反应工程基础(程易)chpt13-internaldiffu

SummaryofChapter12,1.ThemolarfluxofAinabinarymixtureofAandBisa)ForEMCDorfordiluteconcentrationofthesolute,a)Fordiffusionthroughastagnantgas,a)Fornegligiblediffusion,1,Summary(contd),2.TherateofmasstransferfromthebulkfluidtoaboundaryatconcentrationCAsis3.TheSherwoodandSchmidtnumbersare,respectively,4.Ifaheattransfercorrelationexistsforagivensystemandgeometry,themasstransfercorrelationmaybefoundbyreplacingtheNusseltnumberbytheSherwoodnumberandthePrandtlnumberbytheSchmidtnumberintheexistingheattransfercorrelation.,2,Summary(contd),5.Increasingthegas-phasevelocityanddecreasingtheparticlesizewillincreasetheoverallrateofreactionforreactionsthatareexternallymasstransfer-limited.6.Theconversionforexternallymasstransfer-limitedreactionscanbefoundfromtheequation7.Theshrinkingcoremodelstatesthatthetimetoregenerateacokedcatalystpanicleis,3,4,Chapter13DiffusionandReactions,DepartmentofChemicalEngineeringTiefengWangwangtf,5,Objectives,DescribediffusionandreactionsinporouscatalystandinTissueEngineering.DefinetheThielemodulesandtheeffectivenessfactor.Describetheregionsofreactionlimitationsandinternaldiffusionlimitationsandtheconditionsthataffectthem.,6,7,12.1DiffusionandReactioninSphericalCatalystPellets,12.1.1EffectiveDiffusivityTheporesinthepelletarenotstraightandcylindrical;rather,theyareaseriesoftortuous,interconnectingpathsofporebodiesandporethroatswithvaryingcross-sectionalareas.Itisfruitfultodescribediffusionwithineachandeveryoneofthetortuouspathwaysindividually.Defineaneffectivediffusioncoefficientsoastodescribetheaveragediffusiontakingplaceatanypositionrinthepellet.TheradialfluxWArwillbebasedonthetotalarea(voidsandsoIid)normaltodiffusiontransport(i.e.,4r2)ratherthanvoidareaalone.ThisbasisforWArismadepossiblebyproperdefinitionoftheeffectivediffusivityDe.,EffectiveDiffusivity,Theeffectivediffusivityaccountsforthefactthat:Notalloftheareanormaltothedirectionofthefluxisavailable(i.e.,theareaoccupiedbysolids)forthemoleculestodiffuse(p).Thepathsaretortuous().Theporesareofvaryingcross-sectionalareas(c).,8,EffectiveDiffusivity,9,tortuosity,DiffusionMechanisminPoreChannels,10,Moleculardiffusion,11,SimplediffusioninthegasspaceofporousstructureMoleculemeanfreepathissmallerlargerthanporediameterCollisionsbetweenmoleculesdominateoverthosebetweenmoleculeandtheporewallValidathighpressuresandinlargeporesMoleculardiffusionisdescribedbyFickslaw,Knudsendiffusion,12,CollisionswithporewallsdominateoverthosewithothermoleculesValidforlowpressuresandinnarrowpores,Configurationaldiffusion,13,Poreswithmoleculardimensions(0.3-1nm)StronginteractionbetweenmoleculeandtheporewallImportantformicroporouscatalysts,e.g.Zeolites,HighresolutionTEMpictureofZSM-5,Effectofconfigurationaldiffusiononreaction,Configurationaldiffusion,对二甲苯分子直径0.57邻、间二甲苯分子直径0.63,15,12.1.2Differentialequationdescribingdiffusionandreaction,Asteady-statemolebalanceonspeciesA,InOut+Generation=Accumulation,Shellbalanceonacatalystpellet,16,Forequalmolarcounterdiffusionatconstanttotalconcentration:,Wenowneedtoincorporatetheratelaw.,Therateofreactionindifferentforms,17,Rateperunitvolume:,Rateperunitmassofcatalyst:,Rateperunitsurfacearea:,Thesurfaceareaatthecatalystperunitmassofcatalyst,TypicalvalueofSa,150m2/g,rateequationdefinitions,18,Theboundaryconditionsare:,19,12.1.3Dimensionlessform,Theboundaryconditionsare:,20,TheThielemodulusn,WhentheThielemodulusislarge,internaldiffusionusuallylimitstheoverallrateofreaction;Whenitissmall,thesurfacereactionisusuallyrate-limiting;,Forafirst-orderreaction,21,22,12.1.4Solutiontothedifferentequationforafirst-orderreaction,ThieleModulus,Smalln,Mediumn,Largen,12.2InternalEffectivenessFactor,24,E.W.Thiele(1939).“RelationbetweenCatalyticActivityandSizeofParticle”IndustrialandEngineeringChemistry,31,916-920,25,Actualoverallrateofreaction(molesperunittime):,Rateofreactionthatwouldresultsifentireinteriorsurfacewereexposedtotheexternalpelletsurfaceconditions:,Externalsurface,PhysicalInterpretationofAnalysis,27,28,?,Effectivenessfactorfordifferentshapeofcatalyst,29,Effectivenessfactorfornorderreaction,30,ForlargevaluesoftheThielemodulusforannorderreaction,ForlargevaluesoftheThielemodulusforanfirstorderreaction,31,Whenareactionisexothermicandnon-isothemal,theeffectivenessfactorcanbesignificantlygreaterthan1.Multiplestead-statescanexistforvaluesoftheThielemoduluslessthan1andwhenisgreaterthanapproximately0.2.TherewillbenomultiplesteadystareswhenthecriteriondevelopedbyLussisfulfilled.,32,Ratewithoutanydiffusioneffects,=1fornodiffusionresistance,Thissphereexpressionisagoodapproximationforallparticleshapes,Characteristiclength,=Effectivefactor,whichaccountsfortheresistancetoporediffusion,1=Thielemodulus,usefulforpredictingreactorbehaviorfromknownkineticinformation,thusknownk,CWP=Weiszmodulus,usefulforpredictingexperimentssinceitonlyincludesobservations,Effectivediffusioncoefficientinporoussolids,with,where,12.3Falsifiedkinetics,33,Alog-logplotofthemeasuredrateofreaction-rA,asafunctionofthegas-phaseconcentrationCAs,(externalmasstransferiseliminated,thusCAs=CAb),Relatethismeasuredreactionorderntothetruereactionordern.,34,Usingthedefinitionoftheeffectivenessfactor:,ForlargevaluesoftheThielemodulus,is:,(externalmasstransferiseliminated,thusCAs=CAb),35,OverallEffectivenessFactor,WhenbothinternalANDexternaldiffusionresistancesareimportant(i.e.,thesameorderofmagnitude),bothmustbeaccountedforwhenquantifyingkinetics.Itisdesiredtoexpressthekineticsintermsofthebulkconditions,ratherthansurfaceconditions:,OverallEffectivenessFactor,Accountingforreactionbothonandwithinthepellet,themolarratebecomes:Formostcatalyst,internalsurfaceareaissignificantlyhigherthantheexternalsurfacearea:,acistheexternalsurfaceareaperunitreactorvolume,Molarrateofmasstransfer=totalrateofreaction,OverallEffectivenessFactor,reactionrate(internal&externalsurfaces),masstransportrate,internalsurfacesnotallexposedtoCAs,RelationbetweenCAsandCAdefinedbytheas:,UsingMolarrateofmasstransfer=totalrateofreaction,Then,OverallEffectivenessFactor,Summaryoffactorrelationships:,Rearrangingtheexpression:,OverallEffectivenessFactor()Thiseq.isforfirst-orderreaction,Weisz-PraterCriterionforInternalDiffusion,Weisz-PraterCriterionisamethodofdeterminingifagivenprocessisoperatinginadiffusion-orreaction-limitedregimeCWPistheknownastheWeisz-Praterparameter.Allquantitiesareknownormeasured.CWP1,severediffusionlimitations,Assumethattheexternalmasstransferiseliminated,thusCAs=CAb.,MearsCriterion,Masstransfereffectsnegligiblewhenitistruethatwherenisthereactionorder,andthetransfercoefficientskcandh(below)canbeestimatedfromanappropriatecorrelation(i.e.,Thoenes-Kramersforpackedbedflow),n=reactionorderR=catalystparticleradius,mb=bulkdensityofcatalystbed,(1-)c,kg/m3c=soliddensityofcatalystpellet,kg/m3CAb=bulkgasconcentrationofA,mol/m3kc=masstransfercoefficient,m/s,MearsCriterion,Heattransfereffectsnegligiblewhenitistruethat,h=heattransfercoefficient,kJ/m2sKR=gasconstant,kJ/molKHRx=heatofreaction,kJ/molE=activationenergy,kJ/mol,12.6Masstransferandreactioninapackedbedreactor,43,MolefluxofA,Firstorderreaction,Axialdispersionnegligible(relativetoforcedaxialconvection)whendpistheparticlediameterU0isthesuperficialvelocityofthegasDaistheeffectiveaxialdispersioncoefficient,canbesimplifiedas:,Whichcanberewrittenas:,B.C.,Integratingandapplyingboundaryconditionyields:,Theconversionatthereactorsexit,z=L,is,DeterminationofLimitingSituationsfromReactionData,47,Externalmasstransfer-limitedreactionsinpackedbeds:,Limitingconditions,48,49,12.7Experimentalstudyoftheheterogeneouscatalyticreactions,Intrinsicreactionkineticsisobtainedwhenboththeexternalmasstransferandinternaldiffusionareeliminated.,50,12.7.1Eliminatingtheexternaldiffusion,51,Testingtheinfluenceoftheexternaldiffusion,52,12.7.2Eliminatingtheinternaldiffusion,Forkineticsexperiments,thesizeofthecatalystparticlesshouldbesmallerthandp*,12.7.3Experimentalmethodsforfindingrates,ExperimentaldevicesDifferential(flow)reactorIntegral(plugflow)reactorMixedflowreactorBatchreactorforbothgasandsolidInprinciple,anytypeofreactorwithknowncontactingpatternmaybeusedtoexplorethekineticsofcatalyticreactions.,53,ComparisonofExperimentalReactors:Levenspiel3rdp400,Eachrungivesdirectlyavaluefortherateattheaverageconcentrationinthereactor.Aseriesofrunsgivesasetofrate-concentrationdatawhichcanthenbeanalyzedforarateequation.Thesmallconversionsneededindifferentialreactorsrequiremoreaccuratemeasurementsofcomposition,54,DifferentialReactor,x=xout-xinissmall,Theratetobeconstantatallpointswithinthereactor.Thisassumptionisusuallyreasonableonlyforsmallconversionsorforshallowsmallreactors.,55,IntegralReactor,Theratetobeconstantatallpointswithinthereactor.Thisassumptionisusuallyreasonableonlyforsmallconversionsorforshallowsmallreactors.,IntegralAnalysisAspecificmechanismwithitscorrespondingrateequationisputtothetestbyinteg