Review articles on the study of combustion. Combustion Theory and Modelling. Volumes Part 10 1-13

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Mechanism analysis with ILDMs for H combustion on Pd catalysts
2
S. -A. S. Reihani a; G. S. Jackson a
a Department of Mechanical Engineering, University of Maryland College Park, MD, USA
To cite this Article Reihani, S. -A. S. and Jackson, G. S.(2006) 'Mechanism analysis with ILDMs for H combustion on Pd
2
catalysts', Combustion Theory and Modelling, 10: 1, 1 — 20
To link to this Article: DOI: 10.1080/14685240500260596
URL: http://dx.doi.org/10.1080/14685240500260596

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CombustionTheoryandModelling
Vol.10,No. 1,February2006,1–20
Mechanism analysis with ILDMs for H combustion
2
on Pd catalysts
S.-A.S.REIHANIand G.S.JACKSON∗
DepartmentofMechanicalEngineering,UniversityofMarylandCollegePark,MD20742,USA
(Received30June2004;infinalform13December2004)
Thispaperexplorestheusefulnessofintrinsiclow-dimensionalmanifolds(ILDMs)forinterpreting
complexbehaviorofcatalyticcombustionchemistry.Thermodynamicallyconsistentsurfacechem-
istrywithrepulsiveinteractionpotentialsforsomesurfacespeciesisincorporatedwithameanfield
approachandvalidatedagainstearlierexperimentalstudiesforlowtemperaturecombustionofH2over
supportedPd-basedcatalysts.Twosimilarsurfacechemistrymechanisms,modifiedfromanearlier
study,capturethenegativeinfluenceofgas-phaseH2OonH2conversionandthenonlinearbehaviorof
0 H2conversionwithrespecttoH2concentration.Tofurtheranalyzethesemechanismsandtheirdiffer-
01 ences,thedynamicalresponseofadifferentialuniformporouswashcoattofixedgas-phaseflowover
2
theexternalwashcoatsurfaceisstudied.Theinteractionpotentialsbetweensurfacespeciesresultin
y
ar complexbehaviorincludingstrongoscillationsforsomeconditionsandrapiddecompositionofstates
u
n duringapproachtosteady-stateconversion.ThedifferentialreactorsimulationsrevealILDMswith
a
3 J slowmodesinthetransientcatalyticcombustion.H2Oconcentrationintheexternalflowdoesnot
2 significantlyaltertheslowestmodes,butdoesimpacttherateorprogressalongtheILDMtrajectories.

51 Thesystemeigenvaluesandeigenvectorsidentifycriticalaspectsofthethermochemistrythatcan
:
7 guidefurtherexperimentalandcomputationalstudiesformechanismrefinementorreduction.
0

