Comparison Of A One- Dimensional Model Of A High-Temperature Solid- Oxide Electrolysis Stack With CFD And Experimental Results

Transcription

1 INL/EXT EINT Cmparsn Of A One- Dmensnal Mdel Of A Hgh-Temperature Sld- Oxde Electrlyss Stack Wth CFD And Expermental esults 005 ASME Internatnal Mechancal Engneerng Cngress And Expstn J. E. O Bren C. M. Stts G. L. Hawkes Nvember 005 Ths s a preprnt f a paper ntended fr publcatn n a jurnal r prceedngs. Snce changes may nt 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 rceedngs f IMECE ASME Internatnal Mechancal Engneerng Cngress and Expstn Nvember 5-11, 005, Orland, Flrda USA IMECE Cmparsn f a One-Dmensnal Mdel f a Hgh-Temperature Sld-Oxde Electrlyss Stack wth CFD and Expermental esults J. E. O Bren, C. M. Stts, and G. L. Hawkes Idah Natnal Labratry Idah Falls, ID 83415, USA; james.bren@nl.gv ABSTACT A ne-dmensnal mdel has been develped t predct the thermal and electrchemcal behavr f a hgh-temperature steam electrlyss stack. Ths electrlyzer mdel allws fr the determnatn f the average Nernst ptental, cell peratng vltage, gas utlet temperatures, and electrlyzer effcency fr any specfed nlet gas flw rates, current densty, cell actve area, and external heat lss r gan. The mdel ncludes a temperature-dependent area-specfc resstance (AS) that accunts fr the sgnfcant ncrease n electrlyte nc cnductvty that ccurs wth ncreasng temperature. Mdel predctns are shwn t cmpare favrably wth results btaned frm a fully 3-D cmputatnal flud dynamcs mdel. The ne-dmensnal mdel was als emplyed t demnstrate the expected trends n electrlyzer perfrmance ver a range f peratng cndtns ncludng sthermal, adabatc, cnstant steam utlzatn, cnstant flw rate, and the effects f peratng temperature. INTODUCTION A research prgram s under way at the Idah Natnal Labratry t assess the perfrmance f sld-xde cells peratng n the steam electrlyss mde fr hydrgen prductn ver a temperature range f t 900ºC. The research prgram ncludes bth expermental and mdelng actvtes. Expermental actvtes, ncludng bth sngle buttn-cell testng and stack testng have been dcumented n several recent publcatns [e.g., 1-3]. The mdelng actvtes nclude detaled cmputatnal flud dynamcs (CFD) smulatns [4] and system-level mdelng. In rder t evaluate the ptental hydrgen-prductn perfrmance f large-scale hgh-temperature electrlyss (HTE) peratns, we have develped an engneerng prcess mdel at INL usng the cmmercal system-analyss cde HYSYS. Usng ths cde, several detaled prcess flw sheets have been defned that nclude all f the cmpnents that wuld be present n an actual HTE plant such as pumps, cmpressrs, heat exchangers, turbnes, and the electrlyzer. Snce the electrlyzer s nt a standard HYSYS cmpnent, a custm ne-dmensnal electrlyzer mdel was develped fr ncrpratn nt the verall prcess flw sheet. Ths electrlyzer mdel allws fr the determnatn f the average Nernst ptental, cell peratng vltage, gas utlet temperatures, and electrlyzer effcency fr any specfed nlet steam, hydrgen, and sweep-gas flw rates, current densty, cell actve area, and external heat lss r gan. The ne-dmensnal electrlyzer mdel was valdated by cmparsn wth results btaned frm a fully 3-D cmputatnal flud dynamcs mdel and by cmparsn wth expermental results. Ths paper prvdes detals n the ne-dmensnal electrlyzer mdel, cmparsns t CFD and expermental results, and electrlyzer perfrmance predctns based n the ne-dmensnal mdel ver a range f peratng cndtns. NOMENCLATUE A cell per-cell actve area, cm AS area-specfc resstance, Ohm cm F Faraday number, J/V ml G (T ) Gbbs energy f reactn, J/ml H( T ) H sensble enthalpy, J/ml H f enthalpy f frmatn, J/ml current densty, A/cm current, A LHV lw heatng value f hydrgen, J/ml N mlar flw rate, ml/s N cells ttal number f electrlyss cells Q heat transfer rate t electrlyzer, W unversal gas cnstant, J/ml K T temperature, K V vltage, V W electrcal wrk perfrmed n electrlyzer, W y mle fractn verall thermal-t-hydrgen effcency H 1

