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Methane ReformingDemonstration Problem
Revision0;October14 ,2008 Reference: WangShuyanet.al.,Simulationofeffectofcatalyticparticleclusteringonmethane
steamreforminginacirculatingfluidizedbedreformer,ChemicalEngineeringJournal139(2008)136
146.
PurposeandOverview
Steamreformingofmethane(conversionofCH4intosyngas:COandH2)isofinterestforapplications
suchasfuelcells,conversionofnaturalgastoliquidfuels,etc. Similarreactorsareofinterestforcoal
toliquid(CTL)andbiofuelsynthesisapplications.
A
simple
demonstration
problem
has
been
developed
in
SINDA/FLUINT,
using
both
the
Sinaps
nongeometric(sketchpad)GUIandtheThermalDesktopwithFloCADgeometric(CADbased)GUI.
Sincebothsetsofmodelsareavailableforinspectionandforuseasastartingpointortemplate,only
briefdescriptionsareincludedinthisdocumentasgeneralguidance.Abasicunderstandingof
SINDA/FLUINTmodelingisassumed.
ReactionKinetics
Twosimultaneousreactionsoffivespeciesareconsidered:
CH4+H2O CO+3H2 (reaction1)
CO+H2O CO2+H2 (reaction2)
Reaction2isthewatergasshift(WGS)reaction.
Thereferencedpaper(Shuyan,et.al.)containsthereactionkineticsusedinthisproblem,basedonthe
presenceofHaldorTopsoeNi/MgAl2O4spinelcalatyticparticles.Becauseofthedemonstrativenature
ofthisproblem,thedetailsofthecatalystareneglected:thecatalystisassumedtooperateatfull
activity.
Shuyanlistsformulaeforforwardreactionratesforthesereactions,1usingequilibriumconstantsasthe
basisforestimatingreverserates.Assumingfullcatalyticactivity,thecurrentreactionratecanbe
calculatedasafunctionoftemperature,pressure,andpartialpressures.Thetemperaturedependenciesforboththereactionrateconstantsandtheequilibriumconstantsareexponentialfunctionsofan
Arrheniusform.
1 Specifically,equations8,9,11,12,13,and1520.
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NotesonFluidProperties
InSINDA/FLUINT,eachspeciesisassignedaletteridentifier:
Species Symbol LetterIDMethane CH4 M
Water H2O WCarbonmonoxide(gas) CO G
Hydrogen H2 H
Carbondioxide CO2 C
Watermaybeacondensable(twophase)fluid.However,inthiscasethetemperatureswillalwaysbe
highenoughsuchthattheliquidphasewillneveroccur.2Therefore,eitheraperfectgas(8000series
fluid)orarealgas(NEVERLIQ6000seriesfluid)couldhavebeenused.Versionsofsuchfilesare
available(http://www.crtech.com/properties.html)thatwerebuiltfromtheNISTprogramREFPROP,
perhapssubsequentlysimplifiedtoaperfectgasusingtheSINDA/FLUINTPR8000utility.
Unfortunately,theNISTdatabasedoesnotextendtosufficientlyhightemperaturesforCO,CH4,andH2.
Forexample,theuppertemperaturelimitforCOisonly500KinthecurrentversionofREFPROP.
Therefore,propertiesforallfivegasesweregeneratedusingNASAsfreeCEAchemicalequilibrium
programcombinedwithaC&RutilityforconvertingoutputstoFPROPDATAformat.3 Whilethis
interfaceisintendedtopreparefluidsrepresentingequilibriumreactingmixtureswithvariable
molecularweights,theonlymodeinCEAcanbeusedtoproducepropertiesforsingleconstituents
withconstantmolecularweights.Therefore,despitetheresultinggeneralized6000seriesrealgas
fluidtables,itshouldbenotedthattheactualpropertiesreflectCEAsintrinsicassumptionofperfect
gases. Heatofformation(HFORM)anddiffusionvolume(DIFV)informationwerethenaddedtothese
fluidfiles,notingthatCEAusestheheatofformationasthebasisoftheenthalpyat25C.Theheatofformationofwateristhereforediminishedbytheheatofvaporizationtoreflecttheallgasnatureof
thisCEAderivedfluidfile.(Forafulltwophasewaterdescription,theuncorrectedheatofformation
shouldinsteadbeapplied,sincealiquidstateexistsatstandardtemperatureandpressure.)
ReactorDesign
Anintentionallygenericandsimplifiedplugflowreactor(PFR)isassumed.
Inclusionofthesolidcatalystparticlescouldtakeseveralformsasapackedbedofstationaryparticles
heldinplacebystructuredcatalystssupports,freeflowingwiththegastransport,orother
configurationsbutinclusionofthecatalystsinanyformovershadowstheillustrativeintentofthis
demonstrationproblem.Thechosenscenariofocusesonhowtoincorporatethereactionkineticsinto
SINDA/FLUINT.
2 Iftemperaturesbelowthedewpointareincluded,afulltwophasedescriptionofwatershouldbeusedinstead.
Indeed,suchadescription(http://www.crtech.com/properties.html)wasusedaspartofthevalidationeffort
whentemperaturesaslowas25Cwereusedasafeedtemperature.3 http://www.crtech.com/EQfluids.html
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Temperatures,pressures,inletflows,anddimensionsmaybechangedparametricallyinthemodel,with
asubsetofpossibleparametricsettingsusedforthebaselinerunsshowninthetablebelow.
Parameter RegisterName Value Units Comment
Reactor
length
length
1
m
(Arbitrary
choice.)
Longer
lengths
mightbeconsideredasneededto
bringtheoutletconditionscloser
totheequilibriumcondition
Reactorhydraulicdiameter diam 0.008 m (Arbitrarychoice)
Reactorflowarea area 4.e4 m2 Undefinedfinsorslitshapeis
assumed,asneededtoprovide
adequateheattransferarea
Inlettemperature temp_in 800 C (Arbitrarychoice,but
representativeoftypical
applications.)
