Thermodynamic Considerations for Thermal Water Splitting Processes and High Temperature Electrolysis

Transcription

1 INL/CON PEPINT Thermdynamc Cnsderatns fr Thermal Water Splttng Prcesses and gh Temperature Electrlyss IMECE 8 J. E. O Bren Nvember 8 Ths s a preprnt f a paper ntended fr publcatn n a jurnal r prceedngs. Snce changes may be made befre publcatn, ths preprnt shuld nt be cted r reprduced wthut permssn f the authr. Ths dcument was prepared as an accunt f wrk spnsred by an agency f the Unted States Gvernment. Nether the Unted States Gvernment nr any agency theref, r any f ther emplyees, makes any warranty, expressed r mpled, r assumes any legal lablty r respnsblty fr any thrd party s use, r the results f such use, f any nfrmatn, apparatus, prduct r prcess dsclsed n ths reprt, r represents that ts use by such thrd party wuld nt nfrnge prvately wned rghts. The vews expressed n ths paper are nt necessarly thse f the Unted States Gvernment r the spnsrng agency.

2 Prceedngs f the 8 Internatnal Mechancal Engneerng Cngress and Expstn IMECE8 Octber 3 Nvember 6, 8, Bstn, Massachusetts, USA IMECE TEMODYNAMIC CONSIDEATIONS FO TEMAL WATE SPLITTING POCESSES AND IG TEMPEATUE ELECTOLYSIS J. E. O Bren Idah Natnal Labratry Idah Falls, ID 8345, USA ABSTACT A general thermdynamc analyss f hydrgen prductn based n thermal water splttng prcesses s presented. esults f the analyss shw that the verall effcency f any thermal water splttng prcess peratng between tw temperature lmts s prprtnal t the Carnt effcency. Implcatns f thermdynamc effcency lmts and the mpacts f lss mechansms and peratng cndtns are dscussed as they pertan specfcally t hydrgen prductn based n hgh-temperature electrlyss. Overall system perfrmance predctns are als presented fr hghtemperature electrlyss plants pwered by three dfferent advanced nuclear reactr types, ver ther respectve peratng temperature ranges. INTODUCTION There s a grwng nterest n the develpment f largescale nn-fssl hydrgen prductn technlges. Ths nterest s drven by the mmedate demand fr hydrgen fr refnng f ncreasngly lw-qualty petrleum resurces (e.g., the Athabasca l sands, cal) [, ], the expected ntermedateterm demand fr carbn-neutral synthetc fuels [3], and the pssble lng-term demand fr carbn-free hydrgen as an envrnmentally bengn transprtatn fuel [4]. Ths paper presents the techncal case fr hgh-temperature hydrgen prductn prcesses. Large-scale effcent carbn-free hydrgen prductn can be accmplshed by water splttng based n nuclear energy. Tw canddate technlges are under cnsderatn: thermchemcal prcesses and hghtemperature electrlyss, shwn schematcally n Fg.. The prmary energy nput fr thermchemcal prcesses s n the frm f heat, whereas the prmary energy nput fr hghtemperature electrlyss s n the frm f electrcty. wever, assumng the electrcty s generated frm a thermal energy surce, bth thermchemcal and hgh-temperature electrlyss prcesses can be analyzed as thermal water splttng prcesses. Thermchemcal prcesses cmprse a seres f thermally drven chemcal reactns whch have the net effect f water splttng wth hydrgen and xygen as prducts. The ther reactants are recycled durng the prcess. The mst studed thermchemcal prcess fr nuclear hydrgen prductn s the sulfur-dne (SI) prcess [5-6]. The sulfurc acd decmpstn reactn n the SI prcess requres heat addtn at a temperature f apprxmately 9 C. Actve research actvtes n the SI prcess are under way n the US, France, and n Japan. Prmary challenges nclude crrsn, catalyst degradatn, and membranes separatns. gh-temperature electrlyss utlzes a cmbnatn f thermal energy and electrcty t splt water n sld-xde electrlyss cells (SOECs). These cells are smlar t sldxde fuel cells (SOFCs). The feasblty f peratng sldxde cells at hgh temperature n the electrlyss mde has been demnstrated fr bth tubular [7] and planar systems [8-9]. System mdelng studes have been perfrmed t cmpare the predcted verall hydrgen-prductn effcency f the SI prcess wth hgh-temperature electrlyss [-]. esults f these studes ndcate smlar expected perfrmance fr the tw methds. wever, hgh-temperature electrlyss faces fewer techncal challenges t large-scale deplyment. NOMENCLATUE F Faraday number, C/ml AS area-specfc resstance, Ohm cm G gbbs energy f reactn, J/ml f enthalpy f frmatn, J/ml cmpnent sensble enthalpy, J/ml enthalpy f reactn, J/ml

3 Fgure. Nuclear hydrgen prductn cncepts: thermchemcal prcess and hgh-temperature electrlyss. V hgh heatng value current densty, A/cm I current, A j number f electrns transferred per mlecule f hydrgen prduced N mlar hydrgen prductn rate, ml/s P pressure, kpa q heat flux, W/cm Q hgh-temperature heat addtn, J/ml Q L lw-temperature heat rejectn, J/ml Q T sthermal heat transfer rate, W Q heat transfer rate, W u unversal gas cnstant, J/ml K S entrpy f reactn, J/ml K T temperature, K T standard temperature, K T L temperature f heat rejectn, K T temperature f heat addtn, K T reactant temperature, K T P prduct temperature, K V standard-state pen-cell ptental, V V N Nernst ptental, V V p peratng vltage, V V tn thermal neutral vltage, V W wrk, rate bass, W y mle fractn verall thermal-t-hydrgen effcency th pwer cycle thermal effcency electrlyss effcency e GENEAL TEMODYNAMICS OF TEMAL WATE SPLITTING A basc thermdynamc analyss can be appled t a general thermal water-splttng prcess n rder t determne the verall prcess effcency lmts as a functn f temperature. Cnsder the prcess dagram shwn n Fg.. Water enters the cntrl vlume frm the left. Snce the ultmate feedstck fr any large-scale water-splttng peratn wll be lqud water, t s reasnable t cnsder the case n whch water enters the cntrl vlume n the lqud phase at sme temperature T and pressure P. Pure hydrgen and xygen streams ext the cntrl vlume n the rght, als at T and P. Tw heat reservrs are avalable, a hgh-temperature reservr at temperature T and a lw-temperature reservr at temperature T L. eat transfer between these reservrs and the cntrl vlume s ndcated n the fgure as Q and Q L. Nte that there s n wrk crssng the cntrl-vlume bundary. Therefre f the prcess under cnsderatn s hghtemperature electrlyss, bth the pwer cycle (based n a heat engne fr the purpses f ths dscussn) and the electrlyzer are lcated nsde the cntrl vlume. Frm a chemcal reactn standpnt, the water-splttng prcess crrespnds t the dsscatn r reductn f water: O + ½ O () The frst and secnd laws f thermdynamcs can be appled t ths prcess as fllws: st law: Q QL ()