3 ONE-DIMENSIONAL ELECTOLYZE MODEL In general, fr an peratng electrlyss stack, there wll be a temperature change asscated wth the electrlyss prcess. Fr these cases, the energy equatn fr electrlyss prcess can be wrtten as: Q W N [ H H ( T ) H ] f N [ H H ( T ) H ] (1) where Q s the external heat transfer rate t r frm the electrlyzer, W s the rate f electrcal wrk suppled t the electrlyzer, N s the mlar flw rate f each reactant r prduct, H f s the standard-state enthalpy f frmatn f each reactant r prduct and H( T ) H s the sensble enthalpy fr each reactant r prduct. Applyng the energy equatn n 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. (1) 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 avalable frm curve fts r sme ther data base. The slutn prcedure begns wth specfcatn f the cathde-sde 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 the gas 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 1-y H -y N. The current densty and actve cell area are then specfed, yeldng the ttal peratng current. Care must be taken t nsure that the specfed nlet gas flw rates and ttal cell current are cmpatble. The mnmum requred nlet steam mlar flw rate s the same as the steam cnsumptn rate, gven by: N, H O,mn I Acell N H O N cells N cells N () H F F whch s f curse als equal t the hydrgen prductn rate. Once the ttal and per-cell hydrgen prductn rates are 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. (1) can be evaluated. The prduct summatn must be evaluated ntally at a guessed value f the prduct temperature, T. The peratng vltage crrespndng t the specfed current densty s btaned frm: V p f V AS(T) (3) Nernst where the stack area-specfc resstance, AS(T), must be estmated and specfed as a functn f temperature. The cellmean Nernst ptental can then be btaned frm an ntegrated Nernst equatn: V Nernst F( T T )( y 1 y )( y y, O, A, O, A, H, C, H, C T y, O, A y, H, C 1 y H y N G( T ) T ln dy 1/ T y O A y H C yh y,,,, O H ) dy O dt (4) 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, T, s ntally unknwn. Once the AS and the mean Nernst ptental are knwn, the peratng vltage s btaned frm Eqn. (3) and the electrcal wrk term n Eqn. (1) s btaned frm W VpI. An algrthm then must be develped t teratvely slve fr the prduct temperature, T, n rder t satsfy Eqn. (1). Ths algrthm can then be mbedded n a lp s that a full numercal sweep can be perfrmed. We have mplemented ths prcedure n MathCad. The MathCad mdel prvdes accurate estmates f electrlyzer peratng vltage (and crrespndng electrlyzer effcency) and utlet temperatures, fr any specfed electrlyzer heat lss r gan, gas flw rates, current densty, and per-cell AS(T). Ths electrlyzer mdel was develped fr ncrpratn nt system-level electrlyss plant mdels beng develped usng HYSYS system smulatn sftware. Wth a realstc electrlyzer mdel ncrprated nt the verall HYSYS plant mdel, gd estmates f verall hydrgen-prductn effcences can be btaned ver a wde range f prspectve peratng cndtns. redctns btaned frm the 1-D ntegral mdel have been cmpared t results btaned frm a fully 3-D FLUENT smulatn. Cmplete detals f the FLUENT electrlyss stack mdel are prvded n [4]. A cndensed descrptn s presented here. The numercal mdel develped fr ths paper was based n the gemetry f a sngle sld-xde electrlyss cell (SOEC) taken frm a planar stack descrbed n detal n [1, ]. The numercal dman extends frm the center plane f ne separatr plate t the center plane f the next separatr plate. Symmetry bundares are appled at the tp and bttm f the mdel. Three representatns f the numercal mdel are presented n Fg. 1. In the tp left prtn f ths fgure, the full mdel s shwn t scale. Snce the mdel ncludes nly ne cell, the mdel gemetry s qute thn n the vertcal (z) drectn. T shw mre detal, the mdel s shwn n the bttm left prtn f Fg. 1 wth a vertcal exaggeratn f 10 n the z-drectn. An explded vew wth the 10 vertcal exaggeratn s shwn n the rght half f the fgure. In the explded vew, the bttm element s the bttm separatr plate. Snce we are tryng t represent a unt cell extracted frm a larger stack, the bttm and tp separatr plates n the numercal mdel are nly half as thck (.e., 0.19 mm) as the hardware separatr plates. Therefre, the tp and bttm bundares f the numercal mdel represent symmetry planes and the bundary cndtns n thse faces are set accrdngly. The edge rals are shwn attached t the bttm separatr plate. In the stack hardware, the edge rals are