Walltemperature Assumed
equaltothe
inlet
800 C Inletandwalltemperaturesare
assumedtobeequal,butcanbe
independentlyadjustedifneedbe
Inletflowrate moles_in 0.03e3 kmol/s (Arbitrarychoice)
InletmolefractionsofCH4,H20
andotherinletstream
constituents,plusexcesssteam
fractionbeyondstoichiometric
mol_in_m,
mol_in_w,
SteamX
0.5,
0.5,
3.0
Stoichiometric(equalmole
fractions)plus2timesmore
steam.UseSteamX=1.0for
stoichiometricfeedrates.
Outletpressure pres 101325. Pa Thisindirectlysetsthereactor
pressureduetothesmall
pressuredropthroughthereactor
ARefresher:ModelingReactionsinSINDA/FLUINT
TherateofcreationofmassofanyspeciesiisdesignatedXMDOTiinSINDA/FLUINT,withthecaveat
thatiXMDOTi=0:thereisnonetgenerationorlossoftotalmassasaresultofachemicalreaction.A
speciesthatisbeingconsumedwillhaveanegativeXMDOT,andaspeciesthatisbeingproducedwill
haveapositiveXMDOT.Sincethismodelusesmetricunits,XMDOThasunitsofkg/s(lbm/hrwouldbe
theunitsintheEnglishsystem).
WhenXMDOTsarenonzero,thecodewillautomaticallycalculateandapplyacorrectiveheatofreaction
(QCHEM)basedonthefluidproperties(heatsofformationandenthalpybasis).Ifeachfluidusesthe
heatofformationastheenthalpybasisatSTP,thiscorrectiveQCHEMtermiszero.
Whenthedesiredconcentrationofoneormorespeciesisknown(e.g.,wheneithertheequilibrium
concentrationorthereaction/combustionefficiencyisknown),theEQRATEutilitycanbeusedto
generateXMDOTvalues,perhapsobeyingoneormorechemicalreactions(suppliedasstoichiometric
numbers). Forexample,preliminaryCEArunscouldhavegeneratedequilibriumstatepredictions
(perhapsasfunctionsoftemperature),whichcouldhavebeenusedasinputstotheEQRATEutility.
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Ifinsteadonlytherateofreactionisknown(asisthecaseinthisexample),thenEQRATEisnot
applicableandtheXMDOTvaluesshouldinsteadbecalculatedexplicitlybytheuserinuserlogicblock
FLOGIC0atthestartofeachsolutioninterval(i.e.,timesteporsteadystaterelaxationstep).The
XMDOTvalueforeachspeciesiwillbethesumofallthereactionsinwhichitparticipates.
TheresultingsetofXMDOTvaluesisassumedtobeconstant(alongwiththecorrespondingQCHEM)overthenextsolutioninterval.Inotherwords,thespeciesproductionandextinctionratesarebasedon
thetemperaturesandpressuresatthestartoftheinterval,andarenotimplicitlyadjustedfor
temperatureorpressurechangesthatareabouttooccur.4
Asignificantrestrictiononchemicalreactionsisthattheycanonlyapplytotanks(controlvolumes),and
nottojunctions(massless/volumelessstatepoints).NotingthatthemainsolutionroutineSTEADY(aka
FASTIC)treatstankstemporarilyasjunctions,thismeansthatsteadystatesolutionscanonlybe
achievedusingSTDSTL(pseudotransientintegrationtowardatimeindependentstate).Thisinturn
meansthat,unlikemoststeadystateanalyses,chemicalreactionsteadystatesolutionsaredependent
oninitialguesses(especiallyspeciesfractions).
ReactorModel
Thesourceofgasesisrepresentedbytwoplena:one(reactor.1000)representingastoichiometric
mixtureofmethaneandsteam,andanother(reactor.1100)representingexcesssteamthatcanbe
addedtothereactor.Themixtureratiowithinplenumreactor.1000issetusingregisters(e.g.,mol_in_w
forsteam,mol_in_mformethane)basedonmolefractions,whicharethenconvertedintogasmass
fractions(XGiforeachspeciesiasrepresentedbytheregisterxin_m,xin_w,xin_h,xin_c,andxin_g.
Notethatwhilexin_candxin_garebothzero(noinflowingCO2orCO),xin_hisnonzero:itissettoa
verysmallvalue.Anextremelysmallamountofhydrogenisaddedsimplytoavoidtheneedtodealwith
themathematicalsingularitycausedbythepresenceofthepartialpressureofhydrogeninthe
denominatoroftherateequations.
Therearemanywaystorepresenttheinletconditions.Forexample,themassfractionsonasingle
plenumcouldbeset.Alternatively,NplenacouldbeusedforeachoftheNspeciesinvolved,settingthe
massorvolumetricflowrateofeachspeciesbeinginjected.
Inthiscase,asingleSetFlow(SINDA/FLUINTMFRSETconnector)isappliedfromeachplenum,withthe
ratiooftheflowratesbeingcontrolledviatheSteamXregister:SteamX=1forstoichiometricflow,2for
twicethesteamrequired,etc.Thesteadystatecase(namedPFR)isrunatSteamX=1:stoichiometric
inletconditions,orequalmolarflowsofmethaneandsteam,withzeroexcesssteamflowaddedfrom
plenumreactor.1100.
4 Bydefault,SINDA/FLUINTdoesimplicitlyreducereactionsforreactantsthatarepresentinlowconcentrations
andthatvanishduringthesolutioninterval,asdescribedintheUsersManual.Inotherwords,XMDOTscanbean
implicitfunctionofconcentration,buttheyareassumedindependentoftemperatureandpressureduringeach
solutioninterval.Normally,theyareadjustedinastairstepfashionbetweensolutionintervalsaccordingto
calculationsinuserlogic.
