Modeling Analysis of Different Renewable Fuels in an Anode Supported SOFC Andersson, Martin

12 Pages·2017·3.98 MB·English

Modeling Analysis of Different Renewable Fuels in an Anode Supported SOFC
Andersson, Martin; Paradis, Hedvig; Yuan, Jinliang; Sundén, Bengt
Published in:
Journal of Fuel Cell Science and Technology
DOI:
10.1115/1.4002618
2011
Link to publication
Citation for published version (APA):
Andersson, M., Paradis, H., Yuan, J., & Sundén, B. (2011). Modeling Analysis of Different Renewable Fuels in
an Anode Supported SOFC. Journal of Fuel Cell Science and Technology, 8(3).
https://doi.org/10.1115/1.4002618
Total number of authors:
4
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Download date: 10. Feb. 2023
Appendix to Dissertation: Solid Oxide Fuel Cell Modeling at the Cell Scale - Focusing
on Species, Heat, Charge and Momentum Transport as well as the Reaction Kinetics
and Effects by Martin Andersson, Department of Energy Science, Lund University,
2011, ISBN 978-91-7473-180-4.

Paper III
This paper has been published in:

ASME J. Fuel Cell Science and Technology,
Vol. 8, 031013, 2011.

© 2011 ASME.
Modeling Analysis of Different
Renewable Fuels in an Anode
Supported SOFC
MartinAndersson
Itisexpectedthatfuelcellswillplayasignificantroleinafuturesustainableenergy
e-mail: [email protected] systemduetotheirhighenergyefficiencyandpossibilitytouseasrenewablefuels.Fuels,
suchasbiogas,canbeproducedlocallyclosetothecustomers.Theimprovementforfuel
HedvigParadis
cellsduringthepastyearshasbeenfast,butthetechnologyisstillintheearlyphasesof
development;however,thepotentialisenormous.Acomputationalfluiddynamics(CFD)
JinliangYuan
approach(COMSOLMULTIPHYSICS)isemployedtoinvestigateeffectsofdifferentfuelssuch
as biogas, prereformed methanol, ethanol, and natural gas. The effects of fuel inlet
BengtSundén
composition and temperature are studied in terms of temperature distribution, molar
fractiondistribution,andreformingreactionrateswithinasingecellforanintermediate
DepartmentofEnergySciences, temperaturesolidoxidefuelcell.Thedevelopedmodelisbasedonthegoverningequa-
FacultyofEngineering, tions of heat, mass, and momentum transport, which are solved together with global
LundUniversity, reforming reaction kinetics. The result shows that the heat generation within the cell
Box118, dependsmainlyontheinitialfuelcompositionandtheinlettemperature.Thismeansthat
22100Lund,Sweden the choice of internal or external reforming has a significant effect on the operating
performance.Theanodestructureandcatalyticcharacteristichaveamajorimpacton
the reforming reaction rates and also on the cell performance. It is concluded that
biogas,methanol,andethanolaresuitablefuelsinasolidoxidefuelcellsystem,while
morecomplexfuelsneedtobeexternallyreformed. (cid:2)DOI:10.1115/1.4002618(cid:3)
Keywords: SOFC,modeling,biogas,methanol,ethanol,naturalgas,reforming,COMSOL
MULTIPHYSICS
1 IntroductionandProblemStatement withtheelectrochemicalreactionswithintheanode.Intheindi-
Fuelcells(cid:4)FCs(cid:5)arepromisingduetoitsenvironmentaladvan- raepcpteainrteinrnaalrerefoformrmeirng(cid:4)w(cid:4)iItIhRin(cid:5)tahpeprcoealcl(cid:5)h,inthcelorseefocromnitnagctrweaitchtiothnes
tages with higher efficiency and lower emissions of SO, NO,
x x anodewheretheexothermicelectrochemicalreactionstakeplace.
andCO2thanconventionalpowergeneration(cid:2)1(cid:3).Thesolidoxide TheIRreactionsdecreasetherequirementforcellcooling(cid:4)less
fuel cell (cid:4)SOFC(cid:5) works at a high temperature such as surplusofair(cid:5).Lesssteamisneededandfinally,itoffersadvan-
600–1000°C (cid:2)2(cid:3). This allows SOFCs to operate with different
tageswithrespecttothecapitalcost.Uptohalfoftheheatpro-
typesoffuelsfrombothfossilandrenewablesources.Itopensup
duced by the oxidation reaction could be “consumed” by the
foraneasiertransitionfromconventionalpowergenerationwith steam reforming (cid:4)SR(cid:5) process. This would improve the system
hydrocarbonbasedfuelstofuelcellswithpossibilityfordifferent electricalefficiency(cid:2)4,5(cid:3).
fuels,especiallySOFCs.Duetotheincreasingglobalawareness It is known that the use of heavy hydrocarbons (cid:4)C(cid:2)(cid:5) can
ofhowenergyusageaffectstheenvironment,theinterestofre- 4
causeconsiderablecokinganddeactivationproblemswithSOFC
newableenergyhasincreased.SOFCsaregenerallymoretolerant
anodecatalysts.Aprereformercanbreakdownthehydrocarbons
tnoalclyon(cid:4)taasmwineallntasstehxatnerontahlelyr(cid:5)fureeflocrmellsthaenfduethlempaoksessibthileitmytionteinretesrt-- withlongercoalchainstoC1toC2moleculesplusH2andCO(cid:2)6(cid:3).
ingforrenewableenergyresources(cid:2)1(cid:3).Attractivefuels,whichare Animportantpartofthesystemdesignistheheatrecovery,abig
fractionoftheheatgeneratedinthecellcanbeusedforthesteam
consideredinthisstudy,arebiogas,methanol,ethanol,andnatural reformingreaction(cid:2)7(cid:3).
