiegheigrhe H2 O2 CO heahtienagtinvgaluvealoufemofetmhaenthea.nPeC.CPisCCthisetthoetatlotealelcetlreicatrlicpaolwpeorwrerqureirqeudirfeodrfCoOr 2CcOo2mcpormespsrieosnsiodnurdinugrin Equation (14) shows the power generated by the fuel cell (Pfc), where ηfu is the fuel utilization . (1)(1 sequseqstureasttiorant.ioPnr.evPiroeuvsioluitserlaitteurraetuhraeshsahsoswhnowthnaththate tshpeecspifeicipfiocwpeorwrerqureirqeudirfeodr fcormcpormespsrieosnsiaondan efficiency, ηfc is the fuel cell efficiency, nk is the molar flow rate of species ‘k’ (CO or H2) in the fuel-rich refrrigeferriagteiorantiofnCoOf2CfOor2 fsoerquseqstureasttiroantiaotn1a5tB1a5rBisar1i0s71k0W7k/kWg/CkgO2C[O412][,4w1]h,iwchicshuisedusiendtihnisthwisorwk.ork exhaust, ∆gCO,CO2 and ∆gH2,H2O are the mole specific Gibbs’ free energies released from the oxidation ThisThpioswpeorwiserkiespktezpetrozewrohewnhsenquseqstureasttiroantiiosniostnaossteassedss. ed. of CO and H2, respectively. P =−n ∆g 2+n2∆g22 (14) (h (−h h−) h− )0−.470(.4h7(h− h−) h− )0−.530(.5h3(−h h−)h−)− ɳɳ=.= . fc fufcCOCO,COHH,HO (9) ) and the The mole specific standard Gibbs’ free energy released by reaction Equation (8) (∆g◦ temperature is used to calculate the reversible cell potential (Vrev) of the fuel cell as shown in Equation the vthaerivoaursiosutastestpaoteinptosiintsthine sthyestseymst.em. FC nF nF thetChOe 2CtOo2stoatseta4t.eF4o.rFtohretphuerpuorspesosoefsthofetahneaalynsailsyhsiesreh,ewree, wuseeucsoemcboumsbtiuosntiofnmoeftmhaentheatnoegteongeeranterat −∆hFC the theaht einatoirndoerdtoerptroopvirdoevVitdhe=tmheosmt odsirtedcitrecoctmcpoamripsaorniswonithwtithhe tFhFeCFTFHCTsHystseymst.(e1Am1).tuArbtuinrebienxetreaxctrsact th mecmhaecnhicaanliecanleergnyerfgryomfrothme tshCeOs2CsOtr2esatmreabmetwbetewnesetnatseta4tteo4stoatseta5t.eT5h.eTthuerbtuinrebienxeitesxtirtesatmreapmrehpereahtseat The equilibrium constant is calculated as shown in Equation (12) where Pi/P is the ratio of partial thetihnecoinmcionmgiCngO2CsOtr2esatmresaminstihnethieghitgehmtpeemrapteurraeturreecurepceurapteorra,torera, crheaincghisntgatseta5tae, 5aan,danindtihnetlhoewlow pressure of species i and yi/ysyn is the ratio of coefficients of species i in reaction Equation (8). The ratio temtpeemrapteurraeturecurepceurapteorra,torre,acrheaincghinsgtatseta6te. 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