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A10segmentSinapsorFloCADPipe(SINDA/FLUINTHXmacropluswallmodel)isusedtorepresentthe
reactor.Whileincludingthedetailsoftheheatexchange(structural/thermalmodel)isastrengthofthe
C&Rtoolsuite,toavoiddistractingfromtheintentofthisdemonstrationproblem,aninfinitesourceof
energyat800Cisassumed.ThenodesinthePipearethereforechosentobeconstanttemperature
boundarynodes.
Thechoiceof10segmentscanbeadjustedbychangingboththeintegerregisterresolpluseditingthe
Pipemacro.5Higherresolutions(atleastresol=20)areneededtocapturethestronggradientsatthe
inletandtoguaranteethatequilibriumisachievedattheexit.6However,fordemonstrationpurposes
thespatialresolutionisleftintentionallylow.TheSinapsdiagramforthereactorisshowbelow.
ThecorrespondingFloCADdiagramisasfollows:
TanksmustbeusedwithinthePipetoallowspeciessource/sinkrates(XMDOTs)tobespecified:
reactionsarenotpossibleinjunctions.NotethatSTUBEconnectors(inertialessductelements)areused
insteadoftubessincetheflowsconsistoflowdensitygases.Eventhoughthesubsequenttransient
operatesoveranextremelyshorttimescale,tubeswouldnotberequiredunlesssignificant
condensationweretooccur.
TheSTDSTLsolutionmustbeusedtoarriveatasteadystateanswersincechemicalreactionsarenot
possibleinSTEADY,whichtreatstanksasiftheywerejunctions.NormallyaSTEADYsteadystate
solutionisnotverydependentoninitialconditions,andoftenonlyrequires1050iterationstoresolve.
However,anSTDSTLsolutionusesthefulltransienthydrodynamicsolutionalongwithasimultaneous
5 Therestartrecordnumber(integerregisterrecord)willalsohavetobeadjustedbasedontheoutputsofthefirst
case(pfr)sincethesizeoftheSAVEandRSI/RSOfileswillchangeifthemodelsizechanges.6 Assumingtemperaturesarehighenoughtoensureequilibrium.Also,thereactorlengthmayneedtobe
increasedaswell(thiscanbechangedindependentlyofthenumberofsegmentsusedtoresolvethatlength).
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thermalsolution.STDSTLissimilartorunningatransientsolutionuntileverysystemresponseis
constant.Itthereforeissensitivetoinitialconditions(assetviathemolefractionregistersminit_h,
minit_g,etc.whichsetmassfractionsxinit_h,xinit_g,etc.).Thismeansthatsomespeedsavingscanbe
realizedbysettingreasonableinitialconditions,perhapsbasedonpriorruns.Otherwise,poorlyguessed
initialconditionsinvoketheevaluationofasevereyetspurioustransient,wastingcomputational
resourcesandrequiringmorestepNum(aregisterusedtosetthecontrolconstantNLOOPS)to
converge.
Normally,steadystatesolutionsaresoinexpensivethattheyareoftenrecalculatedbeforeeach
transientcaseasinitialconditions.WhilethespeedoftheSTDSTLsolutionisgoodinthiscase,amore
detailed(perhaps2Dor3D)modelmightnotenjoythesameresult.Therefore,theabilitytosavethe
resultsofapriorsteadystatecase(casepfr)andreusetheminafuturetransientcase(case
pfrTransient)isdemonstratedinthismodel(seeRESAVE/RESTARoperationsintheSINDA/FLUINT
manual).BothcasescanbeselectedintheSinapsCaseManagerortheThermalDesktopCaseSet
Managerandexecutedsequentially.Ifthisusagewerefrequent,thenthetwosolutionsshouldbe
combinedintoasinglecasetoavoidtheinefficienciesoftheextrapreprocessandcompilesteps.
Foreachtankinthesystem,atthestartofeachsolutionstep(namely,inFLOGIC0),thefollowing
calculationsshouldbemade:
1. Theratefactors(equilibriumKconstantsandpreexponentialkterms)shouldbeupdatedasafunctionofcurrenttemperature(TL),pressure(PL),andpartialpressures(e.g.,PPGHisthe
partialpressurefractionforspeciesH).
Thetemperaturesandpressuresshouldbeconvertedintoabsoluteunits(e.g.degreesK
insteadofC),whichmeanssubtractingABSZROfromtemperaturesandPATMOSfrom
pressures.Forexample:TLabs=TLrelABSZRO.Inthelogicblocks,theregisteratemp
containstheabsolutetemperatureandaprescontainstheabsolutepressure.
2. Themolarrateforreaction1shouldbecalculated,andusedtosettheXMDOTforeachspeciesinthatequationusingthestoichiometricnumber,notingthatXMDOThasunitsof
kg/s(orlbm/hrforUID=ENG)andthereforethemolecularweightofeachspeciesmustbe
usedasamultiplier.ThesemolecularweightscanbecalculatedviaroutinessuchasVMOLW
orVMOLWPT,butinthisdemonstrationproblemtheyhavebeensetusingregisters(e.g.,
mw_h2o,mw_co2,etc.).Ifaspeciesisnotparticipatinginreaction1(e.g.,CO2inthiscase),
itsXMDOTshouldbezeroed.
3. Themolarrateforreaction2shouldbecalculated,andusedtoupdatetheXMDOTforeachspeciesinthatequation.SinceXMDOTshavealreadybeenupdatedforreaction1,thisstep
involvessummingintothesevalues,whichexplainswhyXMDOTforCO2(XMDOTC)was
zeroedinthepriorstep.