:
t
A Keywords: Catalyticcombustion;Palladium;Hydrogen;Surfacechemistry;ILDM
d
e
d
a
o
l
n
w
o
D 1. Introduction
Uncertainties inthethermodynamicsandrateparametersgoverningsurfacechemistrylimit
theeffectivenessofmanysurfacemechanismstoanarrowrangeofconditions.Thethermo-
chemistryofsurfacespeciesincatalyticcombustioncanbeinfluencedbystronginteraction
potentialsbetweenadsorbedspecies.Interactionpotentialscanleadtosegregationofsurface
species, as illustrated in CO and H oxidation on Pt using Monte-Carlo simulations [1, 2].
2
However, under conditions where surface adsorbates are small and relatively mobile, mean
fieldapproximationsmayprovideacomputationallyefficientapproachformodelingcomplex
phenomenaoncatalystsurfaces,suchasoscillatory[3]orhystereticreactionrates[4]observed
incombustiononPd-basedcatalysts.
NumerousapplicationsofPd-basedcatalyticcombustionhavemotivatedrecentstudiesto
buildsurfacechemistrymechanismswithspeciesinteractionpotentialsforPd-basedcatalysts.
ArecentreviewofPd-basedcatalyticcombustion[5]providesathoroughdiscussionofthe
∗Correspondingauthor.E-mail:[e-mail]
CombustionTheoryandModelling
ISSN:1364-7830(print),1741-3559(online)(cid:2)c 2006Taylor&Francis
http://www.tandf.co.uk/journals
DOI:10.1080/14685240500260596
2 S.-A.S.ReihaniandG.S.Jackson
outstandingquestionsraisedbyexperimentalstudiesregardingcomplexinteractionsofO,H
andC speciesonPd/PdO surfaces.Recentstudieshavedevelopedmean-fieldapproaches
1 x
tosimulatehysteresisinoxidation/reductioncyclesofPd/PdO catalysts[6]andtheimpact
x
ofstoichiometryonlowtemperatureoxidationofH overPd-basedcatalysts[7].Developing
2
therequisitesurfacethermochemistryforcatalyticcombustionofhydrocarbonsonPd-based
catalysts will be predicated by the identification of the critical processes and equilibria in
smaller subset mechanisms for Pd/O /H [7] as well as Pd/O /CO [3]. This paper uses in-
2 2 2
trinsiclow-dimensionalmanifold(ILDM)analysistoinvestigatethecomplexinteractionsof
Pd/O /H inproposedcatalyticcombustionmechanismstogainunderstandingforvalidating
2 2
themechanisms.
The application of ILDMs has been well studied for gas-phase chemistry as introduced
byMaasandPope[8].However,limitedworkhasbeenpresentedontheuseofILDMsfor
complex surface chemistry with one notable exception [9] where ILDMs were applied to
reduce a surface mechanism for CH oxidation over Pt. The current paper employs ILDMs
4
for interpreting surface chemistry mechanisms for low temperature combustion of H over
2
supportedPd-catalysts.Twoalternativemechanismsaremodifiedfromapreviouslypublished
mechanism[7],anddowellatcapturingtheeffectsofH OonH conversionunderconditions
2 2
of excess O . A model problem based on a uniform porous washcoat-supported catalyst is
2
established as a dynamical system for capturing the coupling of surface chemistry with the
0
1
0 gas-phaseinadifferentialreactor.ILDMsassociatedwiththesurfacechemistryareidentified
2

ry andassociatedwiththecatalystbehaviorinthedifferentialreactor.
a
u
n
a
J

3
2
2. Surfacechemistrymechanismandvalidation
1
5
:
7
0
: Theefforttodevelopadetailedmechanismforlow-temperatureH oxidationonsupported
t 2
A
Pd-basedcatalystbuildsontwopreviousstudies.ThefirstisanextensivestudywithTGA/MS
d
e
oad experiments of supported polycrystalline Pd oxidation and reduction to validate a Pd/PdOx
nl mechanism[6].ThesecondstudyinvolvesexperimentalinvestigationsofH oxidationover
w 2
Do supportedPdcatalystsattemperatureslessthan250◦C[7].Thisstudyusedaγ-Al O washcoat
2 3
to support a Pd catalyst in a configuration similar to that reported earlier [4] and focused
on low equivalence ratio (ϕ) conditions where the catalyst maintains an oxidized state. A
thermodynamicallyconsistentH oxidationmechanismwasproposed,whichusedthesurface
2
energies for Pd–O species on a fully oxidized PdO sub-surface from the validated Pd–O
2
mechanism.Thepreliminarymechanismcapturedlight-offtrendsbutfailedtoaccountforthe
inhibitionofH Oandtheimpactofϕonlowtemperatureconversion(lessthan150◦C).Some
2
experimentalresultsfromthatstudyareplottedinfigure1(both(a)and(b)),whichshowsnear
steady-stateconversionforϕ =0.05and0.1,inletmolefractionratiosofXN2,in/XO2,in =20,
andaninletvelocityu =10m/sfora2.0cmlongbed.Thiscorrespondstoaspacevelocity
in
of 500 s−1. Simulation parameters relevant to the experimental characterization include a
washcoatthicknessδ of30µm,washcoatporosityεof0.5,andanannularchannelheight
wc
aroundthewashcoatof0.068cm.
These experimental results are compared to predictions from a catalytic channel model,
which was used both in its original form with a radially uniform washcoat [7], indicated
by the schematic of an axial slice of the model in figure 2(a), and in a more refined form
with a radially discretized washcoat as described in detail elsewhere [9], and illustrated by
the schematic in figure 2(b). Parametric studies with the axially-discretized channel model
wereemployedtoassesshowthesurfaceadsorptionenthalpiesandexpectedsurfacespecies
interaction potentials can be adjusted within constraints of experimental observations from
previousliteraturetosimulateaswellaspossibletheobservedtrendsinH conversionwith
2
MechanismanalysiswithILDMsforH2combustiononPdcatalysts 3
0
1
0
2