4 Fgure 1. Fluent sngle-cell SOEC mdel. fabrcated frm the same materal as the separatr plates, but they are separate peces. The next element n the numercal mdel s the steam/hydrgen flw channel. The flw channels are the regns n the stack between the separatr plate, the edge rals and the electrdes n whch the crrugated/perfrated flw felds are lcated. In the FLUENT mdel, the steam/hydrgen flw channel has been specfed as a hgh-prsty prusmeda regn wth metallc nckel as the sld materal and wth anstrpc permeablty, much hgher n the prmary flw drectn than n the crss flw drectns. The heght f the flw channel s set by the thckness f the edge rals, mm. The next three layers n the numercal mdel are asscated wth the electrlyte/electrde assembly, as shwn n the rght half f Fg. 1. The FLUENT sld-xde fuel cell (SOFC) mdule treats the electrlyte as a -D planar element wth the prpertes f yttra-stablzed zrcna (YSZ). Therefre the electrlyte n the mdel has gemetrcal thckness f zer. On ether sde f the electrlyte are the electrdes whch are created wth 3-D elements. Therefre, the electrlyte/electrde assembly n the mdel s nly as thck as the tw electrdes. Arund the uter perphery f the electrlyte/electrde assembly, we have ncluded an nsulatr wth the prpertes f YSZ. The nsulatr prevents an electrcal shrt crcut between the tp and bttm edge rals. N nc transprt ccurs thrugh ths nsulatr. The next element n the numercal mdel s the ar/xygen flw channel. It has als been specfed as a hgh-prsty prus meda regn wth ferrtc stanless steel as the sld materal and wth the same anstrpc permeabltes and flw channel heght used n the steam/hydrgen flw channel. The tp separatr plate and edge rals are dentcal t thse n the bttm, but the edge rals are rented perpendcular t the bttm edge rals t allw fr the crss-flw arrangement. The bttm separatr plate n the FLUENT mdel serves as the electrcal grund and the tp separatr plate serves as the current surce. Addtnal parameters specfed n the numercal mdel nclude the electrde exchange current denstes and several gap electrcal cntact resstances. These quanttes were determned emprcally by cmparng FLUENT predctns wth stack perfrmance data. The FLUENT mdel uses the electrde exchange current denstes t quantfy the magntude f the actvatn verptentals va a Butler-Vlmer equatn [5]. The gas flw nlets are specfed n the FLUENT mdel as mass-flw nlets, wth the gas nlet temperatures are set at 1103 K and the nlet gas cmpstn determned by specfcatn f the mass fractn f each cmpnent. The gas flw rates used n the mdel were the same as thse used fr the expermental base case, n a per-cell bass. Fr example, the base case fr the steam/hydrgen nlet used a ttal nlet mass flw rate f kg/s, wth ntrgen, hydrgen and steam mass fractns f 1, , and 0.483, respectvely. The base case ar flw rate was kg/s. Detals f the cre mass, mmentum, energy, and speces cnservatn and transprt features f FLUENT are dcumented n detal n the FLUENT user manual (FLUENT, 004). An SOFC mdel adds the electrchemcal reactns, lss mechansms, electrc feld cmputatn, and electrde prus meda cnsttutve relatns (rnkey et al., 004). Ths reference als dcuments the treatment f speces and energy surces and snks arsng frm the electrchemstry at the electrde-electrlyte nterfaces. The FLUENT SOFC userdefned subrutne was mdfed fr ur HTE wrk t allw fr peratn n the SOEC mde. Mdel results prvde detaled prfles f temperature, Nernst ptental, peratng ptental, ande-sde gas cmpstn, cathde-sde gas cmpstn, current densty and hydrgen prductn ver a range f stack peratng cndtns. 3

5 D Integral Mdel D Integral Mdel H utlet, 3-D FLUENT Mdel O utlet, 3-D FLUENT Mdel Operatng Vltage, V nlet N flw (per-cell): 0 sccm 0.9 nlet dewpt: 8.9 C ar sweep rate (per-cell): 371 sccm Current Densty, A/cm 3-D FLUENT Mdel nlet gas temps: C nlet H flw (per-cell): 41.1 sccm Outlet Temperature, C nlet gas temps: C 1050 nlet H flw (per-cell): 41.1 sccm nlet N flw (per-cell): 0 sccm nlet dewpt: 8.9 C ar sweep rate (per-cell): 371 sccm Operatng Vltage, V Fgure. redcted peratng vltage and gas utlet temperatures fr adabatc electrlyzer peratn; cmparsn f 1-D ntegral MathCad mdel wth full 3-D FLUENT smulatn. epresentatve results btaned frm the ntegral electrlyzer mdel fr an adabatc case are presented n Fg., alng wth results btaned frm FLUENT. Fg. shws predcted vltage-current characterstcs and predcted gas utlet temperatures. The 1-D ntegral mdel predcts smewhat hgher peratng vltages cmpared t the FLUENT results. Ths makes the 1-D mdel cnservatve snce hgher peratng vltages crrespnd t lwer electrlyss effcences. The dsparty can be explaned by ntng that the CFD mdel can mre accurately accunt fr the varatn n lcal Nernst ptental and lcal current densty asscated wth the crssflw gemetry f the planar stack. Nte that, fr an peratng vltage near the thermal mnmum (~1.06 V), bth mdels predct utlet temperatures fr ths partcular adabatc case that are abut 30ºC lwer than the nlet temperatures. Ths temperature depressn s due t the fact that the endthermc heat