Iftherewereany3rdor4threactions,thesecouldsimilarlyhavebeensummedintothe
XMDOTvalues.Toavoidanyconfusionwhenthenumberofreactionsislarge,theXMDOTs
shouldbezeroedatthestartofthelogicblock,thenalwayssummedinto(ratherthan
replaced)soasnottooverwritetheeffectsofreactionscalculatedearlierinthesequence.
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Therearetwoplaceswheresuchreactionupdatelogiccanbeplaced:
1. HEADERSUBROUTINES:userdefinedsubroutines,whichcanthenbecalledfromFLOGIC0viaaDOloopincrementingloopID.SincetheIDofeachtankwillchangeforeachcalltothe
updateroutine,dynamictranslationroutines(e.g.,INTLMP,INTSPE)willberequiredto
converttheuseridentifierintotheinternalarraylocation.2. Networklogic:7logicassociatedwitheachnetworkelement(tanks,inthiscase).Expression
styleindirectreferencingcanbeusedintheseblocks.Forexample,VOL#thisreferstothe
volumeofthecurrenttank,PPGH#thisreferstothepartialpressurefractionofhydrogen
(speciesH)inthecurrenttank,andXMDOTH#thisreferstotheXMDOTofthesamespecies
H.
FortheSUBROUTINESapproach(whichisusedinthemodelnotbecauseitisrecommendedbutbecause
itismorewidelyaccessibletoolderversionsandexperiencedusers),theFLOGIC0blockappearsas:
do itest = 1,resol
call reformenddo
whereitest,thevalueiteratedintheDOloop,referstotheuserlumpID(from1toresol=10).Itestisa
globalvaluethatisaccessiblewithintheusersubroutineREFORMaspartoftheCALLCOMMON
commandinthatroutine(whichisinsertedasafile):
subroutine reform
call common
fstart
integer methane,water,co,co2,h2,lump
c
c reactions 1 and 2, from "Simulation of effect of catalytic
c particle clustering on methane steam reforming in ac circulating fluidized bed reformer" Shuyan et al,
c Chem Eng Jnl 139 (2008) p.136-146
c
c H=H2, W=H20, G=CO, M=CH4, C=CO2
c
c itest is assigned in FLOGIC
lump = intlmp('reactor',itest)
methane = intspe('reactor','m')
co2 = intspe('reactor','c')
co = intspe('reactor','g')
h2 = intspe('reactor','h')
water = intspe('reactor','w')
c
if(ppg(h2,lump) .le. 0.0) call abnorm(' reform ',itest,
& ' User routine REFORM cannot handle zero H2 partial pressure ')
c convert to absolute units (if not)
atemp = tl(lump)-abszro
apres = pl(lump)-patmos
c 1/Pa, except for KH20 which is unitless
KCH4 = 6.65e-9*EXP(4604.28/atemp)
7 AvailableinSinapsandFloCADVersions5.2andlater.
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KH2 = 6.12e-14*EXP(9971.13/atemp)
KCO = 8.23e-10*EXP(8497.71/atemp)
KH2O = 1.77e5*EXP(-10666.35/atemp)
DEN = 1.0 + apres*(KCH4*PPG(methane,lump)
& + KH2*PPG(h2,lump) + KCO*PPG(co,lump))
& + KH2O*PPG(water,lump)/PPG(h2,lump)
c reaction 1
c mol-sqrt(Pa)/kg-s
klc1 = 8.336e17*EXP(-28879./atemp)
c Pa^2
Kuc1 = 10266.76e6*EXP(-26830./atemp+30.11)
rxn1 = klc1*(ppg(methane,lump)*ppg(water,lump)/ppg(h2,lump)**2.5
& - apres**2*ppg(co,lump)*sqrt(ppg(h2,lump))/Kuc1)
& /sqrt(apres)/DEN**2
rate1 = rxn1*dl(lump)*vol(lump)
rate1 = (1.0-rateLag)*rate1 + rateLag*cx(lump)
xmdot(methane,lump) = -rate1*mw_ch4
xmdot(water,lump) = -rate1*mw_h2o
xmdot(co,lump) = rate1*mw_co
xmdot(h2,lump) = 3.0*rate1*mw_h2
xmdot(co2,lump) = 0.0
c reaction 2
c mol/kg-Pa-s
klc2 = 12.19*EXP(-8074.3/atemp)
c unitless
Kuc2 = EXP(4400.0/atemp-4.063)
rxn2 = klc2*(ppg(co,lump)*ppg(water,lump)/ppg(h2,lump)
& - ppg(co2,lump)/Kuc2)*apres/DEN**2
rate2 = rxn2*dl(lump)*vol(lump)
rate2 = (1.0-rateLag)*rate2 + rateLag*cy(lump)
xmdot(co,lump) = xmdot(co,lump) - rate2*mw_co
xmdot(water,lump) = xmdot(water,lump) - rate2*mw_h2o
xmdot(co2,lump) = xmdot(co2,lump) + rate2*mw_co2
xmdot(h2,lump) = xmdot(h2,lump) + rate2*mw_h2
c store key data away in otherwise unused CX, CY, CZ cells
c for ease of postprocessing, damping
c
cx(lump) = rate1
cy(lump) = rate2
c a little out of step (uses last QCHEM), and QCHEM is for both reactions,
c but ...