y
r
a
u
n
a
J

3
2

1
5
:
7
0

:
t
A

d
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d
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D
Figure1. Comparisonofexperimentalconversion(after20minofruntime)vs.Tinandcatalyticchannelmodel
predictions:(a)withMechanismAusinguniformanddiscretizedwashcoatmodels;and(b)withMechanismB
usinguniformanddiscretizedwashcoatmodels.DryconditionsreferstoXH2O,in=0.00andwetconditionsrefers
toXH2O,in=0.022.
respecttoϕ and XH2O,ext.Detailsofthesimulationsarereportedelsewhere[7,10]andwill
notbediscussedindetailhere.
Thecomparisonsinfigure1betweencatalyticchannelmodelpredictionswithexperimen-
tal observations illustrate the strengths and deficiencies of the mechanisms in capturing the
kinetically controlled phenomena observed in the low temperature H catalytic combustion
2
overthePd-basedcatalysts.Theexperimentalresultsshowthatbeforemass-transfer-limited
4 S.-A.S.ReihaniandG.S.Jackson
Figure2. Schematicillustratinganaxialslicefromthechannelflowmodel(orthedifferentialreactorfortheILDM
analysis):(a)withauniformporouscatalyticwashcoatmodel;and(b)witharadiallydiscretizedwashcoatmodel.
conversions are reached for T ≥150◦C, H O inthe inlet reduces conversion substantially
in 2
except at T =50◦C where conversion is very low. For ϕ =0.1, both mechanisms capture
in
thistransitiontohighmass-transferlimitedconversionandmodeltheimpactofH Oonthe
2
kineticallycontrolledconversionatlowerT .However,simulationwithbothmechanismsat
in
ϕ =0.05andT ≥150◦Cunder-predictthehighH conversionobservedintheexperiments.
in 2
0 Analysis of results indicates that inaccuracies in the channel-to-washcoat diffusion model
1
0
2 basedonSherwoodnumbercorrelations[11]canonlyplayaminorroleinthesediscrepancies

y
ar asanimposed50%increaseintheSherwoodnumbersleadstoonlya10%riseinpredicted
u
Jan H2conversionforthekineticallysensitiveconditions.Thus,theunder-predictionisprimarily

3 drivenbythekinetics,andtheexternalchanneltowashcoattransportplaysonlyasecondary
2

51 roleinthemodelingresults.Thissuggestsroomforimprovingthemechanisms.Nonetheless,
:
07 thequantitativeagreementforϕ =0.1andatlowTin forϕ =0.05combinedwiththequal-
t: itative agreement for the rise in conversion between T =125◦C and 150◦C for ϕ =0.05
A in