4 nd law: O Q Q L S (3) T TL where s the enthalpy f reactn and S s the entrpy change f the reactn. The verall thermal-t-hydrgen effcency f thermal water splttng prcesses can be defned n terms f the net enthalpy ncrease f the reactn prducts ver the reactants (can als be thught f as the energy cntent r heatng value f the prduced hydrgen), dvded by the (cstly) hgh-temperature heat added t the system: (4) Q Cmbnng the frst and secnd law equatns fr the reversble case and substtutng nt the effcency defntn yelds: T Q Q L T L T / T L (5),max TLS / Nte that the water splttng prcess defned n Fg. s smply the reverse f the cmbustn reactn f hydrgen wth xygen. Therefre the enthalpy f reactn fr the watersplttng prcess s the ppste f the enthalpy f cmbustn, whch by defntn s equal t the heatng value f the hydrgen. Snce fr ur prcess, we have assumed that the water enters the cntrl vlume n the lqud phase, V (6) where V s the hgh heatng value f hydrgen. If we further assume that T and P represent standard cndtns, and that T L = T, (7) TLS G f, O T, P T, P CV ½O Fgure. Schematc f a generc thermal water-splttng prcess peratng between temperatures T and T L. such that the effcency expressn can be rewrtten as:.8 T.6.4.,max maxmum pssble effcency 65% f maxmum T (C) Fgure 3. Theretcal thermal water splttng effcences. T L V T L T G f,. 83 O T The hgh heatng value f the hydrgen and the standard-state Gbbs energy f frmatn fr water are fxed quanttes such that the secnd factr n the rght-hand sde s a cnstant. Ths effcency lmt was als derved fr the sulfur-dne thermchemcal prcess based n an exergy analyss n []. Cmparng Eqn. (8) t Eqn. (4), the hgh-temperature heat requrement fr the prcess can be stated as: Q f, O T TL (8) T G (9) Ths result was derved fr thermchemcal cycles by Abraham and Schrener [3], and appled t slar thermal dsscatn f water by Fletcher and Men [4], wh nted that the maxmum effcences f all thermchemcal prcesses can be related t the effcences f Carnt engnes peratng between the same upper and lwer temperatures. It s necessary nly t add, cnceptually, a reversble fuel cell whch cnverts the hydrgen and xygen t lqud water at the lwer temperature, perfrmng an amunt f electrcal wrk gven by the Gbbs free energy f the reactn. A plt f thermal water splttng effcences s presented n Fg. 3 fr T L = C. The tp curve represents the maxmum pssble water-splttng effcency result gven by Eqn. (8). The bttm curve s smply 65% f ths thermdynamc lmt. The 65% value s based n a typcal percentage f Carnt effcency that can be acheved wth a well engneered mdern pwer cycle. The frst cnclusn t be drawn s that hgh temperature s needed fr effcent hydrgen prductn based n thermal water splttng, regardless f the specfc methd used. If we assume that 65% f the maxmum pssble effcency mght als be achevable wth a well engneered thermal water-splttng prcess, then 3

5 effcences f the magntude gven n the lwer curve f Fg. 3 shuld be expected. Detaled prcess analyses have been perfrmed at INL [] t analyze TE-based hydrgen-prductn systems cupled t advanced nuclear reactrs. esults frm ths study are presented n Fg. 4. Ths fgure shws verall hydrgen prductn effcences, based n hgh heatng value, pltted as a functn f reactr utlet temperature. The fgure ncludes a curve that represents 65% f the thermdynamc maxmum effcency, agan assumng T L = C. Three dfferent advanced-reactr/pwer-cnversn cmbnatns were cnsdered: a helum-cled reactr cupled t a drect recuperatve Braytn cycle, a supercrtcal CO -cled reactr cupled t a drect recmpressn cycle, and a sdum-cled fast reactr cupled t a ankne cycle. The system analyses were perfrmed usng UnSm [5] sftware. Each reactr/pwer-cnversn cmbnatn was analyzed ver an apprprate reactr utlet temperature range. The fgure shws results fr bth TE and lw-temperature electrlyss (LTE). In addtn, an effcency curve fr the SI thermchemcal prcess s shwn [6]. The results presented n Fg. 4 ndcate that, even when detaled prcess mdels are cnsdered, wth realstc cmpnent effcences, heat exchanger perfrmance, and peratng cndtns, verall hydrgen prductn effcences n excess f 5% can be acheved fr TE wth reactr utlet temperatures abve 85 C. Fr reactr utlet temperatures f 6-8 C, the supercrtcal CO /recmpressn pwer cycle s superr t the ecled/braytn cycle cncept. Ths cnclusn s cnsstent wth results presented n [7]. The effcency curve fr the SI prcess als ncludes values abve 5% fr reactr utlet temperatures abve 9 C, but t drps ff quckly wth decreasng temperature, and falls belw values fr LTE cupled t hgh-temperature reactrs fr utlet temperatures belw 8 C. Even LTE benefts frm hgher reactr utlet temperatures because f the mprved pwer cnversn thermal effcences. Current plannng fr NGNP [8] ndcates that reactr utlet temperatures wll be at r belw 9 C, whch favrs TE TEMODYNAMICS OF IG TEMPEATUE ELECTOLYSIS Fcusng nw n electrlyss, cnsder a cntrl vlume surrundng an sthermal electrlyss prcess, as shwn n Fg. 5. In ths case bth wrk and heat nteractns crss the cntrl vlume bundary. The frst law fr ths prcess s gven by: Fr reversble peratn, Such that Q W () Q T () rev S verall thermal t hydrgen effcency (V), % T (C) Fgure 4. Overall thermal-t-hydrgen effcences fr TE cupled t three dfferent reactr types, as a functn f reactr utlet temperature. W rev TS G () The thermdynamc prpertes appearng n Eqn. () are pltted n Fg. 6 as a functn f temperature fr the - O system frm C t C at standard pressure. Ths fgure s ften cted as a mtvatn fr hgh-temperature electrlyss versus lw-temperature electrlyss. It shws that the Gbbs free energy change, G, fr the reactng system decreases wth ncreasng temperature, whle the prduct f temperature and the entrpy change, TS, ncreases. Therefre, fr reversble peratn, the electrcal wrk requrement decreases wth temperature, and a larger fractn f the ttal energy requred fr electrlyss,, can be suppled n the frm f heat. Snce heat-engne-based electrcal wrk s subject t a prductn thermal effcency f typcally 5% r lwer, decreasng the wrk requrement results n hgher verall thermal-t-hydrgen prductn effcences. Nte that the ttal energy requrement,, ncreases nly slghtly wth temperature, and s very clse O 65% f max pssble INL, TE / e ecup Braytn INL, LTE / e ecup Braytn INL, TE / Na-cled ankne INL, LTE / Na-cled ankne INL, TE / Sprcrt CO INL, LTE / Sprcrt CO SI Prcess (GA) Q T, P T, P CV W ½O Fgure 5. Schematc f a water electrlyss prcess peratng at temperature T. 4