gas. The list of potential fuels for SOFC systems also includes
Inthispaper,asingleintermediatetemperatureSOFCdesign,
gasoline,diesel,aviationfuel,ammonia,aceticacid,formicacid, which uses externally reformed renewable fuels (cid:4)prereformed
butanol,butyricacid,andbottledgas.Coalandbiomasscanbe methanolandethanolandbiogas(cid:5)isstudied.Therenewablefuels
used as raw fuels in a gasification process, which takes place
beforethefuelcellstack(cid:2)3(cid:3). arecomparedwithnaturalgasduetothelargequantityofinfor-
mationavailableinopenliterature.Itwouldbeinterestingtoap-
Theaimofthispaperistostudythepossibilityofusingrenew-
plyDIRaswell;however,moreexperimentalstudiesneedtobe
ablefuelsinSOFCs.ThereformingreactionsinSOFCsystems
performedtoachievereliablekineticdataforNi/YSZreforming
canbeconductedbothexternallyandinternally.Theexternalre-
forming(cid:4)ER(cid:5),suchastheprereformerinaSOFCsystem,means ofmethanolandethanol.TheapproachwithIIRisnotyetvery
welldevelopedbutitcanbeaninterestingdesigninthefuture.
thatthereformerisplacedoutsidethecell,whichispossiblefor
alltypesoffuelcells.Theinternalreforming(cid:4)IR(cid:5)meansthatthe 1.1 ElectrochemicalandReformingReactions.Theglobal
reforming reactions occur within the cell. In the direct internal reactionsthattakeplacewithinaSOFCusinghydrogen,carbon
reforming(cid:4)DIR(cid:5)approach,thereformingprocessesoccurtogether monoxide, and methane as fuel can be described as: oxygen is
reducedinthecathode(cid:4)Eq.(cid:4)1(cid:5)(cid:5).Theoxygenionsaretransported
through the electrolyte, but the electrons are prevented to pass
ContributedbytheAdvancedEnergySystemsDivisionofASMEforpublication through the electrolyte. The electrochemical reactions (cid:4)Eqs. (cid:4)2(cid:5)
intheJOURNALOFFUELCELLSCIENCEANDTECHNOLOGY.ManuscriptreceivedAugust and (cid:4)3(cid:5)(cid:5) take place in the anodic three-phase boundary (cid:4)TPB(cid:5).
12,2010;finalmanuscriptreceivedAugust16,2010;publishedonlineMarch1,
2011.Editor:NigelM.Sammes. Methaneneedstobereformed(cid:4)Eq.(cid:4)4(cid:5)(cid:5)beforetheelectrochemi-
JournalofFuelCellScienceandTechnology JUNE2011,Vol.8 / 031013-1
Copyright©2011byASME
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cal reactions. Carbon monoxide can be oxidized in the electro- Table 1 Enthalpy change of reforming reaction for different
chemicalreaction(cid:4)Eq.(cid:4)3(cid:5)(cid:5)butcanalsoreactwithwater(cid:4)Eq.(cid:4)5(cid:5)(cid:5). fuelssuitableforSOFCs†10‡
Thereactionsdescribedherearetheoverallones,moredetailed
riseancotitopnamrtiecciphaatniinsgmisnctahnebeelefcoturoncdhienmRiceafl.r(cid:2)e8a(cid:3)c.tNioontseathtatthemaenthoadniec Fuel (cid:4)k(cid:6)J/(cid:3)mhorl(cid:5) (cid:4)kJ/mogl(cid:6)ep(cid:3)neehrrram/tneoHdl2e(cid:5)ofH2
TPB, it is catalytically converted within the anode into carbon
monoxideandhydrogen,whichareusedasfuelsintheelectro- Methane (cid:4)165 (cid:4)41.2
chemicalreactions(cid:2)9(cid:3), Methanol (cid:4)49.4 (cid:4)16.5
O2+4e−⇔2O2− (cid:4)1(cid:5) EDtMhaEnol (cid:4)(cid:4)117231 (cid:4)(cid:4)2280..82
H +O2−⇔HO+2e− (cid:4)2(cid:5)
2 2
CO+O2−⇔CO +2e− (cid:4)3(cid:5)
2 havetobeanissue,whentheyareproducedinarenewableman-
CH +HO⇔3H +CO (cid:4)4(cid:5) ner,becauseitwillleadtothattheneteffectontheemissionswill
4 2 2 bezero(cid:2)12(cid:3).
CO+HO⇔H +CO (cid:4)5(cid:5) Methanolisinterestingduetoitsreadyavailability,highspe-
2 2 2 cificenergy,andeasystorageandtransportation.Ethanolisalsoa
The net reaction of methanol, ethanol, and dimethyl ether promisingcandidatesinceitisreadilyproducedfromrenewable
(cid:4)DME(cid:5)tohydrogenandcarbonmonoxidearedescribedinEqs. resources.Whencomparingthese,ethanolhasextraadvantagesin
(cid:4)6(cid:5)–(cid:4)8(cid:5),respectively.Theproducedcarbonmonoxidereactsthen terms of power density, nontoxicity, transportation, and storage.