if(rate1 .ne. 0.0) cz(lump) = 1.e-6*qchem(lump)/rate1c
return
end
fstop
Theequivalenttotheabove,usingthenetworklogicapproach,istoplacethefollowingintheFLOGIC0
formforalltanks(whichcanbeeditedsimultaneously):
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c
c reactions 1 and 2, from "Simulation of effect of catalytic
c particle clustering on methane steam reforming in a
c circulating fluidized bed reformer" Shuyan et al,
c Chem Eng Jnl 139 (2008) p.136-146
c
c H=H2, W=H20, G=CO, M=CH4, C=CO2
c
if(ppgh#this .le. 0.0) call abnorm(' reform ',#this,
& ' User logic cannot handle zero H2 partial pressure ')
c convert to absolute units (if not)
atemp = tl#this-abszro
apres = pl#this-patmos
c 1/Pa, except for KH20 which is unitless
KCH4 = 6.65e-9*EXP(4604.28/atemp)
KH2 = 6.12e-14*EXP(9971.13/atemp)
KCO = 8.23e-10*EXP(8497.71/atemp)
KH2O = 1.77e5*EXP(-10666.35/atemp)
DEN = 1.0 + apres*(KCH4*PPGM#this + KH2*PPGH#this + KCO*PPGG#this)
& + KH2O*PPGW#this/PPGH#this
c reaction 1
c mol-sqrt(Pa)/kg-s
klc1 = 8.336e17*EXP(-28879./atemp)
c Pa^2
Kuc1 = 10266.76e6*EXP(-26830./atemp+30.11)
rxn1 = klc1*(ppgm#this*ppgw#this/ppgh#this**2.5
& - apres**2*ppgg#this*sqrt(ppgh#this)/Kuc1)
& /sqrt(apres)/DEN**2
rate1 = rxn1*dl#this*vol#this
rate1 = (1.0-rateLag)*rate1 + rateLag*cx#this
xmdotm#this = -rate1*mw_ch4
xmdotw#this = -rate1*mw_h2o
xmdotg#this = rate1*mw_co
xmdoth#this = 3.0*rate1*mw_h2
xmdotc#this = 0.0
c reaction 2
c mol/kg-Pa-s
klc2 = 12.19*EXP(-8074.3/atemp)
c unitless
Kuc2 = EXP(4400.0/atemp-4.063)
rxn2 = klc2*(ppgg#thisppgw#this)/ppgh#this
& - ppgc#this/Kuc2)*apres/DEN**2
rate2 = rxn2*dl#this*vol#this
rate2 = (1.0-rateLag)*rate2 + rateLag*cy#this
xmdotg#this = xmdotg#this - rate2*mw_co
xmdotw#this = xmdotw#this - rate2*mw_h2o
xmdotc#this = xmdotc#this + rate2*mw_co2
xmdoth#this = xmdoth#this + rate2*mw_h2
c store key data away in otherwise unused CX, CY, CZ cells for ease of postprocessing,
damping
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c
cx#this = rate1
cy#this = rate2
c a little out of step (uses last QCHEM), and QCHEM is for both reactions,
c but ...
if(rate1 .ne. 0.0) cz#this = 1.e-6*qchem#this/rate1
TheaboveisthebasisoftheSinapsmodelpfr_nl.smdlandtheFloCADmodelpfr_nl.dwg,wherethenlinthenamesreferstotheNetworkLogicoption.
Thedifferencetothetwoapproachesislargelyamatterofuserpreference.Networklogicis
expanded/translatedbySinapsorFloCADandinsertedintothespecifiedlocation(FLOGIC0inthiscase).
Notethatthekeydifferenceishowtoreferenceeachproperty:
dl(lump)inHEADERSUBROUTINES,wherelumphasbeencalculatedusingthedynamic
translationfunctionINTLMP,isequivalenttodl#thisinnetworklogic.
ppg(methane,lump)inHEADERSUBROUTINES,wheremethaneisanintegercalculatedusing
thedynamicfunctionINTSPE,isequivalenttoppgm#thisinnetworklogic.
DampingandTimeStepControl:DealingwithTemperatureSensitivities
Inspectionofthekineticratecalculationsaboverevealsthatsomeextrastepswerenecessarytoassure
steadystateconvergence:thepriormolarreactionrates(rate1andrate2)arestoredfromtheprevious
iterationinunused8lumpcoordinatesCXandCY,respectively.(Thisapproachhasaconvenientside
effect:itallowsthosevaluestobepostprocessed.)Thesepriorratesarethenusedtoslowtherateof
changeofXMDOTvaluestoencourageconvergenceinsteadystatesaccordingtotheregisterrateLag,
whichvariesfromaninitialvalueof0.5(midrangedampingviaarunningaveragebetweenthecurrent
andlastvalue)to1.0(heavydampingbytheendofthesteadystate):
rateLag=0.5+0.5*(loopct/stepNum)
wheresstepNumisthenumberofpseudotimestepsallows(usedtosetNLOOPS)andloopctisthe
currentstepnumber.ForreactionN,thisdampingtakesthegeneralformat:
rateNnew=(1.0rateLag)*rateNnew+rateLag*rateNold
Intransients,rateLagissettozero(meaningnodamping)viacasedependentregisters.Inother
words,nodampingisrequiredintransients.However,thedefaulttimesteperrortolerancefactor
DTSIZF,whichdefaultsto0.1(10%max.changepertimestepinanykeyparametersuchaspressure,
speciesfraction,etc.),mustbereducedtoatmost0.02(2%max.change)topreventoscillationsinthetimeplots.9
8 Ifbodyforceshadbeenimportant,thesevariableswouldnotbeavailableforthisusage.Eitherotheropen
variablesmustbesought,orextraregistersmustbedeclaredtoholdthememoryforeachtanksreactionhistory.9 TheexperiencedusermightbewonderingwhysimilarlyreducingRSSIZFisntavalidapproachforSTDSTL
solutions,avoidingtheneedforrunningaveragedamping.ThereasonisthatsmallRSSIZFvalueswouldrequire
excessiveiterations(highLOOPCT)unlesslargevaluesareusedinitially.Moreimportantly,theconvergence
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Whiletheapproachdiffersbetweensteadystate(STDSTL)andtransient(TRANSIENT)solutions,the
causeforthisunusualstepisthesame:theextremetemperaturedependenceofthereactionrates,
whichistobeexpectedbecauseofthepresenceofexponentialintheArrheniusrateequation.