6 6 MJ/kg O Energy Demand per unt mass f steam lqud steam, Ttal Energy Demand G, Electrcal Energy Demand TS, eat Demand P= atm T (C) n magntude t the lwer heatng value f hydrgen. The rat f G t s abut 93% at C and abut 7% at C. Operatn f the electrlyzer at hgh temperature s als desrable frm the standpnt f reactn knetcs and electrlyte cnductvty, bth f whch mprve dramatcally at hgher peratng temperatures. Ptental dsadvantages f hgh-temperature peratn nclude the lmted avalablty f very hgh temperature prcess heat and materals ssues such as crrsn and degradatn. The sld-xde electrlyss cell s a sld-state electrchemcal devce cnsstng f an xygen-n-cnductng electrlyte (e.g., yttra- r scanda-stablzed zrcna) wth prus electrcally cnductng electrdes depsted n ether sde f the electrlyte. A crss-sectn f a planar desgn s shwn n Fg. 7. The desgn depcted n the fgure shws an electrlyte-supprted cell wth a nckel cermet cathde and a pervskte ande such as strntum-dped lanthanum mangante (LSM). In an electrlyte-supprted cell, the electrlyte layer s thcker than ether f the andes. The flw felds cnduct electrcal current thrugh the stack and prvde flw passages fr the prcess gas streams. The separatr plate r bplar plate separates the prcess gas streams. It must als be electrcally cnductng and s usually metallc, such as a ferrtc stanless steel. A wealth f nfrmatn n materals, cnfguratns, and desgns f sld-xde electrchemcal systems s avalable n reference [9]. As shwn n the fgure, a mxture f steam and hydrgen at 75-95C s suppled t the cathde sde f the electrlyte (nte that cathde and ande sdes are ppste t ther fuelcell-mde rles). The half-cell electrchemcal reactns ccur at the trple-phase bundary near the electrde/electrlyte nterface, as shwn n the fgure. Oxygen ns are drawn thrugh the electrlyte by an appled electrchemcal ptental. The ns lberate ther electrns and recmbne t frm mlecular O n the ande sde. The nlet steam-hydrgen mxture cmpstn may be as much as 9% steam, wth the remander hydrgen. ydrgen s ncluded n the nlet stream 3.5 kwh/m 3 Fgure 6. Standard-state energy requrements fr electrlyss as a functn f temperature % O + % % O + 9 % 4 e - 4 e - O O = O O Prus Cathde, Nckel cermet + 4 e - + O = Gastght Electrlyte, YSZ r ScSZ O = O + 4 e - Prus Ande, pervskte, e.g., LSM flw feld flw feld Separatr plate/intercnnect O + Next Nckel Cermet Cathde n rder t mantan reducng cndtns at the cathde. The extng mxture may be as much as 9%. Prduct hydrgen and resdual steam s passed thrugh a cndenser r membrane separatr t purfy the hydrgen. In rder t accmplsh electrlyss, a vltage must be appled acrss the cell that s greater than the pen-cell ptental. The standard-state pen-cell ptental s gven by: G V (3) jf where j s the number f electrns transferred per mlecule f hydrgen prduced. Fr the steam-hydrgen system, j=, as ndcated n Fg. 7 n whch the O = ns are transprted thrugh the sld-xde electrlyte. The standard-state pen-cell ptental apples t the case n whch pure reactants and prducts are separated and at ne standard atmsphere pressure. In mst practcal TE systems, the ncmng steam s mxed wth sme hydrgen and pssbly sme nert gas. Usng the materal set shwn n Fg. 7, nlet hydrgen s requred n rder t mantan reducng cndtns n the nckel cermet electrde. Als, t s nt desrable t run the electrlyzer t % steam utlzatn, because lcalzed steam starvatn wll ccur, severely degradng perfrmance. Therefre, the utlet stream wll nclude bth steam and hydrgen. esdual steam can be remved frm the prduct by cndensatn. On the xygen-evlutn sde f the cells, ar s ften used as a sweep gas, s the xygen partal pressure s nly abut % f the peratng pressure. In addtn, the electrlyss system can perate at elevated pressure. In rder t accunt fr the range f gas cmpstns and pressures that ccur n a real system, the pen-cell (r Nernst) ptental can be btaned frm the Nernst equatn, whch can be wrtten as: / ut y O P V N V ln (4) / jf y yo Pstd Fgure 7. Crss-sectn f a planar hgh temperature electrlyss stack. 5