ded indicatesthatthemechanismsprovideaframeworkforimprovingmodelingpredictionsofH2
loa catalyticcombustionforkineticallysensitiveconditionsatlowϕandTin.
n
w It is noted that both the discretized (15 radial slices) and the uniform washcoat models
o
D
predict similar trends. The higher conversion from the channel model with the discretized
washcoatincomparisontotheuniformwashcoatcanbeattributedtothevariationsthrough
thedepthofthewashcoatallowingforhigherreactionratesintheouterregionofthewashcoat
wherethecatalystismosteffectivelyutilized[10].
Forthemodelpredictionsinfigure1,mechanismmodificationsweremadefromaprevious
Pd–H oxidation mechanism [7], particularly in the thermochemistry of the H-containing
2
surface species. The only changes to the previously validated Pd–O subset [6] of the H
2 2
combustion mechanism arise from additional interaction potentials between H-containing
species and the original Pd–O species. Changes in the surface species’ enthalpies h and
k
their interaction potentials εjk lead to changes in the activation energy barriers Eact,i and
their coverage dependencies that arise when reversibility of the reactions are enforced for
thermodynamicconsistency.Thesecoveragedependenciesaregovernedbytherelationship
between Eact,i forreversiblesurfacereactionsasgivenhere:
(cid:4) (cid:4) (cid:5)(cid:5)
(cid:1)(cid:2) (cid:3) (cid:1) (cid:1)
Eact,i,r = Eact,i,f − νkih0k − νki h0k + (εkjθj) forithreaction (1)
k,g k,s j,s
Inequation1,h0 aretheenthalpiesofspeciesexcludingallinteractionpotentialsε .ν
k jk ki
arethestoichiometriccoefficientsfortheithreaction.Thesummationsrepresenttheheatof
reactionderivedfromameanfieldapproximation,whichincludesinteractionpotentials.
MechanismanalysiswithILDMsforH2combustiononPdcatalysts 5
Table 1. Surfacethermodynamicsrelativetostandardgasphaseenthalpies.Speciesdescriptions
givenin[7].
H0forMechanismA h0forMechanismB
k k
Species (inkJ/gmol) (inkJ/gmol)
Pd(s) 0.0 0.0
Pd–O(s) −115.0+57.5θO(s)+29.0θOH(s) −115.0+57.5θO(s)+29.0θOH(s)
Pd–O(sb) −115.0 −115.0
Pd(sb) −35.0+208θPd(sb)+147θH2O(sb)+ −35.0+208θPd(sb)+208θH2O(sb)
208θH(sb)+104θOH(sb) +104θH(sb)+104θOH(sb)
Pd–O2(sb) −105.0 −105.0
Pd–H(s) −42.0+8.θH(s) −42.0+8.θH(s)
Pd–OH(s) −214.0+29.0θO(s)+14.5θOH(s) −214.0+29.0θO(s)+14.5θOH(s)
Pd–H2O(s) −302.0 −302.0
Pd–H(sb) −57.0+208θPd(sb)+147θH2O(sb)+ –52.0+104θPd(sb)+104θH2O(sb)+
208θH(sb)+104θOH(sb) 52θH(sb)+52θOH(sb)
Pd–OH(sb) −229.0+104θPd(sb)+ −224.0+104θPd(sb)+104θH2O(sb)
73.5θH2O(sb)+104θH(sb)+ +52θH(sb)+52θOH(sb)
52θOH(sb)
Pd–H2O(sb) −332.0+147θPd(sb)+104θH2O(sb) –322.0+208θPd(sb)+208θH2O(sb)
+147θH(sb)+73.5θOH(sb) +104θH(sb)+104θOH(sb)
0
1
0 ThesurfacechemistrymechanismsincludedifferentsurfacePd–Oatominteractions[12]:
2