requrement f the steam dsscatn reactn s larger than the hmc heatng n the peratng vltage range between pen-cell ptental and the thermal-neutral vltage. er-cell gas flw rates fr ths case were based n the flw rates used n recent planar HTE stack tests [1, ]. The 1-D mdel als predcts the crrect value f the thermal neutral vltage fr ºC, 1.87 V. At ths peratng vltage, the utlet temperatures are equal t the nlet temperatures under adabatc cndtns. The 1-D mdel s als useful fr assessng the effect f usng a steam sweep rather than an ar sweep n the xygen sde. Use f a sweep gas that des nt cntan xygen s advantageus because t reduces the Nernst ptental, thereby ncreasng the electrlyss effcency fr a specfed current densty. We are cnsderng the use f steam fr the sweep gas snce t wuld be relatvely easy t separate the steam frm the prduced xygen by cndensatn. The prduced xygen then culd be sld as a cmmdty. Incrpratn f the 1-D mdel nt ur HYSYS system smulatn wll enable a brad range f parametrc studes. esults btaned frm FLUENT were als cmpared t expermental results. Detals f recent SOEC stack testng actvtes are presented n references [1, ]. Only ne set f representatve results are shwn here n Fg. 3. Ths fgure shws expermentally measured vltage-current characterstcs and nternal stack temperatures btaned durng a DC ptental sweep, alng wth FLUENT predctns. The FLUENT mdel ncluded emprcal values fr nternal stack cntact resstances, scaled t match the measured vltage-current values f sweep 4 f Fg. 3 (a). Crrespndng nternal stack temperatures are shwn n Fg. 3 (b). The expermental nternal stack temperatures were btaned frm fur mnature (ncnelsheathed, nch (50 µm) OD, mneral-nsulated, ungrunded, type-k) thermcuples that were nserted nt selected ar-flw channels. The cmparsn between the expermentally btaned stack nternal temperatures and the FLUENT mean electrlyte temperature s nt perfect, prmarly due t the fact that the sweeps were perfrmed at a rate that was t fast t allw the stack t acheve thermal steady-state. Nevertheless, the trends are clearly shwn. Future stack test bjectves wll nclude btanng steady-state nternal stack temperature data. OVEALL OCESS THEMAL-TO-HYDOGEN EFFICIENCY In rder t assess the verall hydrgen prductn effcency f any large-scale water-splttng prcess, an apprprate prcess effcency must be defned that can be appled t a varety f prcesses. The feedstck fr any largescale HTE prcess wll be lqud water at ambent temperature and pressure, and the prducts wll be hydrgen and xygen, ultmately als at ambent temperature. The HTE prcess may ccur at elevated pressure, s the prducts may als be delvered at elevated pressure. In rder t maxmze the verall prcess effcency, t s essental t recuperate as much f the prcess heat as pssble. T cmpare the perfrmance f an HTE prcess t alternate hydrgen prductn technques, we have adpted a general effcency defntn that can be appled t any thermal water-splttng prcess, ncludng HTE, lw-temperature electrlyss (LTE), and thermchemcal prcesses. Snce the prmary energy nput t the thermchemcal prcesses s n the frm f heat, the apprprate general effcency defntn t be appled t all f the technques s the verall thermal-thydrgen effcency, H. Ths effcency s defned as the heatng value f the prduced hydrgen dvded by the ttal thermal nput requred t prduce t. Ether the lw heatng value, LHV, r the hgh heatng value, HHV, f the hydrgen can be used. Frm a prcess effcency vewpnt, snce the feedstck s lqud water, t makes sense t use the hgh heatng value. Frm a utlzatn vewpnt, dependng n the 4

6 stack peratng vltage, V theretcal pen-cell ptentals sweep # sccm N sccm H T (C) T (C) dp, f current densty, (A/cm ) (a) FLUENT redctn T (C) stack nternal 1 stack nternal 3 stack nternal 4 sccm H T (C) dp, stack nternal Stack peratng vltage (V) Fgure 3. Expermentally measured peratng vltages and gas utlet temperatures btaned durng DC ptental sweeps, wth cmparsns t FLUENT results. sweep # 4 sccm N (b) T f (C) ar nlet furnace FLUENT applcatn, t may make mre sense t use the lw heatng value. We wll use the lw-heatng-value defntn n ths paper: LHV H Q The denmnatr n ths effcency defntn quantfes all f the net thermal energy that s cnsumed n the prcess. Therefre, ths summatn ncludes any drect nuclear prcess heat as well as the thermal equvalent f any electrcal wrk delvered t the prcess such as electrlyzer pwer, pwer nput t cmpnents such as pumps, cmpressrs, etc. The thermal equvalent f any electrcal