7 Operatn f a sld-xde stack n the electrlyss mde s fundamentally dfferent than peratn n the fuel-cell mde fr several reasns, asde frm the bvus change n drectn f the electrchemcal reactn. Frm the standpnt f heat transfer, peratn n the fuel-cell mde typcally necesstates the use f sgnfcant excess ar flw n rder t prevent verheatng f the stack. The ptental fr verheatng arses frm tw surces: () the exthermc nature f the hydrgen xdatn reactn, and () hmc heatng asscated wth the electrlyte nc resstance and ther lss mechansms. Cnversely, n the electrlyss mde, the steam reductn reactn s endthermc. Therefre, dependng n the peratng vltage, the net heat generatn n the stack may be negatve, zer, r pstve. Ths phenmenn s llustrated n Fg. 8. The fgure shws the respectve nternal heat snk/surce fluxes n a planar sld-xde stack asscated wth the electrchemcal reactn and the hmc heatng. The hmc heat flux (W/cm ) s gven by: q" AS ( V V ) (5) Ohm where s the current densty (A/cm )and V N s the mean Nernst ptental fr the peratng cell. The reactn heat flux s gven by: q" ( TSe) ( Ge ) (6) F F where S e s the entrpy change fr the actual electrlyss prcess, accuntng fr the reactant and prduct partal pressures. The net heat flux s als shwn n Fg. 8. An area-specfc resstance f.5, an peratng temperature f K, and hydrgen mle fractns f. and.95 at the nlet and utlet, respectvely, were assumed fr these calculatns. In the fuelcell mde, the net heat flux s always pstve and ncreases rapdly wth peratng vltage and current densty. In the electrlyss mde, the net heat flux s negatve fr lw peratng vltages, ncreases t zer at the thermal-neutral vltage, and s pstve at hgher vltages and current denstes. The thermal-neutral vltage can be predcted frm drect applcatn f the rate-based Frst Law t the sthermal system shwn n Fg. 5: (7) Q p W N where, frm Faraday s law, N I / F (8) Lettng Q = (n external heat transfer), W IV, tn yeldng: V tn = /F (9) Nte that the reactn heat flux f Eqn. (6) can als be wrtten n terms f the thermal-neutral vltage as: N heat flux, W/cm pen-cell ptental current densty, A/cm peratng vltage, V Fgure 8. Thermal cntrbutns n electrlyss and fuel cell mdes f peratn. q fuel cell electrlyss " N tn ( V V ) () Snce the enthalpy f reactn,, s strctly a functn f temperature (deal gas apprxmatn), the thermal-neutral vltage s als strctly a functn f temperature, ndependent f cell AS and gas cmpstns. The partcular values f net cell heat flux at ther peratng vltages d hwever depend n cell AS and gas cmpstns. The thermal-neutral vltage ncreases nly slghtly n magntude ver the typcal peratng temperature range fr sld-xde cells, frm.87 V at 8 C t.9 V at C. At typcal sld-xde electrlyss stack temperatures and AS values, peratn at the thermal-neutral vltage yelds current denstes n the..6 A/cm range, whch s very clse t the current densty range that has yelded successful lng-term peratn n sld-xde fuel cell stacks. Operatn at r near the thermal-neutral vltage smplfes thermal management f the stack snce n sgnfcant excess gas flw s requred and cmpnent thermal stresses are mnmzed. In fact, n the electrlyss mde, snce xygen s beng prduced, there s als n theretcal need fr ar flw t supprt the reactn at all. In a large-scale electrlyss plant, the pure xygen prduced by the prcess culd be saved as a valuable cmmdty. wever, there are several gd reasns t cnsder the use f a sweep gas n the xygen sde. Frst, the use f a sweep gas wll mnmze the perfrmance degradatn asscated wth any small leakage f hydrgen frm the steam/hydrgen sde t the xygen sde f the cell. Secnd, there are serus materals ssues asscated wth the handlng f pure xygen at elevated temperatures. Fnally, the use f a sweep gas (especally ne that des nt cntan xygen) n the xygen sde f the electrlyss cell reduces the average mle fractn and partal pressure f xygen, thereby -. thermal neutral vltage -.3 reactn hmc net 6