furtherwithsteamtohydrogenandcarbondioxidebythewater- However,becauseofincompleteoxidization,theethanolprocess-
gasshiftreaction,Eq.(cid:4)5(cid:5)(cid:2)10(cid:3), ing reaction consists of a more complicated multistep reaction
CHOH⇔2H +CO (cid:4)6(cid:5) mechanismandinvolvesanumberofadsorbedintermediatesand
3 2 by-products.Thechemicalformulaforbiomassisgenerallywrit-
CHOH+HO⇔4H +2CO (cid:4)7(cid:5) tenasCxHyOz.Thecoefficientsofx,y,andzcanbecalculatedfor
2 5 2 2 eachbiomass.Biomasscanbeconvertedintobiogas,usuallyby
CH3OCH3+H2O⇔4H2+2CO (cid:4)8(cid:5) asinsatsermobaiicnlbyreoafkmdoewthnanienathnedacbasrbenocnedoiofxoidxeyg(cid:2)e7n(cid:3)..Thebiogascon-
Thesteamreformingreactionratesforsimplefuelsispresentedin SteamreformingofvariousfuelsavailableinSOFCs,suchas
Eqs.(cid:4)4(cid:5)–(cid:4)8(cid:5).Alsomorecomplexhydrocarbons(cid:4)fromrenewable methane(cid:4)biogasandnaturalgas(cid:5),methanol,DME,andethanol,
or fossil origin(cid:5) can be used as raw energy within a fuel cell consumesheat.Theenthalpychangeofthereactionforthemen-
systemforhydrogenproduction.Externalreformingisnecessary tionedfuelscanbeseeninTable1.Ethanolconsumesthemost
duetorelativelylongcarbonchains.Theoverallhydrocarbonre- heatpermoleoffuel.However,whenconsideringthatreforming
formingreactioncanbewrittenas(cid:2)7(cid:3) ofthedifferentfuelsgenerateadifferentamountofhydrogen(cid:4)to
CH O +yO +2·(cid:4)n−y−0.5·z(cid:5)·HO⇔nCO +2 beusedintheelectrochemicalreactions(cid:5),themostheatpermole
n m z 2 2 2 ofhydrogengeneratedisrequiredbythereformingofmethane.
·(cid:4)n−y−0.5·z+0.25·m(cid:5)·H (cid:4)9(cid:5) Globally,alltheheatneededforthereformingreactionsisgener-
2
Equation (cid:4)9(cid:5) states the ideal reforming reaction where the only atedwithinthecell,thankstotheelectrochemicalreactions,anda
higherefficiencycanbeachievedwiththementionedrenewable
productsarepurehydrogenandcarbondioxide.Inrealitywithina
fuelscomparedwithpurehydrogen.Itshouldbementionedthat
fuel cell reformer, there are three ordinary reforming reactions:
SR, partial oxidation (cid:4)POX(cid:5), and autothermal reforming (cid:4)ATR(cid:5). thetemperaturecandecreaseclosetotheinletifthesteamreform-
SR, Eq. (cid:4)10(cid:5), is effective for hydrogen production and largely ingreactionrateistoohigh.
exothermic.InPOX,Eq.(cid:4)11(cid:5),thefuelispartiallyburnedwitha 1.3 Challenges With Renewable Fuels. The direct use of
substoichiometric amount of air. An ATR system contains one hydrocarbonfuelscanleadtothecatalyst’srapiddeactivationby
reactorwithSRandonewithPOX(cid:2)7(cid:3). carbon formation on a traditional SOFC anode and also sulfur
CH O +2·(cid:4)n−z(cid:5)·HO⇔nCO+2·(cid:4)n−z+0.5·m(cid:5)·H poisoning (cid:2)13(cid:3).Ahigh inlet temperature along with internal re-
n m z 2 2 formingofahydrocarboncancauseahightemperaturegradient
(cid:4)10(cid:5) andtensionswithintheanodeclosetothefuelinletduetothefast
steamreformingreactionrate.Thisproblemcanbereducedifthe
CnHmOz+0.5·(cid:4)n−z(cid:5)·O2⇔nCO+0.5·m·H2 (cid:4)11(cid:5) fuelinlettemperatureislowered,partoftheanodegasisrecycled,
anodereformingactivityisreduced,orif(cid:4)partial(cid:5)prereformingis
Itshouldbenotedthatifsufficientamountofheatisavailable,SR
employed(cid:2)5(cid:3).
givesmosthydrogenperamountofrawfuel;however,thecon-
Theprobabilityforcarbondepositionsdependsonthesteam-
version of complex hydrocarbons may be more difficult, com-
paredwithPOX(cid:2)7(cid:3). to-carbonratioandoperatingtemperature.Ithasbeenwellestab-
lishedthatthekeyreactionsoccuroverasurfacelayerofnickel
1.2 RenewableFuels.Usingalternativefuels(cid:4)comparedwith particles.Ifalayerofcarbonisallowedtobuildupandattachto
hydrogen(cid:5)givesSOFCsamajoradvantagebecausepurehydrogen anickelcrystalliterapidcatalystbreakdowncanoccurduetothe
ishighlyflammableandvolatile,whichmakesitproblematicto graphiteformation.Itshouldbenotedthathydrocarbonswitha
handle. Also, hydrogen has low density, which makes storing longer carbon chain than methane have a higher propensity for
costly.Itshouldalsobementionedthatpurehydrogenisexpen- carbondeposition(cid:2)5,14(cid:3).Itisconcludedthatmethaneandmetha-
sive to obtain since it has to be extracted from another source, nolwithappropriatesteamcontentcanbedirectlyfedtoNi/YSZ
mostcommonlynaturalgas(cid:2)11(cid:3). anodewithouttheproblemofcarbonformation(cid:2)6(cid:3).Forfuelswith
Likehydrogen,methanolandethanolareusefulenergycarriers alongercarbonchain,aprereformer(cid:4)withacatalystlesssensitive
ratherthanprimaryfuels(cid:4)naturalgas,coal,etc.(cid:5)throughgasifica- tocarbonformationthanNi/YSZ(cid:5)shouldbeincludedinthefuel
tionorchemicalsynthesisreformingprocesses.Thecharacteris- cellsystem.