Specifically,theXMDOTvaluesarenotadjustedimplicitlybythecodeasafunctionoftemperature.
Rather,XMDOTvalues
are
assumed
constant
over
each
solution
step.Iftoolargeofastepistaken,the
temperatureinthetankwillchangetoomuchandtheassumptionofconstantreactionratesisinvalid:
theabsolutevalueofthepartialderivativeofXMDOTiwithrespecttoTListoohigh.Therefore,either
thetimestepmustbereducedinanticipationofasignificantchangeinXMDOT(thetransient
approach),ortheXMDOTvaluemustbedampedtopreventbinaryoscillations(thesteadystate
approach).
SteadyStateResults
With3timesasmuchsteamasneededforstoichiometricconditions(SteamX=3),andgivenafeed
temperatureof800Candwalltemperaturesof800Caswell,theresultingtemperaturegradientsat
steadystate
are
shown
below.
Inthediagramabove,thefluidspeciesaremixedinjunctionreactor.1001(withoutreactionsyet
permitted),theninjectedattheleftofthediagram,exitingattheright.Thetemperaturesdroptoabout
550Cattheinlet,beforerisingtoabout780Cattheoutlet.Ifalongerreactorhadbeenused,theexit
temperatureswouldhavebeenclosertothewalltemperatureof800C.Iffinerspatialresolutionhad
beenused(forexample,20segmentsinsteadof10),theresultswouldhaverevealedthatthecoldest
spotinthereactorisnotexactlyattheinlet,butisinsteadlocatedafewcentimetersdownstream
whereendothermicreaction#1reachesitspeakrate.
Thecorrespondingpartialpressurefraction(molefraction)forhydrogenisshownnext.
checkerwouldstillpreventconvergencefrombeingdeclaredattheendoftherunsinceitalsocheckstheabsolute
sizeofthepseudotimestepasanindicationofahavingachievedatimeindependentstate.
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Recallingthepresenceofexcesssteam,themolefractionofhydrogenproducedisabout56%inthe
outletstream.
Steadystateanalysesareakeytoolforsizing,sensitivitystudies,etc.Recallthat,unlikemost
SINDA/FLUINTmodels,thetypeofsteadystatesolutionusedforchemicalreactionsisnotinsensitiveto
guessedinitialconditions.Therefore,eithertheruntimeallowed(stepNum)mayhavetobeenlarged,or
moreaccurateinitialconditionsmayneedtobeguessed(registersminit_h,minit_c,etc.),orboth.ForparametricsweepsorSolverruns(sizing,correlationtotest,etc.),theguessedinitialconditionsshould
reflectthefirstcasetobesolved,withonlymodestincreasesinstepNumtoaccommodatevariations
thatmightbeexperiencedduringwhilesolvingforvariedconditions.Moresignificantincreasein
stepNummayberequiredforstatisticaldesignruns(usingtheReliabilityEngineeringModule)sincethe
variationsbetweensamplingsarenotnecessarilygradual:thepriorsteadystateanswersmightnotbe
goodinitialconditionsforthenextsamplingruntobemade.
TransientDemonstrationEvent
AkeyfeatureofSINDA/FLUINTreactingflowmodelingistheabilitytosimulatetransients,includingfast
transienteventssuchaspressurewaves,flowinstabilities,controlsystemactions,andvalvedynamics.
Asademonstrationofthesecapabilities,thesteadystatesolutiondescribedinthelastsectionwillbe
usedastheinitialconditionforanarbitraryevent:thereductionofsteaminjectiontostoichiometric
conditions:athreefolddecreaseinsteamfeedattimezero,withanapproximatelytwofoldreductionin
overallflowrate.
Normally,atransientcaseisrunsimplybyaddingacalltotheTRANSIENTsolutionroutinefollowingthe
calltothesteadystatesolution(STDSTL)withinOPERATIONS.Inthesamplemodelsassociatedwiththis
document,thesteadystateandtransientanalysesareperformedastwoseparatecases:pfrand
pfrTransient,respectively.ThepfrTransientcasestartsbyreadingbacktheinitialconditionsleftforitby
thepfrcase,whichmusthavebeenexecutedbeforehand.Ifsomedimensionorboundaryconditionis
changedthataffectsbothcases,theyshouldbothbeselectedandreruntogether.
Theplotbelowshowsthetransienttemperatureresponseofthereactortoastepreductioninsteam
injection.Astheflowratediminishes,thetemperaturesattheexit(e.g.,TL10,thetemperatureoflump
#10)risereflectingtheirtemporarystagnationnexttoahotwall.Neartheinlet(TL1)thetemperature
actuallygoesdownbeforerisingsincethereislesssteamtocoolfrom800Cbuttheendothermic
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reactioncontinuesataboutthesamerate.Asanewsteadyconditionisestablished,thenetchangeisa
warmingofthemiddleofthereactorandthereforemorecompletereformingoftheinflowingmethane.
Analternativeviewofthissameeventisdepictedbelowintermsofthepartialpressurefraction(mole
fraction)ofhydrogengas.Astheexcesssteamiswithdrawn,thefractionofhydrogenjumpsfirstattheinlet,andthisfrontcanbeseenprogressingthroughthereactorforthefirst0.16seconds.Thereactor
shiftsfromproducing55%H2tomoreoptimum72%(themaximumpossibleis75%).
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ValidationwithAspenPlus
LikeNASAsCEA,AspenTechsAspenPluscanbeusedtopredictequilibriumconstituentfractionsbased
ontheminimizationofGibbsfreeenergy.Inaddition,theenergyinputsneededtosustainan
isothermalprocesscanbecalculated,ascantheenergyrequiredwhenthefeedtemperatureis
substantiallycolderthantheproducttemperature.Finally,thetemperaturedropexperiencedbyhot
steamandmethaneinjectedintoanadiabaticreactorcanalsobecalculated.