8 reducng the pen-cell and peratng ptentals, resultng n hgher electrlyss effcences, as we shall see shrtly. There are sme addtnal thermdynamc mplcatns related t the thermal neutral vltage. In partcular, electrlyzer peratn at r abve the thermal neutral vltage negates the argument that s ften stated as a mtvatn fr hghtemperature electrlyss that a fractn f the ttal energy requrement can be suppled n the frm f heat. In fact, fr sthermal peratn at vltages greater than thermal neutral, heat rejectn s requred. Electrlyss effcency, e, can be defned fr TE, analgus t the defntn f fuel cell effcency []. The electrlyss effcency quantfes the heatng value f the hydrgen prduced by electrlyss per unt f electrcal energy cnsumed n the stack. Based n ths defntn, N e () VI and snce the stack electrcal current s drectly related t the mlar prductn rate f hydrgen va Faraday s law, the electrlyss effcency can be expressed strctly n terms f cell peratng ptentals as: / F Vtn e. () V V p The effcency fr the fuel-cell mde f peratn s the nverse f Eqn. (). A fuel utlzatn factr s ften ncluded n the fuel-cell effcency defntn, but t s nt needed n the electrlyss defntn snce n fuel (nly steam) s wasted at lw utlzatn. It shuld be nted that the value f the effcency defned n ths manner fr electrlyss s greater than. fr peratng vltages lwer than thermal neutral. As an example, fr the reversble standard-state reference case, frm Eqn. (), n a rate bass: W N G IV (3) rev Invkng Faraday s law, the peratng cell ptental fr ths case appraches the reference pen-cell value, V G / F, yeldng: p e, (4) G whch fr steam electrlyss at 85ºC s equal t.34. Fr cases wth varable gas cmpstn r partal pressure, the pen-cell ptental s gven by the Nernst Equatn (4) and the crrespndng effcency lmt vares accrdngly. It s nt desrable t perate an electrlyss stack near the effcency lmt, hwever, because the nly way t apprach ths lmt s t perate wth very lw current densty. There s a trade-ff between effcency and hydrgen prductn rate n selectng an electrlyss stack peratng vltage. Ths trade-ff s llustrated n Fg. 9. The upper curve n the fgure shws the Effcency r current densty Effcency Current Densty V N decrease n electrlyss effcency that ccurs as the per-cell peratng vltage s ncreased abve the pen-cell vltage, V N, accrdng t Eqn. (). Operatn at the thermal-neutral vltage yelds an electrlyss effcency f.. Area-specfc resstance (AS) represents the net effect f all the lss mechansms n the electrlyss stack ncludng, hmc lsses, actvatn and cncentratn verptentals, etc. The bttm curves shw the effect f peratng vltage and AS n the current densty. Ntng that: V p V AS, (5) N AS =.5 Ohm cm Ohm cm Ohm cm 85 C Operatng Vltage f a target current densty (and crrespndng hydrgen prductn rate) s selected, lwer AS values allw fr stack peratn at lwer vltages and crrespndngly hgher effcences. Smlarly, n the fuel-cell mde, there s a tradeff between effcency and maxmum pwer prductn. Maxmum pwer prductn fr sld-xde fuel cells ccurs fr peratn at arund.5 V, whereas maxmum effcency ccurs at the pen-cell ptental, arund. V fr hydrgendmnated SOFC fuel cell nlet gas cmpstns. Dependng n cell perfrmance and ptmzatn parameters, a gd peratng pnt usually ccurs at arund.7 V n the fuel-cell mde f peratn. In the electrlyss mde, a gd tradeff between effcency and hydrgen prductn rate wll ccur at peratng vltages belw /F, arund. V. The challenge s t develp SOEC stacks wth lw AS such that a reasnable current densty wll be achevable at lwer peratng vltages. Lw peratng vltages can als be mantaned at a specfed current densty f the mean Nernst ptental, V, s Nernst lw. The mean Nernst ptental can be reduced by ncreasng the cell peratng temperature, ncreasng the steam cntent and flw rate n the feed stream, r by decreasng the xygen cntent n the sweep gas sde (ande) f the electrlyss cell. Of curse, as the cell current densty and hydrgen prductn rate s ncreased, the average steam cntent n the cathde sde decreases and the average xygen cntent n the ande sde V tn Fgure 9. Effect f peratng vltage and area-specfc resstance n electrlyss effcency. 7

9 ncreases. These cnsderatns ndcate that, fr maxmum cell effcency at a specfed current densty, steam utlzatn shuld be kept lw and a hgh flw rate f a nn-xygencntanng sweep gas shuld be used. Unfrtunately, results f large-scale system analyses [] shw that peratng wth lw steam utlzatn results n lw verall hydrgen prductn system effcences. Fr the system, the thermdynamc beneft f excess steam (lwer average Nernst ptental) s utweghed by the penaltes asscated wth handlng f the excess steam and ncmplete heat recuperatn. Smlar cnclusns were drawn when cnsderng the use f a nn-xygen-cntanng sweep gas (e.g., steam) n the xygen sde. Agan, the thermdynamc benefts were utweghed by system cnsderatns. In fact, the hghest verall effcences fr pressurzed electrlyzers were acheved wth n sweep gas, where the xygen s allwed t evlve frm the cells undluted. ISOTEMAL VS. NON-ISOTEMAL OPEATION The analyses presented s far have all assumed sthermal electrlyss peratn such that the utlet temperature f the prducts s the same as the nlet temperature f the reactants. Fr peratng vltages between the pen-cell ptental and thermal neutral, sthermal peratn requres heat addtn durng the electrlyss prcess. Fr peratng vltages abve thermal neutral, heat rejectn s requred t mantan sthermal peratn. The enthalpy change fr the electrlyss prcess under sthermal cndtns s, by defntn, the enthalpy f reactn,. The enthalpy f reactn fr steam reductn s a weak functn f temperature, wth a numercal value very clse t the lw heatng value f hydrgen ver a wde range f temperatures, as shwn n Fg. 6. The magntude f the heat transfer requred t acheve sthermal peratn, Q T (T ), can be calculated drectly frm the fllwng frm f the frst law: Q ( T ) IV (6) T ( T ) N and snce the hydrgen prductn rate, N s equal t I/F, and the thermal neutral vltage, V tn = (T)/F, Q T ) I( V V ) (7) T ( tn p Nte that ths result predcts pstve heat transfer t the electrlyzer fr peratng vltages less than thermal neutral and negatve heat transfer (.e., heat rejectn frm the electrlyzer) fr peratng vltages greater than thermal neutral. Snce there s n sensble enthalpy change, ths result s vald fr all sthermal cases, even f excess reactants and/r nert gases are present. A graphcal nterpretatn f the sthermal heat requrement n V- crdnates s shwn n Fg.. The fgure shws the heat fluxes requred t mantan sthermal peratn fr a target current densty f.3 A/cm fr tw values f AS:.5 and.5 Ohm cm represented by the area enclsed between the vertcal lne at V = V tn, the vertcal lne V = V p (V p = p current densty (A/cm ) AS =.5 Ohm cm AS =.5 Ohm cm q" T = (V tn - V p ) OCV.3 V fr AS =.5 Ohm cm ; V p =.43 V fr AS =.5 Ohm cm ), and the hrzntal lnes at = and at =.3 A/cm. Nte that the hgher AS case requres an peratng vltage that s abve V tn n rder t acheve the target current densty f.3 A/cm. Cnsequently, the asscated sthermal heat transfer requrement s negatve, ndcatng that heat rejectn s needed t mantan sthermal peratn at that cndtn. Eqn. (7) can als be used t shw that the maxmum sthermal heat addtn peratng pnt crrespnds t an peratng vltage equal t the average f the pen-cell ptental and the thermal neutral vltage. Accrdngly, the maxmum sthermal heat addtn s gven by: V max ( ) tn V Q T I N (8) where V N s the pen-cell ptental. The ttal stack current, I, at any peratng vltage s dependent n the stack AS value, whch s typcally temperature-dependent. Actual hgh-temperature electrlyss prcesses wll generally nt perate sthermally unless the peratng vltage s very clse t the thermal neutral vltage. Fr nn-sthermal cases, the frst law fr electrlyss prcess must be wrtten as: Q W N [ ( T ) ] P f V p < V tn q T > P N [ ( T ) ] (9) In ths frm, all reactng and nn-reactng speces ncluded n the nlet and utlet streams can be accunted fr, ncludng nert gases, nlet hydrgen (ntrduced t mantan reducng cndtns n the steam/hydrgen electrde), and any excess unreacted steam. In general, determnatn f the utlet temperature frm Eqn. (9) s an teratve prcess []. The heat transferred durng the prcess must frst be specfed (e.g., zer fr the adabatc case). The temperature-dependent enthalpy values f all speces must be taken nt accunt. The f 85 C Operatng Vltage V tn =.3 A/cm V p > V tn q T < Fgure. Graphcal nterpretatn f sthermal heat requrements fr tw values f AS. 8