ticsofthesealcohol-basedfuelsareverysimilartoconventional Sulfurneedstoberemovedbeforethefuelentersintothecell
liquid fuels (cid:4)propane, butane, and diesel(cid:5) and can be readily toavoiddegradationwithinthecell.Variousmethodscanbeap-
handled,stored,andtransported(cid:2)10(cid:3).TheCO emissionsdonot plied,suchashightemperaturedesulfurization,whereorganicsul-
2
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(cid:7) (cid:8) (cid:9) (cid:12)
Table2 Cellgeometry†2‡ (cid:8) 1
+(cid:9)·(cid:2)u u−(cid:2) −p+ (cid:10)T−(cid:4)(cid:10)(cid:5)(cid:4)(cid:2)u(cid:5)(cid:11) =F (cid:4)12(cid:5)
(cid:5) (cid:7)
Cellcomponent Thickness p
Celllength 0.1m whereFisthevolumeforcevector,(cid:5)isthepermeabilityofthe
Fuelchannelheight 1mm porousmedium,(cid:7) istheporosity,(cid:8)isthedynamicviscosity,uis
p
Airchannelheight 1mm thevelocityvector,andT istheviscousstresstensor(cid:4)T=v(cid:4)(cid:2)u
Anodethickness 500 (cid:8)m +(cid:4)(cid:2)u(cid:5)T(cid:5)(cid:5).(cid:10)isthesecondviscosityandforgases;itisnormally
Cathodethickness 50 (cid:8)m assumedas(cid:10)=−2(cid:8)/3(cid:2)18(cid:3).Thedensitiesandviscositiesforthe
Electrolytethickness 20 (cid:8)m
Interconnectthickness 500 (cid:8)m ppaerrtaitcuirpea,tiansgdgeasscerisbaerdeidneRpeenfsd.en(cid:2)2t,1o1n(cid:3).loTchaelcgoansciennltertatvioelnocaintidesteamre-
definedasalaminarflowprofile.Theoutletisdefinedaspressure
(cid:4)=1 atm(cid:5).
fur compounds are reduced to hydrogen sulfite and the corre- 2.2 MassTransport.TheMaxwell–Stefanequationformass
spondinghydrocarbon,passingacobaltormolybdenumcatalyst diffusion and convection is used to describe the mass transport
supported on alumina. Adsorption methods can be applied for phenomenaforthegasesinsidethefuelcell(cid:2)17(cid:3).TheMaxwell–
smallerSOFCsystems(cid:2)3(cid:3). Stefan equation is solved for the fuel and air channels and the
Forfuelcellsystems,itisimportanttoconsideratwhatphase electrodes,
the fuel operates as the system can need extra equipments to (cid:7) (cid:8)
hfuaenldcleeltlhgeefnueerlalsltyortiankgesanudppqruoicteesasilnogt.oTfhspeaecqeuaipnmdewnetibgehstiadnedstfhoer (cid:2) −(cid:9)·w(cid:6)n D¯ ·(cid:2)x(cid:4)x −w(cid:5)(cid:2)p·u−DT·(cid:2)T +(cid:9)·u·(cid:2)w =S
somefuelsthisbecomesevenmoreprominentwhenfuelstoring i ij j j j p i T j i
spaceincreases.Methane,DME,ammonia,andbiogasarevapors (cid:4)13(cid:5)
at 1 bar and at 253–293 K. Methanol, ethanol, and diesel are
liquidsundertheseconditions.Thevaporsneedtobepressurized
where w is the mass fraction, x is the molar fraction, n is the
tnoommiackaellythreeafsuoenlasbtolerincogsitn(cid:2)1a5c(cid:3).ommercialpossiblesizewitheco- numberofspecies,DiTisthethermaldiffusioncoefficient,andDij
istheMaxwell–Stefanbinarydiffusioncoefficient.S,sourceterm
i
bychemicalreactions,isonlydefinedfortheinternalreforming
2 MathematicalModel reactions because the electrochemical reactions are assumed to
takeplaceattheinterfacesbetweentheelectrolyteandelectrodes.
Atwo-dimensionalmodelforananode-supportedSOFCisde-
The diffusion coefficient is dependent on temperature, as de-
MveUloLTpIePdHYaSnIdCSim(cid:4)vpelresmioennt3e.d5(cid:5).inEqthueaticoonmsmfoerrcmiaolmseonfttwumar,em, aCsOsM,SaOndL sincvrioblevdedi,naRnedfs.o(cid:2)n2l,y11(cid:3)o.nOenMthaexwaierlls–iSdtee,fannitrodgifefnusainodnocxoyegfefinciaernet
heattransportaresolvedsimultaneously.Thegeometryisdefined
needstobecalculated.Onthefuelside,methane,water,hydro-
inTable2,andasketchoftheinvestigatedcellcanbeseeninFig.
1.Notethedifferenceinscalebetweenthecelllength(cid:4)x-direction, gen, carbon monoxide, and carbon dioxide are present, and ten
pairs of Maxwell–Stefan diffusion coefficient need to be calcu-
asinFig.1(cid:5)andvariouscomponentthicknesses(cid:4)y-direction,asin
lated.Theboundaryconditionsforthemasstransportequationare
Fig.1(cid:5).Itshouldbementionedthatthemodelinthisstudyis2D
definedasmassfractionforthegaschannelinlets;theoutletsare
only,andtheconnectionbetweentheelectrodesandinterconnect definedasconvectiveflux(cid:2)2(cid:3).
cannotbeexplicitlyobservedinthiscase.