ry (1)surfacePdoxide(O(sb))and(2)chemisorbedOatomonPdmetal(O(s)).Theinclusion
a
nu ofdifferentPd–OspeciesalsoforcesthemechanismtoincorporatetwoPd–Hsurfacespecies
a
J
inagreementwithpastexperimentalstudies[13]:(1)H(sb),whichisaHatomrestingina
3
2
1 Pdoxidevacancyand(2)chemisorbedH(s).SimilarlydifferentPd–OHsurfacespeciesand
5
07: Pd–H2O species are incorporated. Surface species enthalpies relative to zero energy levels
: (defined by standard gas-phase enthalpies and pure Pd metal) are presented in table 1. The
t
A
surface thermodynamics for the two mechanisms (A and B) are derived from a parametric
d
e
ad study for tuning the mechanisms, where uncertain interaction potentials were varied within
o
nl reasonablelimits.Thetwomechanismsrepresentsomevariationthatcanbetoleratedwithin
w
o
D theuncertainsurfacethermochemistrywithoutsignificantlyalteringthechannelflowmodel
predictions. The difference between the two thermochemistries are the decreased stability
of OH(sb) and H O(sb) in Mechanism B and changes in the repulsive energies of H(sb)
2
andH O(sb).Theself-repulsionsforchemisorbedO(s)andH(s)arewelldocumentedinthe
2
literature [14]. Repulsions associated with the (sb) species are associated with the electron
deficiencyoftheunsatisfiedoxidevacancy,andtheirrelativestrengthsarenotreadilyfound
withoutdetailedatomisticmodelingwhichisanareaofongoingresearch[15].Thecurrent
mechanismsassumethatrepulsiveinteractionsfor(sb)speciesdependupontheextentthatthe
adsorbatesalleviatethelocallyelectron-richconfigurationofPd(sb).Inthisregard,asingle
OH(sb)isgivenhalftherepulsiveforceofPd(sb).TherepulsiveenergiesassociatedwithH(sb)
andH O(sb)areuncertainandwerevariedbetweenthetwomechanismsasindicatedintable1.
2
The two surface reaction mechanisms, presented in table 2, have the highest sensitivity
for H conversion toward adsorption/desorption reaction rates. Reversible surface reactions
2
help establish the equilibrium surface site fractions, which influence adsorption rates. The
mechanisms differ from the previously reported mechanism [7] in two ways. Firstly, the
increasedstabilityoftheH O(sb)andOH(sb)speciesonisolatedvacanciesresultsinahigher
2
desorptionbarrierforH Ofromtheoxidesurface.Secondly,repulsiveinteractionsforH O(sb)
2 2
andOH(sb)areincluded.
StickingcoefficientsforbothO andH wereassumedtodecaywithT−0.5 tocapturethe
2 2
observeddropinO stickingcoefficientwithT [16].Predictedconversiondependsstrongly
2
on the ratio of H adsorption to O adsorption on both oxide vacancies and metallic sites.
2 2
6 S.-A.S.ReihaniandG.S.Jackson
Table 2. Pd–O2–H2surfacechemistrymechanismusedinnumericalmodel.
Aorstick Eact(kJ/mol) Eact(kJ/mol)
Reactions coefficient forMechanismA forMechanismB
Adsorption/desorptionreactions
1f)O2+2Pd(s)⇒2O(s) 0.8∗T−0.5 0.0 0.0
1r)2O(s)⇒O2+2Pd(s) 5.7∗1021 230–115θO(s) 230–115θO(s)
2f)O2+Pd(sb)⇒O2(sb) 1.0∗T–0.5 0.0 0.0
2r)O2(sb)⇒O2+Pd(sb) 1.0∗1013 70 70
3f)H2+2Pd(s)⇒2H(s) 6.4∗T–0.5 0.0 0.0
3r)2H(s)⇒H2+2Pd(s) 5.7∗1021 84–16θH(s) 84–16θH(s)
4f)H2+Pd(sb)+O(sb)⇒H(sb)+OH(sb) 8.0∗T–0.5 0.0 0.0
4r)OH(sb)+H(sb)⇒H2+Pd(sb)+O(sb) 5.7∗1021 136+Ca4r 126
5f)H2O+Pd(s)⇒H2O(s) 0.50 0.0 0.0
5r)H2O(s)⇒H2O+Pd(s) 1.0∗1013 60.2 60.2
6f)H2O+Pd(sb)⇒H2O(sb) 0.50 0.0 0.0
6r)H2O(sb)⇒H2O+Pd(sb) 1.0∗1013 55.2+Ca6r 45.2
Reversiblesurfacereactions
7)O(s)⇔O(sb) 5.0∗1011 90 90
8)O2(sb)+Pd(sb)⇔2O(sb) 5.7∗1021 0.0 0.0
9)O2(sb)+Pd(s)⇔O(sb)+O(s) 5.7∗1021 185–57.5θO(s) 185–57.5θO(s)
10)H(s)+Pd(sb)⇔H(sb)+Pd(s) 5.7∗1021 50 50
11)H(s)+O(s)⇔OH(s)+Pd(s) 5.7∗1021 45 45
0
y 201 1123))HO(Hs)(s+)+OHOH(s)(s⇔)⇔H2HO2(Os)(s+)+PdO(s(s)) 55..77∗∗11002211 15052 15052
uar 14)OH(sb)+Pd(s)⇔H(s)+O(sb) 5.7∗1021 102+8θH(s) 97+8θH(s)
Jan 1165))OHH(s()s+b)O+HP(sdb(s)b⇔)⇔H2HO((ssbb))++OP(ds(bs)) 55..77∗∗11002211 401+22Ca15f 14202
3
1 2 17)H2O(sb)+Pd(sb)⇔H(sb)+OH(sb) 5.7∗1021 121 121
7:5 18)OH(sb)+OH(sb)⇔H2O(sb)+O(sb) 5.7∗1021 81 81
0

