反应工程基础(程易)chpt12-externaldiffu

SummaryofChapter11 Typesofadsorption a Chemisorption b Physicaladsorption TheLangmuirisothermrelatingtheconcentrationofspeciesAonthesurfacetothepartialpressureofAinthegasphaseisThesequenceofstepsforthesolid catalyzedisomerization A B a MasstransferofAfromthebulkfluidtotheexternalsurfaceofthepellet b DiffusionofAintotheinteriorofthepellet c AdsorptionofAontothecatalyticsurface d SurfacereactionofAtoformB e DesorptionofBfromthesurface f DiffusionofBfromthepelletinteriortotheexternalsurface g MasstransferofBawayfromthesolidsurfacetothebulkfluid 1 Assumingthatmasstransferisnotrare limiting therateofadsorptionisTherateofsurfacereactionisTherateofdesorptionisAtsteadystate Thetotalconcentrationofsiresis 2 Ifweassumethatthesurfacereactionisrate limiting wesetChemicalvapordeposition 3 rate limiting Catalystdeactivation Thecatalystactivityisdefinedas TherateofreactionatanytimetisTherateofcatalystdecayisForfirst orderdecay Forsecond orderdecay 8 Forslowcatalystdecaytheideaofatemperature timetrajectoryistoincreasethetemperatureinsuchawaythattherateofreactionremainsconstant 4 5 Chapter12ExternalDiffusionEffectsonHeterogeneousReactions DepartmentofChemicalEngineeringTiefengWangwangtf Objectives DiscussFick sLawanddiffusion Definethemasstransfercoefficient explainwhatitisfunctionofandhowitismeasuredorcalculated AnalyzePBRsinwhichmasstransferlimitstherateofreaction Discusshowonegoesfromaregionmasstransferlimitationtoreactionlimitation Applytheshrinkingcoremodeltoanalyzecatalystregeneration 7 11 1Diffusionfundamentals11 1 1Definition Molarflux WAz mol m2 s Molarflowrate FAz AcWAz mol s Diffusionisthespontaneousinterminglingormixingofmoleculesbyrandomthermalmotion Concentrationgradientresultsinamolarfluxofthespeciesinthedirectionoftheconcentrationgradient Molarbalance 8 z x y x x y z z x x y y z z x y z z x y z MolarfluxWA withunitofmol m2 s In Out Generation Accumulation In Out inzdirection Generation Accumulation MolarfluxbalanceofspeciesA 9 Divideby x y zforrectangularcoordinates Forcylindricalcoordinates rederive Invectorform 10 11 1 2Molarflux Twocontributionstomolarflux 1 MoleculardiffusionfluxJA 2 ConvectivefluxresultingfromthebulkmotionBA yAisthemolarfractionofA Viistheparticlevelocityofspeciesi andVisthemolaraveragevelocity TotalmolarfluxofA WA IntermsofthemolarfractionofA IntermsoftheconcentrationofA 11 1 3Fick sfirstlaw Heatfluxinonedimension Fourier slaw Shearstress Newton slaw Masstransferflux Fick slaw 11 Whatistheconditionforthiseq Relationshipbetweenfluxandgradient JAzisascalar 12 Fick sfirstlaw TalentedinmathematicsandphysicsFick sfirstcontributionasaphysicistwasmadein1855whenhewasjust26yearsold Fick slaw Thegeneral3 dimensionalconstitutiveequationsforJA cthetotalconcentration mol dm3 DABthediffusivityofAinB m2 s yAthemolefractionofA JAisavector AdolphFick 1829 1901 Germany MolarfluxofA 13 Intermsofconcentrationforconstanttotalconcentration 11 2Binarydiffusion EvaluatingtheMolarFluxEquimolarcounterdiffusion EMCD DiluteconcentrationsDiffusionthroughastagnantGasForcedconvectionDiffusionandconvectivetransport 14 Inequimolarcounterdiffusion EMCD foreverymoleofAthatdiffusesinagivendirection onemoleofBdiffusesintheoppositedirection EquimolarCounterDiffusion EMCD Forconstanttotalconcentration DiluteConcentration Themolefractionofthediffusingsoluteissmall