2.3 Heat Transport. The temperature distribution is calcu-
2.1 Momentum Transport. The gases flow inside the fuel lated separately for the gas phase (cid:4)in air and fuel channels and
cellcomponents,suchasintheairandfuelchannels,andinthe electrodes(cid:5)andforthesolidphase(cid:4)interconnects,electrodes,and
porous electrodes. The Darcy–Brinkman equation is introduced electrolyte(cid:5).Heatistransferredbetweenthephasesatthechannel
andsolvedforthegasflowinthefuelandairchannelsandinthe
wallsandintheporouselectrodes.Thegeneralheatconduction
porous materials simultaneously (cid:2)16,17(cid:3). The Darcy–Brinkman
equationisusedtocalculatethetemperaturedistributionforthe
equation (cid:4)Eq. (cid:4)12(cid:5)(cid:5) is transformed into the standard Navier– solidmaterials,i.e.,electrolyte,interconnect,andelectrodes(cid:2)17(cid:3),
Stokes equation when (cid:4)(cid:5)→(cid:6)(cid:5) and (cid:4)(cid:7) =1(cid:5) and into the Darcy
p
equationas(cid:4)Da→0(cid:5).DaistheDarcynumber.Thederivationof
the Navier–Stokes and Darcy equations from the Darcy– (cid:2)(cid:4)−ks·(cid:2)Ts(cid:5)=Qs (cid:4)14(cid:5)
BrinkmanequationcanbefoundinRef.(cid:2)16(cid:3),
wherek isthethermalconductivityofthesolids,T isthesolid
s s
temperature,andQ istheheatsource(cid:4)heattransferbetweenthe
s
solidandgasphasesandheatgenerationduetoOhmicpolariza-
tion(cid:5).NotethatheatgeneratedduetoOhmicpolarizationisas-
sumedtoenterthesolidphase(cid:4)asapartofQ(cid:5),heatgeneration
s
duetoelectrochemicalreactions,concentrationandactivationpo-
larizationaresimplifiedanddefinedasinterfaceconditions,such
asforthemasstransport.Thetemperaturedistributionforthegas
mixturesinthefuelandairchannelsandintheporouselectrodes
iscalculatedas(cid:2)17(cid:3)
(cid:2)(cid:4)−k ·(cid:2)T(cid:5)=Q −(cid:9)·c ·u·(cid:2)T (cid:4)15(cid:5)
g g g g p,g g
inwhichc isthegasphaseheatcapacity,T isthetemperature
p,g g
inthegasphase,andQ istheheattransferbetweenthegasand
g
solid phases. Because the Reynolds number is small, the heat
transfer coefficient (cid:4)h (cid:5) in the porous electrodes (cid:4)spherical
s,g,por
Fig.1 Sketchofananode-supportedSOFC,nottoscale particlesareassumed(cid:5)canbecalculatedas(cid:2)19(cid:3)
JournalofFuelCellScienceandTechnology JUNE2011,Vol.8 / 031013-3
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(cid:7) (cid:8)
2·k T·(cid:3)S
h = g (cid:4)16(cid:5) q =q +q =−i· r+(cid:11) +(cid:11) (cid:4)22(cid:5)
s,g,por d 0 r losses n ·F act,e conc,e
p e
wduhcetrievidtyp.iTshteheheealetcttrraondsefeprarbteictwleedeniamtheetegraasnadnkdgsioslitdhepghaassecodne-- wfahceerecoqn0diistiothne(cid:5),hqeartisgetnheerahteedatatgethneeriantteedrfaincseid(cid:4)espethceificeedllasduinetetro-
pendsonthetemperaturedifferenceandtheparticleareatovol- changeinenthalpy,andqlossesistheheatgeneratedduetopoten-
umeratioas(cid:2)20(cid:3) tial losses inside the cell.The amount of heat generated due to
electrochemicalreactionscanbecalculatedas(cid:2)28(cid:3)
Q =h ·(cid:4)T −T(cid:5)=AV·h ·(cid:4)T −T(cid:5) (cid:4)17(cid:5)
g v g s s,g,por g s T·i
ianrewahtoichvohluvmisethraetivoo,lwumhiechheisatutsreadnsffoerrhceoaetffitrcainensftearnbdetAwVeeinstthhee qr=−T·(cid:3)Sr·n˙=−(cid:3)SrneF (cid:4)23(cid:5)
solidandgasphase.Notethatthesurfacetovolumeratioforheat i
transferishigherthanthatforchemicalreactionsbecausenotall n˙= (cid:4)24(cid:5)
nF
the available surface is covered with active nickel catalyst.The e
heattransferareatovolumeratioequalstothematerialspecific wheren˙isthemolarfluxdensity(cid:4)mol/(cid:4)m2s(cid:5)(cid:5)and(cid:3)S isentropy
r
availablearea(cid:4)areaperweight(cid:5)timesthedensity.Theheatcapac- change of reaction (cid:4)−50.2 J/(cid:4)Kmol(cid:5)(cid:5), calculated from data in
ityandthethermalconductivityinthegasphasedependonthe Ref.(cid:2)29(cid:3).Theheatgenerationduetoactivationandconcentration
temperature and the concentration, as described in Refs. (cid:2)2,11(cid:3). polarizationscanbecalculatedas(cid:2)27,30(cid:3)
TheheatingduetoOhmicpolarizationisdescribedinSec.2.4.