10 AS =.5 Ohm cm AS =. Ohm cm AS =. Ohm cm 5 AS =.5 Ohm cm AS =. Ohm cm AS =. Ohm cm q" net (W/cm ). -. T (K) V p V p (a) (b) Fgure. (a) eat flux requred fr sthermal peratn; (b) Outlet temperature fr adabatc peratn; steamhydrgen nlet flw rate:.85 gm/mn/cm, y =., sweep ar nlet flw rate:.56 gm/mn/cm, T n = 73 K. slutn prcedure begns wth specfcatn f the cathdesde nlet flw rates f steam, hydrgen, and any nert carrer gas such as ntrgen (f applcable). The nlet flw rate f the sweep gas (e.g., ar r steam) n the ande sde must als be specfed. Specfcatn f these flw rates allws fr the determnatn f the nlet mle fractns f steam, hydrgen, and xygen that appear n the Nernst equatn. The steam mle fractn s expressed n terms f the hydrgen mle fractn as -y -y N. The desred current densty and actve cell area are then specfed, yeldng the ttal peratng current. The crrespndng hydrgen prductn rate s btaned frm Faraday s law. Once the per-cell hydrgen prductn rate s knwn, the utlet flw rates f hydrgen and steam n the cathde sde and xygen n the ande sde can be determned. The flw rates f any nert gases, the ande-sde sweep gas, and any excess steam r hydrgen are the same at the nlet and the utlet. Once all these flw rates are knwn, the summatns n Eqn. (9) can be evaluated. The prduct summatn must be evaluated ntally at a guessed value f the prduct temperature, T P. The peratng vltage crrespndng t the specfed current densty s btaned frm Eqn. (5), where the stack area-specfc resstance, AS, must be estmated and specfed as a functn f temperature. T accunt fr the varatn n temperature and cmpstn acrss an peratng cell, the mean Nernst ptental can be btaned frm an ntegrated versn f the Nernst equatn: TP V N F( T P T )( y y )( y y, O, A, O, A,, C,, C y y N G ( T ) ut ln / T y y y yo y, O, A, O, A y,, C,, C dy ) dy O dt (3) where y, O, A s the ande-sde nlet mle fractn f xygen, etc. Nte that the upper lmt f ntegratn n the temperature ntegral s ntally unknwn. Once the AS and the mean Nernst ptental are knwn, the peratng vltage s btaned frm Eqn. (5) and the electrcal wrk term n Eqn. (9) s btaned frm W VpI. An algrthm then must be develped t teratvely slve fr the prduct temperature, T P, n rder t satsfy Eqn. (9). esults f sample parametrc calculatns based n ths prcedure are presented n Fg.. The nlet mass flw rates f steam-hydrgen and sweep ar per cm f actve cell area are ndcated n the captn. The calculatns were perfrmed fr an nlet hydrgen mle fractn f. and an nlet temperature f 8 C (73 K). Fg. (a) shws the heat flux requred t mantan sthermal peratn as a functn f per-cell peratng vltage fr three dfferent AS values. Ths heat flux s pstve (heat addtn requred) fr vltages between pencell and thermal neutral and negatve fr hgher peratng vltages. The peak heat flux requrement ccurs halfway between the pen-cell ptental and the thermal neutral vltage. The magntude f the peak heat flux s hghest fr the lwest AS value snce the current densty (and hydrgen prductn rate) crrespndng t each vltage value s hghest fr the lwest AS value. Fg. (b) shws the mean utlet gas temperature as a functn f per-cell peratng vltage fr adabatc peratn fr three dfferent AS values. Fr adabatc cndtns, utlet temperatures are lwer than nlet temperatures fr vltages between pen-cell and thermal neutral. Fr hgher vltages, utlet temperatures ncrease rapdly wth vltage. Agan, the lw-as case exhbts the largest effect due t ts hgher current densty at each peratng vltage. Actual electrlyzers wll generally perate at cndtns that are nether sthermal, nr adabatc. These tw cases represent lmts. Fr ptmal perfrmance, sthermal peratn at an peratng vltage belw thermal neutral s 9