pwer cnsumed n the prcess s the pwer dvded by the thermal effcency f the pwer cycle. We are usng an assumed pwer-cycle thermal effcency f 45% fr the cmparsns made n ths paper. An advanced pwer cycle drven by a hgh-temperature nuclear reactr shuld easly be able t acheve ths thermal effcency value [6]. Fr an electrlyss prcess, the prmary cntrbutn t the summatn n the denmnatr f Eqn. (5) s the thermal equvalent f the electrcal energy nput t the electrlyzer. Fr a thermchemcal prcess, the prmary cntrbutn t the summatn n the denmnatr f Eqn. (5) s drect nuclear prcess heat. All ther drect thermal nputs are als ncluded. Drect thermal nputs nclude any net (nt recuperated) heat requred t heat the prcess streams up t the electrlyzer peratng temperature and any drect heatng f the electrlyzer tself requred fr sthermal peratn. The ne-dmensnal electrlyzer mdel ncludes tw nlet streams, ne fr steam/hydrgen n the cathde sde and the ther fr a sweep gas n the ande sde. ssble sweep cndtns cnsdered n ths study nclude ar sweep, steam sweep, and n sweep. Any value f drect electrlyzer heat addtn can als be nput t the mdel. The heat addtn cases f nterest are adabatc and sthermal. Zer heat addtn crrespnds t adabatc cases. Snce there s n sensble enthalpy change fr the sthermal case, the magntude f the (5) heat transfer requred t acheve sthermal peratn, Q (T ), can be calculated drectly frm the fllwng frm f the frst law: Q H ( T ) IV (6) ( T ) NH and snce the hydrgen prductn rate, N H s equal t I/F, and the thermal neutral vltage, V tn = H (T)/F, Q T ) I( V tn V ) (7) ( 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. The utlet streams leave the electrlyzer at a temperature that s dependent n the ttal flw rate, the amunt f heat addtn (e.g., sthermal r adabatc electrlyss) t the electrlyzer, and the peratng vltage (e.g., see Fg. ). The peratng vltage als has a sgnfcant effect n the electrlyss effcency. We can derve an expressn fr the hydrgen prductn effcency as a functn f the peratng vltage fr an electrlyss prcess. Fr a cntrl vlume drawn nly arund the electrlyss stack, wth W e =VI, nlet and utlet streams at T,, and usng the enthalpy f reactn, H at the peratng temperature n the defntn f an electrlyzer thermal-t-hydrgen effcency, H,e, drect applcatn f the frst law yelds: H, e FV p H (1/ 1) H Therefre lwer peratng vltages always yeld hgher effcences. Lw peratng vltages can be acheved n practce, wth reasnable current denstes, nly f the electrlyzer area-specfc resstance s lw. Nte that at V p = V tn, Eqn. (8) yelds H =. Operatn at the thermal neutral vltage yelds the same verall hydrgen prductn effcency p (8) 5

7 5 = 0 T e = C H,e E V p Fgure 4. Electrlyzer thermal-t-hydrgen effcences as a functn f pwer-cycle thermal effcency and electrlyzer percell peratng vltage. V tn as that f the pwer cycle. Lettng V p = E = G /F, Eqn. (8) yelds H H e( E) (9), G (1/ 1) H whch s the verall effcency crrespndng t peratn at the reference pen-cell ptental, E. Ths value 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: V c E ut y ln jf yh H O 1/ yo std 1/ (10) Fr a specfed temperature, the pen-cell ptental can be sgnfcantly lwer than E 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 f a Nernst ptental as pssble, snce the peratng cell current densty s prprtnal t the dfference between the peratng vltage and the Nernst ptental. If the Nernst ptental s lw, a reasnable current densty can be acheved wth a lw peratng vltage, and therefre wth hgh effcency, accrdng t Eqn. (8). The effect f peratng ptental n electrlyzer thermal-t-hydrgen effcency s llustrated n Fg. 4. Ths fgure shws a seres f verall effcency curves, ver a range f assumed pwer-prductn effcency values fr an electrlyss temperature f ºC. 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 10% 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 nn-xygen-cntanng sweep gas shuld be cnsdered wth a hgh flw rate. Ths s why we are cnsderng the use f steam as a sweep gas n the xygen sde f these cells. The steam can be separated frm the xygen later by a heat-recuperatng cndensatn prcess, yeldng a pure xygen prduct at lw temperature. As an example HTE peratng cndtn, assume T = ºC, = 1 atm, y HO = 0.95, y H = 0.05, y O = 0.05, AS = Ohm cm, and =. Under these cndtns, the Nernst ptental s 0.77 V. If we wsh t acheve a current densty f A/cm, the requred peratng vltage wuld be V, yeldng an electrlyzer thermal-t-hydrgen prductn effcency f 4 fr the assumed pwerprductn effcency f. 