反應(yīng)工程基礎(chǔ)(程易)chpt13-internaldiffu

SummaryofChapter121.ThemolarfluxofAinabinarymixtureofAandBisa)ForEMCDorfordiluteconcentrationofthesolute,a)Fordiffusionthroughastagnantgas,a)Fornegligiblediffusion,

1ppt課件Summary(cont’d)2.TherateofmasstransferfromthebulkfluidtoaboundaryatconcentrationCAsis3.TheSherwoodandSchmidtnumbersare,respectively,4.Ifaheattransfercorrelationexistsforagivensystemandgeometry,themasstransfercorrelationmaybefoundbyreplacingtheNusseltnumberbytheSherwoodnumberandthe

PrandtlnumberbytheSchmidtnumberintheexistingheattransfercorrelation.2ppt課件Summary(cont’d)5.Increasingthegas-phasevelocityanddecreasingtheparticlesizewillincreasetheoverallrateofreactionforreactionsthatareexternallymasstransfer-limited.6.Theconversionforexternallymasstransfer-limitedreactionscanbefoundfromtheequation7.Theshrinkingcoremodelstatesthatthetimetoregenerateacokedcatalystpanicleis3ppt課件Chapter13

DiffusionandReactionsDepartmentofChemicalEngineeringTiefengWangwangtf@4ppt課件ObjectivesDescribediffusionandreactionsinporouscatalystandinTissueEngineering.DefinetheThielemodulesandtheeffectivenessfactor.Describetheregionsofreactionlimitationsandinternaldiffusionlimitationsandtheconditionsthataffectthem.5ppt課件6ppt課件12.1DiffusionandReactioninSphericalCatalystPellets12.1.1EffectiveDiffusivityTheporesinthepelletarenotstraightandcylindrical;rather,theyareaseriesoftortuous,interconnectingpathsofporebodiesandporethroatswithvaryingcross-sectionalareas.Itisfruitfultodescribediffusionwithineachandeveryoneofthetortuouspathwaysindividually.Defineaneffectivediffusioncoefficientsoastodescribetheaveragediffusiontakingplaceatanypositionrinthepellet.TheradialfluxWArwillbebasedonthetotalarea(voidsandsoIid)normaltodiffusiontransport(i.e.,4r2)ratherthanvoidareaalone.ThisbasisforWArismadepossiblebyproperdefinitionoftheeffectivediffusivityDe.7ppt課件EffectiveDiffusivityTheeffectivediffusivityaccountsforthefactthat:Notalloftheareanormaltothedirectionofthefluxisavailable(i.e.,theareaoccupiedbysolids)forthemoleculestodiffuse(p).Thepathsaretortuous().Theporesareofvaryingcross-sectionalareas(c).8ppt課件EffectiveDiffusivitytortuosity9ppt課件DiffusionMechanisminPoreChannels10ppt課件MoleculardiffusionSimplediffusioninthegasspaceofporousstructureMoleculemeanfreepathissmallerlargerthanporediameterCollisionsbetweenmoleculesdominateoverthosebetweenmoleculeandtheporewallValidathighpressuresandinlargeporesMoleculardiffusionisdescribedbyFick’slaw11ppt課件KnudsendiffusionCollisionswithporewallsdominateoverthosewithothermoleculesValidforlowpressuresandinnarrowpores12ppt課件ConfigurationaldiffusionPoreswithmoleculardimensions(0.3-1nm)StronginteractionbetweenmoleculeandtheporewallImportantformicroporouscatalysts,e.g.ZeolitesHighresolutionTEMpictureofZSM-513ppt課件EffectofconfigurationaldiffusiononreactionConfigurationaldiffusion對二甲苯分子直徑0.57鄰、間二甲苯分子直徑0.6314ppt課件12.1.2DifferentialequationdescribingdiffusionandreactionAsteady-statemolebalanceonspeciesAIn–Out+Generation=AccumulationShellbalanceonacatalystpellet15ppt課件Forequalmolarcounterdiffusionatconstanttotalconcentration:Wenowneedtoincorporatetheratelaw.16ppt課件TherateofreactionindifferentformsRateperunitvolume:Rateperunitmassofcatalyst:Rateperunitsurfacearea:Thesurfaceareaatthecatalystperunitmassofcatalyst,TypicalvalueofSa,150m2/grateequationdefinitions17ppt課件Theboundaryconditionsare:18ppt課件12.1.3DimensionlessformTheboundaryconditionsare:19ppt課件TheThielemodulusnWhentheThielemodulusislarge,internaldiffusionusuallylimitstheoverallrateofreaction;Whenitissmall,thesurfacereactionisusuallyrate-limiting;20ppt課件Forafirst-orderreaction21ppt課件12.1.4Solutiontothedifferentequationforafirst-orderreaction22ppt課件ThieleModulusSmallnMediumnLargen23ppt課件12.2InternalEffectivenessFactorE.W.Thiele(1939).“RelationbetweenCatalyticActivityandSizeofParticle”IndustrialandEngineeringChemistry,31,916-92024ppt課件Actualoverallrateofreaction(molesperunittime):Rateofreactionthatwouldresultsifentireinteriorsurfacewereexposedtotheexternalpelletsurfaceconditions:Externalsurface25ppt課件26ppt課件PhysicalInterpretationofAnalysis27ppt課件??28ppt課件Effectivenessfactorfordifferentshapeofcatalyst29ppt課件EffectivenessfactorfornorderreactionForlargevaluesoftheThielemodulusforannorderreaction,ForlargevaluesoftheThielemodulusforanfirstorderreaction,30ppt課件Whenareactionisexothermicandnon-isothemal,theeffectivenessfactorcanbesignificantlygreaterthan1.Multiplestead-statescanexistforvaluesoftheThielemoduluslessthan1andwhenisgreaterthanapproximately0.2.TherewillbenomultiplesteadystareswhenthecriteriondevelopedbyLussisfulfilled.31ppt課件Ratewithoutanydiffusioneffects=1fornodiffusionresistanceThissphereexpressionisagoodapproximationforallparticleshapesCharacteristiclength