Theinletgastemperatureisdefinedbytheoperatingtempera- qlosses=−i·(cid:4)(cid:11)act,e+(cid:11)conc,e(cid:5) (cid:4)25(cid:5)
ture(cid:4)1000K(cid:5),andtheoutletoneisdefinedasaconvectiveflux. Theconcentrationpolarizationsduetoconcentrationdifferences
Theboundariesatthetopandatthebottomofthecellaredefined insidethecellarespecifiedas(cid:2)(cid:7)26(cid:3) (cid:8)
bysymmetriesbecauseitisassumedthatthecellissurroundedby
othercellswiththesametemperaturedistribution.Theheatflux (cid:11) = RT ln pH2O,TPB·pH2,b (cid:4)26(cid:5)
betweentheelectrodes/interconnectandgaschannelsarespecified conc,a n F p ·p
attwochannelwalls,locatedoppositetoeachother,withacon- e,a H(cid:7)2,TPB H(cid:8)2O,b
stantNusseltnumber(cid:4)4.094(cid:5)fromRef.(cid:2)21(cid:3),basedonthefully
developedflowforarectangularduct(cid:4)aspectratiois1forboth (cid:11) = RT ln pO2,b (cid:4)27(cid:5)
channels(cid:5).Thecellisalsoheatedduetochangeinentropyinthe conc,c ne,cF pO2,TPB
electrochemicalreactionsandconcentrationandactivationpolar-
wherep standsforthepartialpressureattheboundaryTPB
izations,asdescribedinSec.2.4. i,TPB
andp isthepartialpressureattheinterfacebetweengaschannel
i,b
2.4 ElectrochemicalReactions.Twoapproachesfordefining and electrode. Chemical reactions involve energy barriers (cid:4)i.e.,
theelectrochemicalreactionscanbefoundinliterature,eitheras activationpolarization(cid:5),whichmustbeovercomebythereacting
source terms in the governing equations (cid:2)22,23(cid:3) or as interface species.Theactivationpolarizationcanbeconsideredastheextra
conditionsdefinedattheelectrode/electrolyteinterfaces(cid:2)24,25(cid:3). potential needed to overcome the energy barrier of the rate-
Thelaterapproachisemployedinthisstudybecausethethickness determiningsteptoavaluethatthereactionproceedsatadesired
oftheactivelayerissufficientlythin,comparedwiththethickness rate(cid:2)30(cid:3),
(cid:7) (cid:8)
of the electrode (cid:2)24,25(cid:3). The charge transfer equations are not
2RT i
solved in this study; however, the temperature effects from (cid:11) = sinh−1 e (cid:4)28(cid:5)
Ohmic, concentration, and activation polarization losses are in- act,e neF 2·i0,e
cludedintheequationsforheattransport. (cid:7) (cid:8)
cheBmoitchahlyrdearocgtieonnsanwditcharobxoyngemnoinoonxsid(cid:4)Eeqcsa.n(cid:4)2p(cid:5)aratnicdip(cid:4)a3t(cid:5)e(cid:5).inTheeleeclteroc-- i0,e=nRTFk(cid:2)eexp −RETe (cid:4)29(cid:5)
e
trochemical oxidation of hydrogen is several times higher than
where i is the exchange current density. The pre-exponential
thatofcarbonmonoxidewhilethewater-gasshiftreactionisrela- 0,e
tivelyfast(cid:2)23(cid:3).Thecontributionofoxidationofcarbonmonoxide factor (cid:4)k(cid:2)(cid:5) is 2.35(cid:14)1011 (cid:15)−1m−2 for the cathode and 6.54
hasbeenneglectedinthisstudy.Thecellaveragecurrentdensity (cid:14)1011 (cid:15)−1m−2fortheanode,respectively.Theactivationenergy
inthisstudyisspecifiedas0.3 A/cm2. (cid:4)E(cid:5)is137kJ/molforthecathodeand140kJ/molfortheanode
Ohmicpolarizationoccursduetoresistanceoftheflowofions (cid:2)26(cid:3).
intheelectrolyteandelectricalresistanceintheelectrodes.The
2.5 InternalReformingReactions.Sufficientactivityforthe
electrodesandelectrolyteareheatedduetothiseffect(cid:2)26,27(cid:3), reformingreactionsisprovidedinsidetheSOFCanode(cid:2)31(cid:3).Re-
Q =i·(cid:11)ohm (cid:4)18(cid:5) asicotinondekpiennedtiecnstforonmthReeafc.t(cid:2)i3v2e(cid:3)afroeratthoevsotelaummererfaotriom(cid:5)inagnd(cid:4)afnroemxpRreesf-.
ohm (cid:12) (cid:2)33(cid:3) for the water-gas shift reactions are used to calculate the
reaction rates in this work. Other global kinetic models can be
(cid:11) =R ·i (cid:4)19(cid:5) found in Refs. (cid:2)34,35(cid:3). The catalytic steam reforming reaction
ohm ohm
occurs at the surface of the nickel catalyst and is specified as
Rohm=(cid:13)(cid:12)a+(cid:13)(cid:12)el+(cid:13)(cid:12)c (cid:4)20(cid:5) (cid:2)32,36(cid:3) (cid:7) (cid:7)−225(cid:14)103(cid:8)
a el c r =AV· 943exp ·p p
where (cid:12)is the component thickness and Rohm is the electrolyte r (cid:7)R·T (cid:8) CH4 (cid:8)H2O
area-specificOhmicresistance.Theelectronic/ionicconductivities −1937
(cid:4)(cid:13)(cid:5)arecalculatedasdescribedinRef.(cid:2)26(cid:3). −7.74(cid:14)10−9exp R·T ·pCOpH32 (cid:4)30(cid:5)
Heatgeneratedduetoelectrochemicalreactionsandduetopo-
larization losses are, as previously described, defined at the wherepiisthepartialpressureofgasspeciesi,Tisthetempera-
electrodes/electrolyteinterfaces, ture,r isthereactionrate,andAV istheactiveareatovolume
ratio.Equation(cid:4)30(cid:5)originatesfromexperimentsperformedatthe
−n·(cid:4)−k(cid:2)T(cid:5)− =q (cid:4)21(cid:5) Research Center Jülish, and the anode material consists of Ni-
0
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8YSZsubstratewithastandardcompositionofCH O Ni(cid:2)36(cid:3). Table3 Inletmolarfractions
n m z
The range for the AV (cid:4)related to catalytic kinetic reactions(cid:5)
varies in literature between 1(cid:14)105 m2/m3 (cid:2)37(cid:3) and 2.2 H2 CO CO2 CH4 H2O
(cid:14)106 m2/m3(cid:2)32(cid:3)forSOFCanodes.Themeasuredspecificsur-
facearea(cid:4)m2/g(cid:5)forNi/YSZmaterialdevelopedforSOFCanodes Methanol,SF=3 0.270 0.115 0.051 0.017 0.547
Methanol,SF=5 0.247 0.072 0.042 0.011 0.628
(cid:4)withaporesizeof225nm(cid:5)is70(cid:14)106 m2/m3(cid:2)38(cid:3).Notethat Ethanol,SF=3 0.359 0.114 0.030 0.112 0.385
notallthesurfacesareavailableforcatalyticreactionsduetothe Ethanol,SF=5 0.312 0.081 0.036 0.080 0.491
distribution of catalyst, nonavailable pores, and mass transfer Biogassteammixture 0.03 0 0.27 0.36 0.34
limitations among others. An AV of 2.2(cid:14)106 m2/m3, corre- 30%prereformed
sponding to 3.1% of the total Ni/YSZ specific area to volume naturalgas(cid:2)11(cid:3) 0.263 0.0294 0.0436 0.171 0.493
ratio,isusedinthiswork.Thetrendforthedevelopmentduring
thepastyearsisinthedirectionofemployingsmallerparticlesto
getlargerAV.