ItisimportanttorememberthatalloftheAspenPluscalculationsassumedequilibriumconditionsto
exist,whereastheSINDA/FLUINTpredictionsweremadebysimulatingfiniteratereactionsasaprocess.
Inotherwords,tobeabletopredicttheheataddedtoastoichiometricstreaminjectedat25Cand
heatedto(say)1200C,thereactorwallsweresetto1200Candsufficientreactorlengthwasaddedas
neededtoprovidetheheattransferrequiredtoaccomplishthistask.Theexitstatewasthencompared
withAspenPluspredictions,andtheheataddedtothestreamviaheattransferwastalliedtogeneratea
totalnetpower.
Comparedwiththemodelspresentedabove(andincludedwiththissample),uptothreedifferences
weremadeinthevariationofthedemonstrationmodelthatwasusedtogeneratecomparisonresults:
1) Thelengthwasincreased(upto40m)
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2) Theresolutionwasincreased(from10segmentsto20)3) Atwophasedescriptionofwater(REFPROPderivedf6070_water.inc)wassubstitutedwhen
25Cinletconditionswereused,suchthatthefactthatwaterisliquidatSTPcouldbe
included.
Theresultsofthisvalidationexercisearesummarizedbelow.
Sixdiabaticcaseswerecompared,threewithbothfeedandproductsatthesametemperature(500C,
800C,and1000C),andthreewithfeedat25Cwhileproducttemperaturesremainedthesame.The
predictedspeciesmolefractionsaretabulatedbelow,alongwiththetwopowerrates(QfpforTf=Tp,
andQ25forTf=25C).Thedifferencesareexpressedaspercentages,whicharecalculatedbasedontotal
massforspeciesfractions.
500C 800C 1000C
Aspen S/F diff. Aspen S/F diff. Aspen S/F diff.
CH4 0.3203 0.3188 0.14% 0.0269 0.0262 0.07% 0.0009 0.0009 0.00%
H2O 0.2493 0.2475 0.18% 0.0199 0.0196 0.03% 0.0008 0.0008 0.00%
CO 0.0189 0.0193 0.04% 0.2296 0.2304 0.07% 0.2495 0.2495 0.00%
CO2 0.0710 0.0713 0.03% 0.0069 0.0066 0.04% 0.0001 0.0001 0.00%
H2 0.3406 0.3431 0.25% 0.7166 0.7173 0.06% 0.7488 0.7487 0.00%
Qfp(kJ/mol) 126.99 128.13 0.89% 319.45 318.64 0.26% 393.94 393.49 0.11%
Q25(kJ/mol) 42.18 42.70 1.22% 201.77 202.14 0.19% 225.40 224.58 0.36%
Notethattheagreementimprovesasthetemperaturerises(fasterreactionratesmakingequilibriuma
morelikelyresult),butisverygoodevenforthe500Ccaseconsideringthatthetwoprogramsdonot
usethesameapproach(theAspendataassumesequilibrium,andthisparticularSINDA/FLUINTrunuses
reactionkinetics),nordotheyusetheexactsameequilibriumconstants(thoughapparentlytheyare
veryclose),andthattheenthalpyfunctions(fluidproperties)aredifferentaswell.
Threemorecaseswerecomparedbasedonisothermalprocesses,withinlettemperaturesbeing500C,
800C,and1000C.Equalmolefractionsofmethaneandsteamwereused:stoichiometricconditions.
Theresultsareshownbelow.Again,thespeciesfractiondifferenceswerecalculatedonthebasisoftotal
mass.Thetemperaturedifferenceswerecalculatedonthebasisoftemperaturedropfromtheinlet.
500C 800C 1000C
Aspen S/F diff. Aspen S/F diff. Aspen S/F diff.
CH4 0.4342 0.4346 0.04% 0.3438 0.3430 0.08% 0.2842 0.2828 0.14%
H2O 0.4020 0.4026 0.06% 0.2775 0.2765 0.10% 0.2103 0.2087 0.16%
CO 0.0006 0.0006 0.00% 0.0118 0.0120 0.02% 0.0340 0.0345 0.06%
CO2 0.0323 0.0320 0.02% 0.0663 0.0665 0.02% 0.0739 0.0741 0.02%
H2 0.1309 0.1301 0.08% 0.3006 0.3020 0.14% 0.3977 0.3999 0.23%
Tprod(C) 367.5 368.3 0.61% 477.6 476.9 0.22% 531.3 530.3 0.21%
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DemonstrationUseofaCEA-derivedEquilibriumFluid
ItisnoteworthythattheAspenPlusequilibriumcalculationyieldedresultssimilartoafiniterate
approach,evenattemperaturesaslowas370C.Thisobservationmeansthatavariablemolecular
weightequilibriumfluidmaybeappropriate,atleastwhenthefeedratiosarenotalteredduringthe
courseofananalysis.10
Todemonstratethismodelingapproach,avariationoftheabovemodelwasmadeandisavailablein
Sinapsform.
First,CEAwasrunforastoichiometricmixtureofwaterandmethane,restrictingtheresultingmixture
toonlythefivespeciesusedintheoriginalanalysis(i.e.,excludingcarbon,otherminorspecies,ions,
etc.).ThistableofCEAequilibriumdatawasconvertedintoasingleSINDA/FLUINTFPROPblockusing
thecea2fproputility,11 andtheheatofformationwassettobethesameastheenthalpyofthisnew
fluidatSTP.
ThisnewfluidwasthenusedinthePFRmodelasspeciesE,suchthatwhenM(methane)andW
(water)arereacted,theyresultinthisvariableweightequilibriumfluidasfollows:
CH4+H2O E (equivalentreaction)
ThespeciesH(hydrogen),G(carbonmonoxide),andC(carbondioxide)arethereforeeliminatedfrom
themodel.NotethatmethaneandwaterconstitutesignificantportionsoffluidE,especiallybelow
600C.