BAisneglectedcomparedwithJA thusForporouscatalystwithsmallporeradii Knudsendiffusionoccurswhenmeanfreepathofmoleculesisgreaterthancatalystporediameter Knudsendiffusivity Thisapproximationisalmostalwaysusedformoleculesdiffusingwithinaqueoussystemswhentheconvectivemotionissmall WB 0Involvemorethanonephasewhereonespeciesreadilydiffusetotheotherphase A whileanotheronecannot B DiffusionthroughaStagnantGas WB 0 ForcedConvection 18 JAzissmallincomparisonwithbulkflowcontribution JAx JAz whereAcisthecross sectionalareaandvisthevolumetricflowrate AlthoughJAzisneglected JAxmaynotnecessarilybeneglected DiffusionandConvectiveTransport Diffusionandconvectivetransport Forone dimensionatsteadystate 1 Specifyaconcentrationataboundary2 Specifyafluxataboundarya Nomasstransferacrossaboundary e g atpipewall therefore TypesofBoundaryConditions Cross sectionofapipe b Reactionataboundaryisequaltothemolarflux Cont d 3 PlanesofSymmetry e g cylinder c Diffusionfluxtoaboundary fromz dtoz 0 isequaltotheconvectivefluxawayfromtheboundary atz 0 ModelingDiffusionWithoutReaction Step1 PerformadifferentialmolebalanceonaparticularspeciesAStep2 SubstituteforFAzintermsofWAzStep3 ReplaceWAzbytheexpressionfortheconcentrationgradientStep4 StatetheboundaryconditionsStep5 SolvefortheconcentrationprofileStep6 SolveforthemolarfluxLookatExample11 1 Example11 1 23 ForspeciesAindiluteconcentration concentrationprofilefollows Themolarfluxcanbedeterminedbyusingequation Themolarfluxcanbecalculatedfromconcentrationprofileby EMCDalsoproducessamemolarfluxequationasabove 11 2 4TandPDependenceofDAB 24 Gas Bulk Knudsen Liquid Solid Phasecm2 sm2 sTandPDependences OrderofMagnitude 11 2 5ModelingDiffusionwithChemicalReaction Step1 DefinetheproblemandstatetheassumptionsStep2 DefinethesystemonwhichthebalancesaretobemadeStep3 PerformthedifferentialmolebalanceonaparticularspeciesStep4 ObtainadifferentialequationinWAbyrearrangingyourbalanceequationproperlyandtakingthelimitasthevolumeoftheelementgoestozeroStep5 SubstitutetheappropriateexpressioninvolvingtheconcentrationgradientforWAfromsec11 2toobtainasecond orderdifferentialequationfortheconcentrationofA Step6 ExpressthereactionraterAintermsofconcentrationandsubstituteintoadifferentialequationStep7 StatetheappropriateboundaryandinitialconditionsStep8 PutthedifferentialequationsandboundaryconditionsindimensionlessformStep9 SolvetheresultingdifferentialequationfortheconcentrationprofileStep10 DifferentiatetheconcentrationprofiletoobtainanexpressionforthemolarfluxofAStep11 Substitutenumericalvaluesforsymbols 11 2 5 ModelingDiffusionwithChemicalReaction 27 11 3Externalresistancetomasstransfer11 3 1Masstransferboundarylayer Thefluidvelocityinthevicinityofthesphericalpelletwillvarywithpositionaroundthesphere Thehydrodynamicboundarylayerisusuallydefinedasthedistancefromasolidobjecttowherethefluidvelocityis99 ofthebulkvelocityU0 Similarly themasstransferboundarylayerthickness isdefinedasthedistancefromasolidobjecttowheretheconcentrationofthediffusingspeciesreaches99 ofthebulkconcentration 28 11 3 2Masstransfercoefficient ConcentrationprofileforEMCDinstagnantfilmmodel Inthisstagnantfilmmodel alltheresistancetomasstransferislumpedintothethickness Thereciprocalofthemasstransfercoefficientcanbethoughtofasthisresistance 29 11 3 3Correlationforthemasstransfercoefficient