d At: a4C3θoHv2eOr(asgb)e+d6ep1eθnHd(seb)nc+ie3s0.f5oθrOMH(sebc),hC.1A5:f=C44r3=θP−d(s1b)04+θP3d0(s.b5)θ−H2O7(s3b.)5+θH42O3(θsbH)(s−b)+10241θ.H5(θsOb)H(−sb)5.2θOH(sb) C6r=61θPd(sb) +
e
d
a
o
l
n
w
o DissociativeH adsorptionismodeledtooccurbothonmetallicPd(s)pairs(reaction3f)and
D 2
onvacancy/oxidepairs(reaction4f)inordertoachieveadequatelowtemperatureconversion.
ExperimentalstudieshaveshownthatstickingcoefficientsofH onPdshouldbe∼5Xormore
2
thanthoseofO topredictPd-basedH sensorperformance[17].Inaslightmodificationfrom
2 2
thepreviousmechanism,theH coefficientonboththemetalandtheoxidesurfacewasset
2
to8X(insteadof10X)theO stickingcoefficient.ThehighH coefficientisborneoutinthe
2 2
experiments,whichshowthateveninexcessO ,supportedPdOparticlescanundergopartial
2
reductionatlowtemperatures.
Thetwomechanismsintable2capturethetrendsinexperimentalobservationsforϕ =0.1
for the range of temperatures shown in figure 1 and have qualitative agreement with the
observations for ϕ =0.05. It should be noted that these mechanisms are only suited for
predictingH combustionatlowϕ wherethereisnobulkPdOreduction.Simulationresults
2
with a detailed gas phase H /O mechanism indicated that over 99% of the H combustion
2 2 2
wasduetosurfacereactionsforT <200◦C,andthusfurthersimulationsignoredgasphase
ext
chemistry.
3. Modeldescription
To facilitate ILDM analysis of the surface chemistry mechanism, a numerical model of the
supportedwashcoatlayerisformulatedasauniformdifferentialreactorsuchthatthesystem
MechanismanalysiswithILDMsforH2combustiononPdcatalysts 7
of governing equations can be identified as a dynamical system dependent only on local
conditions.Suchareactormodelisillustratedbytheschematicshowninfigure2(a).Surface
reactionsareinfluencedbyheatandmasstransportfromthesurroundinggas-phaseflowand
bythermalconductionthroughthesolidmatrixofthecatalystsupport.
The model solves the transient differential algebraic equations that govern the washcoat
temperature T, gas phase mass fractions Y , and surface species mole fractions θ on the
k k
supportedcatalystparticles.Gasphasedensityρ ismodeledwiththeidealgasequation.For
theuniformporouswashcoat,conservationofgasphasespecies(k=1,k )isgivenbythe
gas
followingequation:
(cid:4) (cid:5)
∂Y (cid:1)
ρε k =εω˙ W +a s˙ W −Y (W s˙ ) +a ρ¯YV −a ρ¯V(Y¯ −Y ) (2)
∂t k k cat k k k k k wc k wc k k
k,g
where the overbar implies mean conditions between the washcoat and the external flow. In
equation2,εiswashcoatporosity,W ismolecularweightofspeciesk,anda anda are
k cat wc
thecatalystsurfaceareaandexternalgeometricalareaofwashcoat,bothperunitvolumeof
washcoat.Gas-phasereactionratesperunitvolumeω˙ canbeincorporatedinthemodel,but
k
arenotincludedinthecurrentsimulationsasdiscussedearlier.Calculationofthediffusiveflux
ofspeciesYV betweenthewashcoatandtheexternalflowarediscussedbelow.TheStefan
k
10 velocityV outofthewashcoatlayerarisesfromchangesinρand/ornetadsorption/desorption
0
2
fromthesurface.
y
r
nua Withsurfacereactionratesperunitareaofcatalysts˙k,conservationofsurfacespecies(for
Ja k=kgas+1,kgas+ksurf)isgovernedbythefollowingequation
3
2
∂θ
07:51 (cid:10)cat ∂tk =s˙k (3)