=Effectivefactor,whichaccountsfortheresistancetoporediffusion1

=Thielemodulus,usefulforpredictingreactorbehaviorfromknownkineticinformation,thusknownk’’CWP=Weiszmodulus,usefulforpredictingexperimentssinceitonlyincludesobservationsEffectivediffusioncoefficientinporoussolidswithwhere32ppt課件12.3FalsifiedkineticsAlog-logplotofthemeasuredrateofreaction-rA,asafunctionofthegas-phaseconcentrationCAs,(externalmasstransferiseliminated,thusCAs=CAb)Relatethismeasuredreactionordern'tothetruereactionordern.33ppt課件Usingthedefinitionoftheeffectivenessfactor:ForlargevaluesoftheThielemodulus,is:(externalmasstransferiseliminated,thusCAs=CAb)34ppt課件35ppt課件OverallEffectivenessFactorWhenbothinternalANDexternaldiffusionresistancesareimportant(i.e.,thesameorderofmagnitude),bothmustbeaccountedforwhenquantifyingkinetics.Itisdesiredtoexpressthekineticsintermsofthebulkconditions,ratherthansurfaceconditions:36ppt課件OverallEffectivenessFactorAccountingforreactionbothonandwithinthepellet,themolarratebecomes:Formostcatalyst,internalsurfaceareaissignificantlyhigherthantheexternalsurfacearea:acistheexternalsurfaceareaperunitreactorvolumeMolarrateofmasstransfer=totalrateofreaction37ppt課件OverallEffectivenessFactorreactionrate