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 50% 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 range, yeldng verall thermal-t-hydrgen-prductn effcences f less than 35%. It shuld be emphaszed that ths dscussn f electrlyzer thermal-t-hydrgen effcency based n Eqn. (8) and Fg. 4 des nt cnsder the entre HTE system. The cntrl vlume fr ths dscussn s drawn nly arund the electrlyzer and the nlet and utlet streams are assumed t be at the same hgh temperature (.e., sthermal peratn). N cnsderatn f heat up f the prcess streams t the electrlyzer temperature s ncluded. In fact, due t the relatve heat capacty rates f the prduct gas streams and the lqud water nlet stream n the verall HTE system, net heat addtn wll always be requred t supply at least sme f the enthalpy f vaprzatn f the 6

8 lqud water and t bst the electrlyzer nlet stream (steam/hydrgen) t the desred stack nlet temperature (- 850ºC), s these effcency values are ptmstc. Nevertheless, ths analyss prvdes gudance fr ptmzng the perfrmance f the electrlyzer tself. ESULTS OF AAMETIC STUDIES The ne-dmensnal electrlyzer mdel was develped prmarly fr ncrpratn nt a larger system-level HTE prcess mdel. But t s als useful as a stand-alne tl fr evaluatng electrlyzer perfrmance under varus peratng cndtns. A summary f the cases that have been studed s prvded n Table 1. The secnd clumn n the table desgnates the sweep gas cndtn: ar sweep, steam sweep, r n sweep. The thrd clumn specfes the electrlyzer thermal bundary cndtn: sthermal r adabatc. Fr peratng vltages between pen-cell and thermal neutral, sthermal peratn requres drect heatng f the electrlyzer by sme means. The furth and ffth clumns specfy the ttal stack nlet flw rates f fuel (cmpstn fxed at 0.95 mle-fractn H O, 0.05 mle-fractn H ) and sweep gas. The sxth and seventh clumns defne the per-cell area-specfc resstance (AS) f the electrlyzer stack at a temperature f 1100 K. The AS value used n the electrlyzer mdule was ether fxed r temperature-dependent per the fllwng Arrhenus equatn: AS( T ) AS exp (11) 1100K T ( K) where AS 1100K represents the user-specfed cell AS at the temperature 1100 K. Ths cnstant allws ne t shft the entre AS curve t hgher r lwer AS values, t mmc lwer r hgher perfrmng cells, respectvely. Ths equatn fr AS(T) s based n emprcal data btaned frm an actual peratng stack, mdfed t allw user specfcatn f the AS value at 1100 K. The temperature dependence f the AS s mprtant fr analyzng adabatc cases (snce the utlet temperature n these cases s generally dfferent than the nlet temperature) and fr evaluatng the effect f electrlyzer nlet temperature n verall prcess effcency. In rder t shw the trends that can be expected wth hgher r lwer AS, three values f AS 1100K have been ncluded n ths study. The AS 1100K value f.0 Ohm cm represents a per-cell stackaverage AS value at 1100 K that s achevable wth exstng technlgy. The AS 1100K value f 1.0 shuld be achevable wth mprvements n materal and fabrcatn technlgy n the near term. The value f s an ptmstc value that has been bserved n buttn cells, but wll be dffcult t acheve n a stack f ths desgn (planar, wth electrlyte-supprted cells) n the shrt term. The fnal tw clumns n Table 1 defne the stack nlet temperature and peratng pressure. epresentatve results btaned wth the ne-dmensnal mdel are presented n Fgs. 5 and 6. Electrlyzer gas utlet temperatures are pltted n Fgure 5(a) as a functn f peratng vltage fr adabatc electrlyzer peratn wth varus cell ASs. Fr peratng vltages between the pencell ptental and thermal neutral, the endthermc heat f reactn requrement s larger than the hmc heatng, resultng n an electrlyzer utlet temperature that s lwer than the nlet. The thermal mnmum vltage crrespndng t the mnmum utlet temperature s apprxmately 1.06 V. Lwer AS values tend t ncrease the magntude f ths temperature depressn. Fr Case, the AS s allwed t vary wth temperature accrdng t Eq. (13). Snce the AS value ncreases wth decreasng temperature, ths case shws a smaller utlet temperature depressn than the cmparable fxed AS case (Case 1). All fur temperature prfles return t the electrlyzer nlet temperature at the thermal neutral vltage (~1.85 V). Beynd the thermal neutral vltage, utlet temperatures ncrease rapdly, snce the rate f hmc heatng nw exceeds the endthermc heat requrement. The per-cell heat requrement fr sthermal electrlyzer peratn s shwn n Fg. 5(b) fr several AS values. Fr peratng vltages less than thermal