Themasstransfercoefficientkcisanalogoustotheheattransfercoefficienth Forheattransfer Heatflux Forforcedconvection theheattransfercoefficientisnormallycorrelatedintermsofthreedimensionlessgroups isthermaldiffusivity m2 s where FordifferentRerange 30 ForhighReynoldsnumber ForzeroorverysmallReynoldsnumber Analogueofmasstransfertoheattransfer 11 3 4Masstransfertoasingleparticle molarfluxtocatalystsurface reactionrateonsurface FastReactionKinetics Fastreactionkinetics toincreasekc SlowReactionKinetics Forslowreactionkinetics krisindependentoffluidvelocityparticlesize 35 Regionsofmasstransfer limitedandreaction limitedreactions 36 11 3 5MassTransfer LimitedReactionsinPackedBeds Inmasstransfer dominatedreactions thesurfacereactionissorapidthattherateoftransferofreactantfromthebulkgasorliquidphasetothesurfacelimitstheoverallrateofreaction Consequently masstransfer limitedreactionsrespondquitedifferentlytochangesintemperatureandflowconditionsthandotherate limitedreactionsdiscussedinpreviouschapters Molarbalanceinapacked bedreactor 37 In Out Generation Accumulation rA rateofgenerationofAperunitcatalyticsurfacearea mol s m2ac externalsurfaceareaofcatalystpervolumeofcatalyticbed m2 m3 voidfractiondp particlediameter mAc cross sectionalareaoftubecontainingthecatalyst m2 38 ThemolarflowrateofAintheaxialdirectionis Ifdispersionisnegligible Tosimplifyfurtherthecasestudies assumeconstantU Uisthesuperficialmolaraveragevelocitythroughthebed m s Boundarycondition Assumingreactionisatsteadystate Then Integratingwithboundarycondition atz 0 CA CA0 Thus Analyticalsolution MasstransferlimitedCA CAs 11 3 6 Theeffectsoftemperatureandflowrateonconversion 40 Thecorrelationforthemasstransfercoefficientflowthroughapackedbed ThoenesandKranmers 1958 Forconstantfluidpropertiesandparticlediameter Whatifthegasvelocityiscontinuallyincreased Othermasstransfercorrelations 41 MostmasstransfercorrelationsareintermsofColburnJfactor JD asafunctionoftheReynoldsnumber JDisdefinedas DwideviandUpadhyay scorrelation 11 4Parametersensitivity Example11 4Foramasstransfer limitedreaction 42 X v0 v0 v0 X 0 865 v0 X 11 5ShrinkingCoremodel Thecoke C depositintothecoreofcatalystthroughpores O2diffusetothecatalystandreactionhappensto clean thecatalyst Thecoreisshrinkingwithtime Step1 ThemolebalanceonO2betweenrandr r 44 In Out Generation Accumulation Step2 MolarfluxforEMCD 45 whereDeisaneffectivediffusivityintheporouscatalyst Step3 Combiningtheabovetwoequationsyields Step4 Theboundaryconditionsare Step5 TheradialprofileoftheconcentrationofA 46 47 Step6 ThemolarfluxofO2tothegas carboninterface Step7 Overallbalanceonelementalcarbon In Out Generation Accumulation 48 Step8 TherateofdisappearanceofcarbonisequaltothefluxofO2tothegas carboninterface I C t 0 R R0 Thetimeneededtofullyregenerateacokedcatalystparticlebyconsumingallcarbon tc is Step9 IntegratingwithlimitsR R0atr 0 thetimenecessaryforthecarbonsolidinterfacetorecedeinwardtoaradiusRis Fora1cmdiameterpelletwitha0 04volumefractionofcarbon theregenerationtimeistheorderof10s FluidizedCatalyticCracker FCC 12 5 2DissolutionofMonodispersedSolidParticles SpeciesAmustdiffusetothesurfacetoreactwithsolidBattheliquid solidinterface ZeroorderinBandfirstorderinA Therateofmasstransfertothesurfaceisequaltotherateofsurfacereaction 51 whereisthediameteratwhichtheresistancestomasstransferandreactionrateareequal For