methane reforming demonstration problem

7/31/2019 Methane Reforming Demonstration Problem

1/19

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.


2/19

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


3/19

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.


4/19

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.


5/19

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).


6/19

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.


7/19

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.


8/19

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):


9/19

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


10/19

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


11/19

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.


12/19

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


13/19

reactioncontinuesataboutthesamerate.Asanewsteadyconditionisestablished,thenetchangeisa

warmingofthemiddleofthereactorandthereforemorecompletereformingoftheinflowingmethane.

Analternativeviewofthissameeventisdepictedbelowintermsofthepartialpressurefraction(mole

fraction)ofhydrogengas.Astheexcesssteamiswithdrawn,thefractionofhydrogenjumpsfirstattheinlet,andthisfrontcanbeseenprogressingthroughthereactorforthefirst0.16seconds.Thereactor

shiftsfromproducing55%H2tomoreoptimum72%(themaximumpossibleis75%).


14/19

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)


15/19

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%


16/19

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


17/19

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.


18/19

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.


19/19

methane reforming demonstration problem

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