11 desrable. In ths case, sme f the electrlyss energy s ndeed suppled n the frm f heat. One way t supply the requred heat drectly t the stack s thrugh the use f a heated sweep gas. T,P =T,e DIFFEENT EAT ADDITION TEMPEATUES FO TE POWE CYCLE AND TE ELECTOLYZE Snce the prmary energy nput t a hgh-temperature electrlyzer s electrcal wrk, the electrlyzer des nt necessarly have t be drectly cupled t the same heat surce used fr the pwer cycle. If we wsh t fcus n watersplttng by electrlyss, and we are nterested n determnng the verall thermal-t-hydrgen effcency lmts fr a wde range f cases, we can start by drawng a cntrl vlume arund the cmbnatn f the pwer cycle and the electrlyzer, as shwn n Fg.. The fgure als shws tw ndvdual cntrl vlumes, CV and CV arund the pwer cycle and the electrlyzer, respectvely. Accrdng t the schematc, we are allwng fr the pssblty that the heat addtn temperature fr the pwer cycle may be dfferent than the heat addtn temperature fr the electrlyzer. Nte that the wrk prduced by the pwer cycle s fed drectly t the electrlyzer and that n wrk crsses the cmbned cntrl-vlume bundary (CV+CV). Applyng the verall thermal-t-hydrgen effcency defntn t the cmbned cntrl vlume, (3) QTt Q, P Q, e And ntng that fr the deal case, Q we btan: W net, P ; Q, e T, es( T, e) th the (3) (33) T, es( T, e) th e If the ntal and fnal temperature and pressure are desgnated t be equal t the standard-state reference values, T=T, P= P, the enthalpy change f the electrlyss reactn s the same as the heatng value f the hydrgen prduced. Snce the feedstream at T and P wuld be n the lqud phase, the prcess effcency shuld be defned n terms f the hgh heatng value, V. But the lw heatng value, LV, culd als be used. Usng the hgh heatng value, V (34) V T, es ( T, e) th, P e T,P =35C,T,e varable T(C) Fgure 3. Ideal thermal-t-hydrgen effcences fr varable and fxed values f T,P. OatT,P T, P Q,P W e T, e Q,e at T, P Separate cnsderatn f the Frst Law and Secnd Law t CV and CV yelds the maxmum pssble thermal effcency f the pwer cycle (.e., Carnt) and the maxmum pssble electrlyss effcency: T L th, P, max ; T, P CV Q L,P T Q L,e / O at T, P CV Fgure. Schematc fr determnatn f verall thermalt-hydrgen effcency fr an electrlyss prcess. V e, max (35) V S T ) ( T T ) T S ( T ) (, e, e where S ( T ) s the entrpy change fr the electrlyss reactn evaluated at T and S ( T L ) s the entrpy change fr the reactn evaluated at T L. It shuld be nted that the L L L

12 electrlyss effcency, e reactants and prducts at T, P, based n V reactants and prducts at T, P, based n (T) T (K) Fgure 4. Maxmum pssble electrlyss effcences pltted as a functn f the heat surce temperature, T,e. deal verall thermal-t-hydrgen effcency, T, predcted by Eqns. (34) and (35) yelds the same values as thse predcted by Eqn. (8), shwn n Fg. 3, f the heat addtn temperatures fr the pwer cycle, T,P, and the electrlyss prcess, T,e, are equal. Eqns. (8) and (34) can be shwn t be equvalent algebracally as well, agan fr the case f T =T,P = T,e. Ths maxmum pssble water splttng effcency s reprduced n Fg. 3, fr the case f varable T,P = T,e. If we are nterested n the case f T,P < T,e, such as the case n whch the hghtemperature electrlyss prcess s drven by a cnventnal pwer cycle (e.g., a PW drvng a rankne cycle) that has a lwer temperature f heat addtn than the electrlyss peratng temperature, then Eqn. (34) can stll be used t evaluate the deal verall thermal-t-hydrgen effcency. Fr example, f we let T, P = 35ºC, and allw T, e t be a varable, Eqn. () yelds the secnd result shwn n Fg. 3. Ths effcency curve has a much shallwer slpe, mplyng that the ptental gans t be realzed frm hgh-temperature electrlyss are mdest, f the pwer-cycle heat addtn temperature (and thermal effcency) s fxed. Nte that the lw-temperature end f ths curve crrespnds t the effcency lmt fr cnventnal lw-temperature electrlyss wth a 35ºC temperature f heat addtn fr the pwer cycle. Actual lw-temperature electrlyss verall effcency values are typcally arund 35%, whch s clse t 65% f the lwtemperature thermdynamc lmt shwn n the fgure. A plt f the thermdynamc lmts fr electrlyss effcency, e, gven by Eqn. (35), fr T L =T, P=P, s presented n the tp curve f Fg. 4 as a functn f the heat surce temperature, T,e. Ths fgure als shws the electrlyss effcency lmt gven by Eqn. (4), whch crrespnds t T=T,e, P= P and s based n the enthalpy f reactn at the electrlyss temperature,. Agan, these lmts can nly be apprached when peratng near the Nernst ptental, wth crrespndngly lw current denstes. But the curves d llustrate the ptental advantage f hgh temperature peratn. Nte that these electrlyss effcency curves have a steeper slpe wth respect t temperature than the verall thermal-t-hydrgen effcency curve shwn n Fg. 3 fr the case f a fxed pwer-surce heat-addtn temperature. Ths s because the electrlyss effcency smply quantfes the hydrgen generatn rate per unt f electrcal pwer cnsumed. It des nt accunt fr any addtnal net heat requrement (a large percentage f the requred heatng can be recuperated) that mght be asscated wth bstng the steam up t the fnal electrlyss temperature. Fr example, f the fnal temperature bst s acheved thrugh electrcal resstance heatng, the pwer cnsumed n the heater wuld have t be taken nt accunt n evaluatng the verall pwer-t-hydrgen effcency. We can als derve an expressn fr the verall hydrgen prductn effcency as a functn f the peratng vltage fr an electrlyss prcess. Fr ths case, cnsder cntrl vlume CV f Fg. and let W e =VI. Fr a cntrl vlume drawn arund the electrlyss stack, wth nlet and utlet streams at T, P, drect applcatn f the frst law and the defntn f the verall thermal-t-hydrgen effcency yelds: FVp(/ th ) (36) Nte that at V p = V tn, ths result yelds T = P. S peratn at the thermal neutral vltage yelds the same verall hydrgen prductn effcency as that f the pwer cycle. Lettng V p = V, Eqn. (36) yelds, V th G ( ) th th (37) whch s the verall effcency crrespndng t peratn at the reference ptental, V. Ths effcency s always hgher than the pwer-prductn thermal effcency. The pen-cell ptental crrespndng t the electrlyzer peratng cndtns, ncludng temperature and gas partal pressures, s gven by the Nernst equatn, Eqn (4). Fr a specfed temperature, the pen-cell ptental s lwer than V fr hgh steam mle fractn, lw hydrgen mle fractn, lw xygen mle fractn, and lw peratng pressure. Fr electrlyss, t s desrable t have as lw an pen-cell ptental as pssble, snce the peratng cell current densty s prprtnal t the dfference between the peratng vltage and the pen-cell vltage. If the pen-cell vltage s lw, a reasnable current densty can be acheved wth a lw peratng vltage, and therefre wth hgh effcency, accrdng t Eqn. (36). The effect f peratng ptental n verall thermal-t-hydrgen effcency s llustrated n Fg. 5. Ths fgure shws a seres f verall effcency curves, ver a range f assumed pwerprductn effcency values fr an electrlyss temperature f 8ºC. Nte that peratng at any vltage lwer than thermal neutral yelds a hydrgen-prductn effcency that s greater than the pwer-cycle thermal effcency. On the steam/hydrgen sde f the electrlyss cell, the use f hgh nlet steam mle fractn and a hgh ttal steam flw rate s desrable, subject t the cnstrant that a hydrgen cntent f 5