:
At where(cid:10)catisthecatalystsitedensity.Conservationofenergyinwashcoatisgivenby:
d
ownloade (ρCp)∂∂Tt +=−acat(cid:1)k,g (hks˙kWk)−ε(cid:1)k,g (hkω˙kWk)−acat(cid:1)k,s (hks˙kWk)
D (cid:1) (cid:1)
+a h (T −T)+a ρ¯ ((h¯ −h )YV )−a ρ¯V (h¯ Y¯ −h Y )
wc T ext wc k k k wc k k k k
k,g k,g
(4)
wheretheweightedspecificheatcapacityρC includesthegasandsolidphases.Although
p
transformation in bulk phase catalyst species are not included in this study, the developed
modelcanbeappliedforfuturestudieslookingatconditionswhereH reducesthebulkofa
2
PdO catalyst.
x
TofacilitateclearerassessmentoftheILDMsthatgovernthesurfacechemistrymechanism,
heat and mass transport are determined with fixed external flow conditions such that the
dynamicalresponseofthesystemiscontrolledstrictlybychangeswithinthewashcoatmedia.
Forthemassandheattransportbetweenthefixedexternalflowandthewashcoat,diffusive
fluxesaremodeledwiththeuseofNusselt(Nu)andSherwood(Sh )numbercorrelationsused
k
inthechannelflowmodel[11].Thesefluxesattheinterfacebetweenthechannelflowandthe
outerwashcoatsurfacearedefinedbythefollowingequations:
YV = DkmShk(Yk,ext−Yk) for k =1, k , (5)
k gas
d
hyd
Nuλ (T −T)
h (T −T)= gas ext at y =0.0. (6)
T ext
d
hyd
8 S.-A.S.ReihaniandG.S.Jackson
Gas-phasetransportpropertiesvarywithcompositionandT basedonCHEMKIN’skinetic
theoryalgorithms.StandardJANAFtablesareusedtomodelgas-phasethermodynamicprop-
erties with respect to temperature. Because conditions in the current study have significant
dilutionofthereactants,amixture-averagedformofthebinarydiffusioncoefficient D is
km
used for diffusion coefficients. Thermal diffusion is incorporated into the D for the light
km
gas phase species (H ). The washcoat pores are assumed to be substantially larger than the
2
molecularmeanfreepath,andthusKnudsendiffusionhasanegligibleimpactondiffusionin
thewashcoat.
Theabovetransientconservationequationsareintegratednumericallywithrespecttotime
usingthenumericalintegrationschemeLIMEX[18]untiltimet=1000s,atwhichpointforall
non-oscillatorycasesasteady-statesolutionhasbeenreached.Thisnumericalmodelisused
tostudythetwomechanismspresentedintable2.Toensuredifferentialreactorbehaviorfor
clearerkineticevaluations,celllengthforthemodelissetto10µmwithwashcoatthicknesses
δ of10µmandreactorsubstratethicknessδ of75µm.Thecatalyticwashcoatiscomposed
wc sub
ofγ-Al O withaporosity,ε =0.5,acatalystloadingof5.5mgofPdpercm3 ofwashcoat
2 3
volume,andacatalystdispersionof0.1.Externalflowconditionsfollowtheaforementioned
rangeofexperimentalconditions.
Figures3aand3bshowpredictionsusingMechanismAoftransientprofilesofH conversion
2
0 inthewashcoat(=1−YH2/YH2,ext)andsurfacesitefractions(θk)forthedifferentialwashcoat
201 reactorunderbothdryandwet(XH2O,ext =0.022)conditionsatText =100◦C,ϕ =0.1,and
ary XN2,ext/XO2,ext =20.Theθk plottedinfigure3showatransitionfromaninitiallyoxidized
anu catalystwithθO(sb) =0.9toconditionswherethesurfacehassignificantcoverageofOH(sb)