(internal&externalsurfaces)masstransportrateinternalsurfacesnotallexposedtoCAsRelationbetweenCAsandCAdefinedbytheas:UsingMolarrateofmasstransfer=totalrateofreactionThen,38ppt課件OverallEffectivenessFactorSummaryoffactorrelationships:Rearrangingtheexpression:OverallEffectivenessFactor()Thiseq.isforfirst-orderreaction39ppt課件Weisz-PraterCriterionforInternalDiffusionWeisz-PraterCriterionisamethodofdeterminingifagivenprocessisoperatinginadiffusion-orreaction-limitedregimeCWPistheknownastheWeisz-Praterparameter.Allquantitiesareknownormeasured.CWP<<1,noCinthepellet(kineticallylimited)CWP>>1,severediffusionlimitationsAssumethattheexternalmasstransferiseliminated,thusCAs=CAb.40ppt課件Mears’CriterionMasstransfereffectsnegligiblewhenitistruethatwherenisthereactionorder,andthetransfercoefficientskcandh(below)canbeestimatedfromanappropriatecorrelation(i.e.,Thoenes-Kramersforpackedbedflow)n=reactionorderR=catalystparticleradius,mb=bulkdensityofcatalystbed,(1-)c,kg/m3c=soliddensityofcatalystpellet,kg/m3CAb=bulkgasconcentrationofA,mol/m3kc=masstransfercoefficient,m/s41ppt課件Mears’CriterionHeattransfereffectsnegligiblewhenitistruethath=heattransfercoefficient,kJ/m2sKR=gasconstant,kJ/molKHRx=heatofreaction,kJ/molE=activationenergy,kJ/mol42ppt課件12.6Masstransferandreactioninapackedbedreactor43ppt課件MolefluxofAFirstorderreaction44ppt課件Axialdispersionnegligible(relativetoforcedaxial

convection)whendpistheparticlediameterU0isthesuperficialvelocityofthegasDaistheeffectiveaxialdispersioncoefficientcanbesimplifiedas:45ppt課件Whichcanberewrittenas:B.C.Integratingandapplyingboundaryconditionyields:Theconversionatthereactor’sexit,z=L,is46ppt課件DeterminationofLimitingSituationsfromReactionDataExternalmasstransfer-limitedreactionsinpackedbeds:47ppt課件LimitingconditionsTypeoflimitationVariationofreactionratewith:VelocityParticlesizeTemperatureExternaldiffusionU1/2(dp)-3/2~linearInternaldiffusionIndependent(dp)-1ExponentialSurfacereactionIndependentIndependentExponential48ppt課件12.7ExperimentalstudyoftheheterogeneouscatalyticreactionsIntrinsicreactionkineticsisobtainedwhenboththeexternalmasstransferandinternaldiffusionareeliminated.49ppt課件12.7.1Eliminatingtheexternaldiffusion50ppt課件Testingtheinfluenceoftheexternaldiffusion51ppt課件12.7.2Eliminatingtheinternaldiffusiondpdp*xAInternaldiffusionhasnoinfluenceInternaldiffusionaffectstherateForkineticsexperiments,thesizeofthecatalystparticlesshouldbesmallerthandp*52ppt課件12.7.3ExperimentalmethodsforfindingratesExperimentaldevicesDifferential(flow)reactorIntegral(plugflow)reactorMixedflowreactorBatchreactorforbothgasandsolidInprinciple,anytypeofreactorwithknowncontactingpatternmaybeusedtoexplorethekineticsofcatalyticreactions.ComparisonofExperimentalReactors:Levenspiel3rdp40053ppt課件Eachrungivesdirectlyavaluefortherateattheaverageconcentrationinthereactor.Aseriesofrunsgivesasetofrate-concentrationdatawhichcanthenbeanalyzedforarateequation.ThesmallconversionsneededindifferentialreactorsrequiremoreaccuratemeasurementsofcompositionDifferentialReactorFA0

FA0x=xout-xin

issmallTheratetobeconstantatallpointswithinthereactor.Thisassumptionisusuallyreasonableonlyforsmallconversionsorforshallowsmallreactors.54ppt課件IntegralReactorTheratetobeconstantatallpointswithinthereactor.Thisassumptionisusuallyreasonableonlyforsmallconversionsorforshallowsmallreactors.IntegralAnalysisAspecificmechanismwithitscorrespondingrateequationisputtothetestbyintegratingthebasicperformanceequationtogive,D