13 V th = T e = 8 C V p Fgure 5. Overall hydrgen prductn effcences as a functn f pwer-prductn thermal effcency and electrlyzer per-cell peratng vltage. % must be used n rder t mantan reducng cndtns n the steam/hydrgen electrde. On the xygen sde, a lw average xygen mle fractn s desrable. Therefre, a nnxygen-cntanng sweep gas shuld be used wth a hgh flw rate. As dscussed, prevusly, hwever, these thermdynamc effects can be utweghed by ther system cnsderatns such as ncmplete heat recuperatn, handlng f excess nnreacted steam, cmpressn wrk fr sweep gases, etc., when perfrmng detaled system analyses wth realstc cmpnent effcences and heat exchanger characterstcs. As an example TE peratng cndtn, assume T = 8ºC, P = atm, y O =.95, y =.5, y O =.5, AS =.5 Ohm cm, and th =.45. Under these cndtns, the Nernst ptental s.77 V. If we wsh t acheve a current densty f.5 A/cm, the requred peratng vltage wuld be.897 V, yeldng a hydrgen prductn effcency f.54 fr the assumed pwer-prductn effcency f.45. S, wth favrable peratng cndtns, hgh-temperature electrlyss can yeld verall hydrgen-prductn effcences that are hgher than the pwer-cycle thermal effcency. Furthermre, f the electrlyss prcess s pwered by a hgh-effcency advanced reactr/pwer cycle, verall thermal-t-hydrgen effcences greater than 5% can be acheved. Cnventnal lw-temperature electrlyss wuld crrespnd t a pwer-cycle effcency arund 35% and, due t lwer pen-cell ptentals and hgher verptentals, a per-cell peratng vltage n the.6.7 range, yeldng verall thermal-t-hydrgen-prductn effcences f less than 35%. CONCLUSIONS Thermdynamc perfrmance lmts fr thermal water splttng prcesses have been presented. Thermchemcal and electrlytc prcesses can bth be ncluded n ths categry f the electrcal pwer requred fr electrlyss s based n sme V tn knd f heat engne, such as a gas turbne cupled t a hghtemperature reactr. General perfrmance predctns based n smple thermdynamc analyses are cnsstent wth results btaned wth detaled system analyses. The unque thermal characterstcs f hgh-temperature electrlyss prcesses were dscussed, ncludng the sgnfcance f the thermal neutral vltage and ts relatnshp t the endthermc reactn heat requrement, the electrlyss effcency, and the sthermal net heat requrement. The effect f area-specfc resstance (AS) and peratng vltage n electrlyzer effcency was dscussed. Lw AS values allw fr lw peratng vltages and crrespndngly hgh effcences, whle stll achevng reasnable current denstes. Analyss f nn-sthermal peratn s utlned, alng wth results f parametrc studes. Cnsderatn f verall hydrgen prductn effcences fr cases wth dfferent heat addtn temperatures fr the pwer cycle and the electrlyzer shws that the ptental gans t be realzed frm hgh-temperature electrlyss are mdest, f the pwer-cycle heat addtn temperature (and thermal effcency) s fxed. ACKNOWLEDGMENTS Ths wrk was supprted by the Idah Natnal Labratry, Labratry Drected esearch and Develpment prgram and by the U.S. Department f Energy, Offce f Nuclear Energy, Nuclear ydrgen Intatve Prgram. COPYIGT STATEMENT Ths manuscrpt has been authred by Battelle Energy Allance, LLC under Cntract N. DE-AC7-5ID457 wth the U.S. Department f Energy. The Unted States Gvernment retans and the publsher, by acceptng the artcle fr publcatn, acknwledges that the Unted States Gvernment retans a nnexclusve, pad-up, rrevcable, wrld-wde lcense t publsh r reprduce the publshed frm f ths manuscrpt, r allw thers t d s, fr Unted States Gvernment purpses. EFEENCES. Lews, D., ydrgen and ts relatnshp wth nuclear energy, Prgress n Nuclear Energy, Vl. 5, pp, 394-4, 8.. Frsberg, C. W., Nuclear ydrgen Prductn fr Lqud ydrcarbn Transprt Fuels, Prceedngs, AIChE Annual Mtg., pp , r, M., Nuclear Energy fr Transprtatn: Paths thrugh Electrcty, ydrgen, and Lqud Fuels, Prgress n Nuclear Energy, Vl. 5, pp. 4-46, Sctt, D. S., Smellng Land, The ydrgen Defense aganst Clmate Catastrphe, Canadan ydrgen Asscatn, Brwn, L. C., Lentsch,. D., Besenbruch, G. E., Schultz, K.., Alternatve Flwsheets fr the Sulfur-Idne Thermchemcal ydrgen Cycle, AIChE Jurnal, Aprl 3.

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