J
andOH(s).Forthedrycase,thistransitionleadstooscillatorybehavior(ofthesurfacesite
3
2
fractionsandtheH conversion).Whilemildoscillationswereobservedinthemassspectrom-
51 2
7: etermeasurementsinthecatalystchannelexperimentsforsomeconditions,theoscillations
0
: wereminimalcomparedtothoseshowninfigure3a.However,channelflowsimulationsusing
t
A MechanismAunderdryinletconditionspredictedsignificantlydampedoscillations(<10%
d
e
oad of mean H2 conversion) due to the production of H2O along the channel. Gas phase H2O
nl suppressestheoscillationsasindicatedbythewetcaseinfigure3b.Thissuggeststhevalue
w
o
D ofdifferentialreactorstotestkineticmechanisms.
Figure4ashowshowtheslightchangesinMechanismBsuppresstheoscillationsentirely
forthedrycaseatT =100◦Candϕ =0.1.ThelackofpredictedoscillationswithMech-
ext
anismBcaninpartbeattributedtothereducedstabilityofthesurfacespeciesOH(sb)and
H O(sb)whichpreventsthebuild-upofthesespeciesasconversionincreases.Alltheresults
2
infigure4aforboththedryandwetcasesindicatemultipletimescalesfrom(cid:8)1sto(cid:9) 10s
impacting the surface site fractions and similarly the H conversion with respect to time.
2
The rapid (<1 s)changes of H conversion would likely only be observed in a differential
2
reactor, of order 1 mm in length, because variation in gas and surface conditions length-
wise along longer reactors will mask the effects of sharp local transitions on exhaust gas
measurements.
Themultipletimescalesandtheoscillatorybehaviorillustratedinfigures3and4suggest
thatILDMsmayprovideinsighttothissystembyisolatingtheslowertimescaleprocesses.
Tothisend,thegoverningequationsfortheporouscatalyticwashcoatcanbewrittenas:
∂∂U(cid:12)t = B(cid:12)(cid:12) −1(U(cid:12) )((cid:10)(cid:12)(Text,Yk,ext,U(cid:12) )+ (cid:13)(cid:12) (U(cid:12) ))= F(cid:12) (U(cid:12) ) (7)
where, U(cid:12) thesolutionvectorincludesT,Y ,andθ inthecatalyticwashcoat. B(cid:12)(cid:12) (U(cid:12) )denotes
k k
thematrixmultiplierofthetransientderivatives, (cid:10)(cid:12) denotesfluxtermsduetodiffusionand
Stefanvelocityconvectionto/fromtheexternalflow,and (cid:13)(cid:12) isthelocalsourcetermsdueto
MechanismanalysiswithILDMsforH2combustiononPdcatalysts 9
0
1
0
2

y
r
a
u
n
a
J

3
2

1
5
:
7
0

:
t
A

d
e
d
a
o
l
n
w
o
D
Figure3. TransientprofilesofH2 conversionandsurfacesitefractionsinuniformdifferentialreactoratText=
–1(cid:1)00–◦CO(asnbd),φ−−=•−0−.1OwHit(hsbM),e−c−h(cid:2)a−n−ismOHA(sfo),rH(a2)−d−r◦y−a−ndO((bs)b)w,e−t−((cid:3)X−H−2OH,e2xOt=(s)0,.—02(cid:4)2—)cHon(ds)i.tions.−−−H2Conversion
reactions.BecauseTextandYk,extarefixedinthisproblem,thederivativesaresimplyafunction
(cid:12) (cid:12)
F ofthewashcoatstatespecifiedby U.
To identify the time-scales of this system around a point in state space, the Jacobian
and associated eigenvalues and eigenvectors are evaluated for the system and the different
modes are sorted into slow (subscript s) and fast (subscript f) modes via the following