Thereactionrate(cid:4)Eq.(cid:4)30(cid:5)(cid:5)isoftheArrheniustype.Itconsists 5(cid:4)formethanolandethanol(cid:5)arecalculatedfromtheexperiments
ofthreeparts,partialpressures,pre-exponentialfactor,andacti- performedinRef.(cid:2)6(cid:3).Aftertheprereformingofethanol,thefuel
vationenergy.Thepre-exponentialfactordescribestheamountof mixturecontainssomeethyleneandetan.Tosimplifythecalcu-
collisionsbetweenthemoleculeswithinthereactionandtheex- lation and due to the lack of kinetic information in considering
ponential expression with the activation energy describes the reformingofethyleneandetanonNi/YSZcatalyst,theseconcen-
probabilityforthereactiontooccur.Thepre-exponentialfactors trationsareassumedtobemethane.Forthecaseofbiogas,asmall
dependstronglyonthepropertiesoftheanodematerialandthe fractionofhydrogenisaddedtoenableelectrochemicalreactions
temperature.Theactivationenergyisbasedonthecatalyticchar- close to the inlet as well, and steam is added to avoid carbon
acteristics, such as chemical composition. The large difference deposition and to be used in the reforming reactions. The fuel
between the activation energies in open literature composition for 30% prereformed natural gas is defined by the
(cid:2)11,32,34–36,39(cid:3) makes it probable that more parameters have InternationalEnergyAgency(cid:4)IEA(cid:5)andisfrequentlyusedinlit-
significant influences on the reaction rate. To truly enhance the erature. The flow rates for the different cases are calculated to
understanding of these phenomena, microscale modeling is keepthefuelutilizationbeing80%.Theflowrateofairiskept
needed. constantforallcasesandtheoxygenutilizationissettobe20%.
Different approaches for defining the water-gas shift reaction
can be found in literature: (cid:4)1(cid:5) global reaction mechanism that 3 ResultsandDiscussion
considersreactionintheanodeonly(cid:2)9,23,33(cid:3),(cid:4)2(cid:5)globalreaction
Thepredictedtemperaturedistributionforthecasewithprere-
mechanism that considers reaction in the anode and in the fuel
formedmethanolwithinitialSFsof3and5canbeseeninFigs.
channel (cid:2)32,40(cid:3), and (cid:4)3(cid:5) a more advanced reaction mechanism
2 and 3, respectively. Increased SF means a slightly decreased
that includes catalytic surface reaction kinetics for integrated temperaturerise(cid:4)5Kdifferenceinthemaximumtemperaturebe-
steam reforming, water-gas shift reaction, and the Boudouard tweenthesetwocases(cid:5)duetoahigherflowrateintheflowchan-
mechanism(cid:2)8,41(cid:3).Basedontheglobalschemefortheanode,the nel(cid:4)tokeepthefuelutilizationto80%(cid:5).Itshouldbementioned
expressionforthecatalyzedwater-gasshiftreactioninRef.(cid:2)33(cid:3)
thattheflowrateintheairchannelissignificantlyhigherthanin
hasbeenselectedinthisstudy:
(cid:7) (cid:8) the fuel channel. The temperature difference in the y-direction
p p (cid:4)Fig.4(cid:5)intheairchannelsoccursbecausetheconvectiveheatflux
r =k · p p − H2 CO2 (cid:4)31(cid:5) arebiggerintheairchannel(cid:4)comparedwiththefuelchannel(cid:5)due
s sf H2O CO Kps totherelativelylargerairflowrate.
Therateconstant(cid:4)k (cid:5)andtheequilibriumconstant(cid:4)K (cid:5)aretem- ThetemperaturedistributionforbiogasisshowninFig.5,that
perature dependentsfexpressions calculated from exppserimental forprereformedethanol(cid:4)SF=3(cid:5)isshowninFig.6,andthatfor
data,asdescribedinRef.(cid:2)33(cid:3). 30%prereformednaturalgasisshowninFig.7.Thecasewith
ThesourcetermsS (cid:4)implementedintheMaxwellStefanequa- biogasandnaturalgascontainsmoremethanecomparedwiththat
i
tionformasstransport(cid:5),duetothecatalyticalreformingreactions, ofprereformedethanolandmethanol.Ahigherfractionofmeth-
aredefinedas(cid:2)23(cid:3) anemeansadecreasedtotaltemperatureriseduetotheheatcon-
sumptioninthesteamreformingreaction.
SH2=(cid:4)3rr+rs(cid:5)·MH2 (cid:4)32(cid:5) The developed model is also used to simulate cases with an
evenhigherconcentrationofmethaneandalsoahigherinlettem-
S =−r ·M (cid:4)33(cid:5) perature(cid:4)comparedwiththecasesinTable3(cid:5).Thelimitationtobe
CH4 r CH4
S =(cid:4)−r −r(cid:5)·M (cid:4)34(cid:5)
H2O r s H2O
S =(cid:4)r −r(cid:5)·M (cid:4)35(cid:5)
CO r s CO
where M is the molecular weight and S is the source term of
i i
speciesi.Thelastspecies(cid:4)CO(cid:5)canbeobtainedbecausethesum
2
of the mass fractions equals unity. The heat generation/
consumptionduetothereformingreactionsisspecifiedin(cid:2)11(cid:3)
(cid:6)
Q = r ·(cid:3)h (cid:4)36(cid:5)
s i i
i
where(cid:3)h istheenthalpychangeduetothereactionsandQ is
i s
theheatgenerationinthesolidphase.