neutral, hmc heatng s nsuffcent t supply the endthermc heat f reactn and addtnal heat must be added t the electrlyzer (pstve values) t supplement the hmc heatng. Maxmum heat addtn s requred at the thermal mnmum vltage (~1.06 V). Table 1. Matrx f test cases analyzed fr a 10-cell, 64 cm per-cell actve area, stack. Inlet cmpstn s 0.95 mle-fractn H O, 0.05 mle-fractn H fr all cases. Case # Sweep Gas Electrlyzer Thermal BC Fuel Mass Flw ate (kg/hr) Sweep Mass Flw ate (kg/hr) 7 AS at 1100 K AS Inlet T (K) ressure (a) 1 steam adabatc fxed steam adabatc varable steam adabatc fxed steam adabatc fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed ar sthermal fxed nne sthermal fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed steam sthermal fxed

9 Temperature (K) Case 1 (AS = hm cm ) Case (AS(T) = hm cm at 1100 K) Case 3 (AS = 1 hm cm ) Case 4 (AS = hm cm ) Heat Added er Cell (W) Case 5 (AS = hm cm ) Case 6 (AS = 1 hm cm ) Case 7 (AS = hm cm ) Operatng Vltage er Cell (Vlts) (a) Operatng Vltage er Cell (Vlts) (b) Fgure 5. (a) Electrlyzer utlet temperature versus peratng vltage fr adabatc peratn; (b) requred heat addtn fr sthermal electrlyzer peratn. Fr peratng vltages beynd thermal neutral, electrlyzer heat rejectn s requred t mantan sthermal cndtns. Fg. 6 depcts estmated electrlyzer thermal-t-hydrgen prductn effcences H,e, defned n Eq. (8), fr the varus sthermal cases lsted n Table 1, as a functn f current densty. Each thermal-t-hydrgen effcency value s based upn the enthalpy f reactn H at the stack peratng temperature and the cell peratng vltage crrespndng t the current densty shwn, fr a cnstant pwer-cycle effcency =. Fgure 6(a) shws the decrease n hydrgen-prductn effcency wth ncreasng current densty. In fact, peak thermal-t-hydrgen prductn effcences ccur at zer current densty hghest effcences are at the lwest prductn rates In addtn, fr a specfed current densty, the thermal-t-hydrgen prductn effcency mprves fr lwer AS values. Fg. 6(b) llustrates the effect f sweep gas upn hydrgen prductn effcency. The mle-fractn r partal pressure f O n the sweep sde f the electrlyzer cell affects the Nernst ptental, as can be seen n Eqn. (10). Mnmzng the cell-mean xygen partal pressure mnmzes the Nernst ptental. Fr a gven AS, the current densty and hydrgen prductn rate s prprtnal t the dfference between the peratng vltage and the Nernst ptental. Therefre, by mnmzng the Nernst ptental the requred peratng vltage fr a gven hydrgen prductn rate s mnmzed and prductn effcency s ncreased. In Fgure 6(b), the n-sweep case (Case 9) shws the lwest thermal-t-hydrgen prductn effcences. In ths case, the partal pressure f O s always 1. Effcences fr the ar-sweep case (Case 8) shw apprxmately the same values as fr the n-sweep case, except at the lwest current denstes. Hwever, the steam sweep case (Case 5) shws mprved perfrmance. Incrpratn f the electrlyzer mdel nt the verall system mdel wll allw us t determne whether these trends hld up fr the system as a whle, cnsderng heat recuperatn ssues. Fg. 6(c) demnstrates the ncrease n verall thermal-thydrgen prductn effcency wth electrlyzer temperature fr sthermal electrlyzer peratn. Heat f reactn, gas cmpnent thermal prpertes, Nernst vltage, AS, and pwercycle effcency are all functns f temperature. Fr Cases 5, 10, and 11, AS and pwer-cycle effcency were held cnstant at hm-cm and, respectvely. Hgher temperatures reduce the amunt f electrcal energy requred t break the chemcal bnds n the water mlecules. Ths results n a lwer Nernst ptental. Therefre, the mnmum electrcal energy demand fr electrlyss decreases wth ncreased temperature. The thermal energy requrement, hwever, ncreases wth ncreasng temperature. As a result, the ttal energy demand, H, ncreases very slghtly wth temperature. The advantage f hgh-temperature peratn les wth the substtutn f electrcal energy wth thermal energy, yeldng an verall effcency gan. In fact, under favrable peratng cndtns, hgh-temperature electrlyss can yeld verall hydrgenprductn effcences that are sgnfcantly hgher than the pwer-cycle thermal effcency. The effect f peratng pressure upn electrlyzer thermalt-hydrgen effcency s reverse that f temperature, as shwn n Fg. 6(d). Hgher pressure peratn ncreases the Nernst ptental, and cnsequently the peratng vltage requred t prduce a specfed current densty. Increasng the flw rate f steam/hydrgen n the cathde sde and sweep gas n the ande sde f the electrlyzer results n reduced Nernst and peratng ptentals and crrespndngly ncreased electrlyss effcency. Ths effect s shwn n Fg. 7. Usng case 5 as a base case, effcences fr flw rates crrespndng t 5, 10, and 0 tmes the base flw are shwn n the fgure as a functn f current densty. The ncreased flw rates yeld ncreased effcences f a few percentage pnts. Frm an verall system standpnt, hwever, ths strategy wuld nt be desrable snce t wuld requre recyclng large amunts f excess steam and wuld als requre large heat exchangers fr recuperatn. 8