Byassumingequilibrium,thekineticratecalculationsareeliminated.Infact,reactionsinallbutthefirst
tankareeliminatedaswell:downstreamreactionsaretakencareofbytemperature andpressure
dependentshiftswithintheequilibriumfluiditself.WhiletheutilityEQRATEcouldhavebeenusedtoset
XMDOTvalues,insteadthereactionratesinthefirsttank(tank1)weresetinFLOGIC0applyinga
reactionefficiencybasedoninflowingmethane,whichwaspresumedtobethelimitingreagent.A
newregisterconvert,setto0.999,declaresthat99.9%ofincomingmethanewillbecombinedwithan
equalmolaramountofwaterandreplacedbyanequalmassofequilibriumfluidE. Inflowingmethane
massflowiscalculatedastheproductofthemassfractionupstreaminjunction1000,xgM1001and
theincomingmassflowrateinpath3,fr3:
xmdotM1 = -xgM1001*fr3*convert
xmdotW1 = xmdotM1*mw_h2o/mw_ch4
xmdotE1 = -(xmdotM1+xmdotM1)
Becauseexcesssteamaffectstheequilibriumpoint,theequilibriumfluidEshouldonlybeusedto
replaceastoichiometricmixtureofmethaneandwater.Indeed,whensuchastoichiometric(SteamX=1)
10Excessoxidizer(e.g.,air)canusuallybeaddedorsubtractedfromanequilibriumfluidrepresentingthehot
productsofcombustion.Thiswouldonlybetrueforamethanereformerinthespecialcaseoftheadditionor
subtractionofachemicallyinertsubstance. Seewww.crtech.comandtheSINDA/FLUINTUsersManualforfurther
details.11 http://www.crtech.com/EQfluids.html
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mixturewastested,theresultingtemperaturesinadiabaticcasesmatchedverywellagainsttheAspen
PlusanalysisandfullreactingflowmixtureSINDA/FLUINTanalysispresentedabove.
Asafirstapproximation,iftheexcesssteamcouldbeassumedtobeindependentoftherestofthe
mixture,
CH4+3H2O E+2H2O (equivalentreaction,excesssteam:SteamX=3)
thentheSteamX=3steadystatecasepresentedinapriorsectioncouldberepeatedwiththe
equilibriumfluidapproach,yieldingsimilar(butnotcompletelyequivalent)results:
Ifthemolarratioofsteamtomethaneweretoremainat3:1,amoreaccurateapproachwouldbeto
createanewequilibriumfluidEforthatscenariousinganotherCEArunandFPROPconversion(whichis
atriviallyeasyprocess):
CH4+3H2O E (equivalentreaction,SteamX=3,newequilibriumfluid)
Usinganequilibriumfluidapproachreducesthenumberofspeciestrackedfrom5to3,andalso
eliminatestheextremesensitivityofthereactionratestotemperaturebyassumingtheyreinfinitely
large.Theresultisasignificantincreaseincomputationalspeed,andmorerobustconvergencethatis
muchlesssensitivetocoarselyguessedinitialconditions.
However,theabilitytoresolvetheinternaldetailsoftheequilibriumfluidarelostasacompromise.For
example,onecannolongerplotthefractionofhydrogensincetheactualcurrentamountofhydrogenis
hiddenwithinthechemicalcontrolvolumethattheequilibriumfluidrepresents.Toovercomethis
limitation,aseparateCEAruncouldbemadeusingtheSINDA/FLUINTpredictedtemperaturesand
pressurestocalculatethefractionalconstituentsoftheequilibriumfluidatoneormorepoints.12
Whenusedwithappropriatecautions,validatingassumptionsasneeded,theequilibriumfluidmethodcanbeapowerfulcompanionapproachtoperformpreliminarysizingandsensitivityanalyses,for
example.Ifkineticratesarenotknown,itmightbetheonlyapproachavailableforfirstorder
estimationsandbracketinganalyses.
12FutureplanscallfortheinclusionofallCEAcapabilitieswithinSINDA/FLUINT,whichwouldeliminatethis
additionalpostsimulationstep.
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SideNote:Carbon(coke)Formation
Atonebarpressure,withequalmolarinputsofmethaneandsteam(stoichiometricconditions),CEA
predictsthefollowingmolefractionsversustemperature(indegreesC).
Asisevidencedbytheaboveequilibrium(Gibbsfreeenergyminimization)analysis,thefractionof
carbon(coke,graphite)peaksatabout600C,atwhichpointtherearemoremolesofcarboninthe
mixturethaneitherCOorCO2.Whilethepresenceofcarbonhasbeenneglectedinthisdemonstration
case,itclearlymustbeincludedforamorecompletetreatment.Therefore,thissectionprovidesbrief
notesonhowsuchamoredetailedmodelcouldbeconstructed.
Toincludecarboninthemethanereformingmodel,anotherspeciesmustbeintroduced:onethatdoes
notcontributetothegaspressure.EventhoughtherearenosolidspeciesperseinSINDA/FLUINT,a
9000seriesnonvolatileliquidisanadequatesubstitute,withfakeviscosityandsurfacetensionvaluesas
neededtocomplywithinputrequirements.Bydefault,thisfluidwillbeassumedtomixhomogeneously
withtheremainingspecies.
Threemorechemicalreactionswouldneedtobeincluded:
CH4 C+2H2 (reaction3)
2CO C+CO2 (reaction4)
CO+H2 C+H2O (reaction5)
Equations2530ofthereferencedpaper(Shuyan,et.al.)providetherelevantequilibriumKconstants
andpreexponentialktermsforthesereactions.
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