2.6 CellOperatingConditions.Theinvestigationperformed
inthisstudyconcernsbiogas,prereformedmethanol,ethanol,and
naturalgas.TheinletmolarfractionsarespecifiedinTable3.The Fig. 2 Gas phase temperature distribution for prereformed
molarfractionsbasedoninitialsteam-to-fuelratios(cid:4)SFs(cid:5)of3and methanol„SF=3…
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Fig. 3 Gas phase temperature distribution for prereformed Fig. 6 Gas phase temperature distribution for prereformed
methanol„SF=5… ethanol„SF=3…
consideredisthattheprobabilityofcarbondepositionincreases occur,asobservedinFig.8,wheretheinletgastemperaturefor
whentheSCistoolow.Thepotentialtroublewithahightem- thecasewithbiogasisincreasedwith100K.Notethattheheat
peraturegradientclosetothefuelinletcanbemanagedwithlow- generatedbytheelectrochemicalreactionsandpolarizationlosses
eringtheinlettemperatureordilutingthefuelsinceahighertem- isstillhigherthantheheatconsumedbythereformingreactions
perature or a less diluted fuel gives a higher steam reforming whenthecompletecellisstudied.
reactionrateandalsoahighertemperaturegradient.Thisisnota Thepredictedmolarfractionsinthefuelchannelforthepar-
problem,forthecasesspecifiedinTable3,sincearelativelylow ticipatinggasspeciesalongtheflowdirectionforthecasewith
inlettemperature(cid:4)1000K(cid:5)aswellasprereformedfuelmixturesis prereformedmethanol(cid:4)SF=3(cid:5)areshowninFig.9,andthosefor
used.Theactivationenergyinthemethanesteamreformingreac- thecasewithbiogasareshowninFig.10.Hydrogenisconsumed
tionishighforthiscase;i.e.,theprobabilityforreactionisvery and water is generated (cid:4)due to the electrochemical reactions(cid:5)
low.Acatalyticcompositionwithdecreasedactivationenergywill alongtheflowdirectionforalltheinvestigatedsituations.Thereis
causeasteepertemperaturegradient.Whentheinlettemperature a consumption of water as carbon monoxide and methane are
is increased, a high temperature gradient close to the inlet can reformed.Dependingontheinletfraction,adecreaseinthemolar
fractionofwatercanbeobservedclosetotheinlet,e.g.,forthe
Fig. 4 Gas phase temperature distribution for prereformed Fig. 7 Gas phase temperature distribution for 30% prere-
methanol„SF=3…inthemiddleofthecell„atx=0.05 m… formednaturalgas
Fig. 5 Gas phase temperature distribution for biogas-steam Fig. 8 Gas phase temperature distribution for biogas-steam
mixture mixturewithanincreasedinlettemperature
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Fig.11 Reactionrate„inmol/„m3s……forthesteamreforming
reaction within the anode for the case with biogas-steam
Fig.9 Molarfractionofthegasspeciesinthefuelchannel
alongtheflowdirectionforprereformedmethanol„SF=3… mixture
is possible to change the reaction rate, either by changing the
particlesizeofactivecatalystortheporousstructure,i.e.,active
cases with prereformed methanol.The molar fraction of carbon
catalyticarea.
monoxidedependsonthewater-gasshiftreaction.Thecasewith
AsshowninFig.13,highreactionratesforthewater-gasshift
biogas contains initially very little hydrogen. The generation of
reactionareobtainedwhentheinletconcentrationsarefarfrom
morehydrogendependsonthesteamreformingreaction,which
equilibrium conditions in terms of temperature and concentra-
dependsontheactiveareatovolumeratio,temperature,andgas
tions,forexample,formethanolwiththeSFof3.Thereaction
species concentrations. Note that the total amount of molecules
(cid:4)within the fuel cell(cid:5) increases as the steam reforming reaction rateforthewater-gasshiftreactionintheanodeforthecasewith
biogasisshowninFig.14.Thereactionproceedsinitiallytothe
proceedstotheright.
Forthesituationswithhighinletconcentrationsofmethane(cid:4)for left due to a low concentration of carbon monoxide and a high
example,thecasewithbiogas,showninFig.11(cid:5),thesteamre- concentration of carbon dioxide.As hydrogen is consumed and
formingreactionrate(cid:4)withintheanode(cid:5)ishighaslongashigh watergeneratedbytheelectrochemicalreactionwithintheanode,
thisreactionproceedstotheright.Thewater-gasshiftreactionis
concentrationofmethaneisavailable.Thelowerrateclosetothe
inletisduetoalowertemperature.Thereactionrateexpression
has,aspreviouslymentioned,highactivationenergy.Thisisthe
reason for the relatively low reaction rate, which enables the
methane steam reforming reaction rate to be similar within the
entirelengthoftheanode.Itshouldbementionedthattheback-
wardreactionrateisnegligible,comparedwiththeforwardreac-
tionrateforthesituationsappliedinthisstudy.Thereactionrate
increasesasthetemperatureandconcentrationofsteamincrease
and decreases as the concentration of methane decreases. Note
thatthereisadifferenceinscalebetweenthex-andy-directions.
Thesteamreformingreactionrateintheanodeforthecasewith
prereformed methanol (cid:4)SF=3(cid:5) is shown in Fig. 12. It contains
initiallyverylittlemethane.Thisgivesalowinitialsteamreform-
ingreactionrate,whichincreasesasthecarbonmonoxideandthe
hydrogenareconsumed,aswellasthetemperatureisincreased.It
Fig.12 Reactionrate„inmol/„m3s……forthesteamreforming
reactionwithintheanodeforprereformedmethanol„SF=3…
Fig.10 Molarfractionofthegasspeciesinthefuelchannel Fig.13 Reactionrate„inmol/„m3s……forthewater-gasshift
alongtheflowdirectionforbiogas-steammixture reactionwithintheanodeforprereformedmethanol„SF=3…
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