10 H (g/hr) Case 5 ( hm cm AS, Steam Sweep, 1100 K Inlet) Case 6 (1 hm cm AS, Steam Sweep, 1100 K Inlet) Case 7 ( hm cm AS, Steam Sweep, 1100 K Inlet) H (g/hr) Case 5 ( hm cm AS, Steam Sweep, 1100 K Inlet) Case 8 ( hm cm AS, Ar Sweep, 1100 K Inlet) Case 9 ( hm cm AS, N Sweep, 1100 K Inlet) H,e H,e (amps/cm ) (a) H (g/hr) (amps/cm ) (b) H (g/hr) Case 5 ( hm cm AS, Steam Sweep, =0.1 Ma) Case 1 ( hm cm AS, Steam Sweep, =1.0 Ma) Case 13 ( hm cm AS, Steam Sweep, =5.0 Ma) H,e H,e Case 5 ( hm cm AS, Steam Sweep, 1100 K Inlet) Case 10 ( hm cm AS, Steam Sweep, 1150 K Inlet) Case 11 ( hm cm AS, Steam Sweep, 100 K Inlet) (amps/cm ) (amps/cm ) (c) (d) Fgure 6. Electrlyzer thermal-t-hydrgen effcences as a functn f current densty: effect f (a) AS, (b) sweep gas, (c) peratng temperature, and (d) peratng pressure. CONCLUSIONS A ne-dmensnal mdel has been created t study the thermal and electrchemcal behavr f hgh temperature steam electrlyss n a planar sld xde electrlyss stack. Detals f the mdel have been presented n ths paper. The mdel allws determnatn f the average Nernst ptental, cell peratng vltage, gas utlet temperatures, extent f hmc 9

11 H,e , A/cm case 5, 1x flw case 14, 5x flw case 15, 10x flw case 16, 0x flw Fgure 7. Effect f flw rates n electrlyzer thermalt-hydrgen effcences. heatng, and electrlyzer effcency fr any specfed nlet gas flw rates, current denstes, cell actve area, and external heat lss r gan. The cell AS s accunted fr thrugh a temperature-dependent crrelatn derved frm emprcal data frm an actual peratng electrlyss stack, allwng user specfcatn f the AS value at 1100 K. esults frm the ne-dmensnal mdel have been cmpared t results frm a fully 3-D cmputatnal flud dynamcs mdel. The 1-D mdel crrectly calculated the thermal neutral vltage. The 1-D mdel predcted slghtly hgher peratng vltages cmpared t the CFD results, makng the ne-dmensnal mdel cnservatve snce hgher peratng vltages crrespnd t lwer electrlyss effcences. arametrc studes were cnducted usng the 1-D mdel t evaluate electrlyzer perfrmance and effcency under varus peratng cndtns. educng the cell AS as well as reducng the sweep gas O partal pressure was shwn t ncrease electrlyzer effcency. Electrlyzer effcency was als mprved fr hgher temperature peratn and lwer pressure peratn. Under certan cndtns, electrlyzer thermal-t-hydrgen prductn effcency was shwn capable f exceedng the electrcal pwer cycle effcency. 10-Cell lanar Sld-Oxde Electrlyss Stack, rceedngs, ASME 3rd Internatnal Cnference n Fuel Cell Scence, Engneerng, and Technlgy, May 3 5, 005, Ypslant, MI.. O Bren, J. E., Herrng, J. S., Stts, C. M., Lessng,. A., Hgh-Temperature Electrlyss fr Hydrgen rductn Frm Nuclear Energy, t be presented at the 11 th Internatnal Tpcal Meetng n Nuclear eactr Thermal-Hydraulcs NUETH-11, pes alace Cnference Center, Avgnn, France, Octber -6, O Bren, J. E., Stts, C. M., Herrng, J. S., Lessng,. A., Hartvgsen, J. J., and Elangvan, S., erfrmance Measurements f Sld-Oxde Electrlyss Cells fr Hydrgen rductn frm Nuclear Energy, Jurnal f Fuel Cell Scence and Technlgy, Vl. 3, August 005, pp Hawkes, G. L., O Bren, J. E., Stts, C. M., Herrng, J. S., Shahnam, M., CFD Mdel f a lanar Sld Oxde Electrlyss Cell fr Hydrgen rductn frm Nuclear Energy, t be presented at the 11th Internatnal Tpcal Meetng n Nuclear eactr Thermal-Hydraulcs NUETH-11, pes alace Cnference Center, Avgnn, France, Octber -6, rnkey, M., Shahnam, M., and gers, W. A., SOFC FLUENT Mdel Thery Gude and User Manual, elease Versn 1.0, FLUENT, Inc., Yldz, B., Hhnhlt, K., and Kazm, M. S., H rductn Usng Hgh Temperature Steam Electrlyss Supprted by Advanced Gas eactrs wth Supercrtcal CO Cycles, MIT-NES-T-00, December 004. ACKNOWLEDGMENTS Ths wrk was spnsred by the US Department f Energy, Offce f Nuclear Energy, Scence and Technlgy. Ceramatec, Inc. s partcpatng thrugh a subcntract wth INEEL. EFEENCES 1. O Bren, J. E., Stts, C. M., Herrng, J. S., and Hartvgsen, J. J., Hydrgen rductn erfrmance f a 10