反应工程基础(程易)chpt14-fixedbedrea

SummaryofChapter13 Theconcentrationprofileforafirst orderreactionoccurringinasphericalcatalystpelletiswhere 1istheThielemodulus Forafirst orderreactionTheinternaleffectivenessfactorandoveralleffectivenessfactor 1 Summary cont d ForlargevaluesoftheThielemodulusforannorderreaction Forinternaldiffusioncontrol themereactionorderisrelatedtothemeasuredreactionorderbyThetrueandapparentactivationenergiesarerelatedby 2 Summary cont d TheWeisz PraterParameterTheWeisz Pratercriteriondictatesthat IfCWP 1 internaldiffusionlimitationspresentMearsCriteriaforNeglectingExternalDiffusionandHeatTransfer 3 4 Chapter14Fixed BedReactor DepartmentofChemicalEngineeringTiefengWangwangtf Contents Introductionoffixed bedreactorAdiabaticfixedbedreactorFixed bedreactorwithheatingorcoolingModelofthefixed bedreactor 5 14 1Typesofthefixedbedreactor 6 7 Fixed bedreactorsformethanolsynthesis 8 多段冷激式反应器 列管式合成反应器 径向反应器 9 Fluidizedbedreactor 10 Selectionofthereactortype 11 Reactortypepreferredasafunctionofonstreamtimeofthecatalystbetweentworegenerations vanSwaaijetal Chem Eng J 2002 90 25 45 Charactersofthefixed bedreactor Inpassingthroughfixedbeds gasesapproximateplugflow Ifefficientcontactinginareactorisofprimaryimportance thenthefixedbedisfavored Effectivetemperaturecontroloflargefixedbedscanbedifficultbecausesuchsystemsarecharacterizedbyalowheatconductivity Ifoperationsaretoberestrictedwithinanarrowtemperaturerange thenthefluidizedbedisfavored Fixedbedscannotuseverysmallsizesofcatalystbecauseofpluggingandhigh pressuredrop whereasfluidizedbedsarewellabletousesmall sizeparticles Ifthecatalysthastobetreated regenerated frequentlybecauseitdeactivatesrapidly thentheliquid likefluidizedstateallowsittobepumpedeasilyfromunittounit Thereisnocatalystattritioninthefixed bedreactor 12 Temperatureprofileofthefixedbedreactor 13 Exothermicreaction Hotspot 14 2PressureDropinthePackedBedReactor Inliquidphase effectofpressuredropcanbeignored Ingasphase foranidealgas theconcentrationofreactingspeciesiisForisothermaloperation 14 where SeeSection4 5 AnalyzethefollowingsecondordergasphasereactionthatoccursisothermallyinaPBR2A B CMolebalance mustusedifferentialform Ratelaw Stoichiometry Combine Needtofind P P0 asafunctionofW orVifyouhaveaPFR 15 Pressuredropinapackedbed P P0 f Volume V orf catalystweight W Majoritygasphasereactionshappenedinapackedbedofcatalystparticles EquationusedtocalculatepressuredropistheErgunEqn 16 ErgunEquation 17 b bulkdensity c solidcatalystdensity porosity voidfraction Pressuredropinreactor Forsinglereaction Forisothermaloperation T T0with 0 18 ThisEqn isformultiplereactionsandreactioninamembranereactor Reactionwithpressuredrop 19 1 0 a b d c e EffectofpressuredroponP a CA b rA c X d and e Reactionwithpressuredrop 20 A B 2ndorderisothermalreaction Ratelaw Stoichiometry Gasphaseisothermalreactionwith 0 Molebalance Combining Separatingvariables IntegratingwithlimitsX 0whenW 0andsubstitutingforFA0 CA0 0yields 21 Solvingforconversiongives Solvingforcatalystweight wehave 22 14 3Adiabaticfixed bedreactor 23 Dependenceof rAonT Inageneralform Forirreversiblereaction T rA Forfirst orderreactions Forreversibleexothermicreactions rAhasamaximum andE E Withfixedconversion 24 14 3 1Equilibriumtemperatureandoptimumtemperature when rA 0 thetemperatureistheequilibriumtemperatureTewhen rAgetsitsmaximum thetemperatureistheoptimum Topt Foreachconversionx Teisobtainedbysetting Toptisobtainedbysetting 25 CurvesofTeandToptforreversibleexothermicreactions Therelationshipbetweentheequilibriumandoptimumtemperatures Foraspecificconversion thesamereactionratecorrespondstotwotemperatures onesmallerthanTopt andtheotherlargerthanTopt 26 14 3 2Adiabatictubularreactor EnergybalanceforadiabaticoperationofPFR Differentialmolebalance AlmostalwayswewilluseanODEsolver Femlab Matlab Eq 8 30 Fogler TR referenceT Adiabatictemperatureandequilibriumconversion 28 Exothermicreactions T0 T01 Xe Energybalance Adiabatictemp Equilibrium T01 T0 For1st orderreaction MakeXe Tcurve Meanheatcapacity Theelementaryreversiblegas phasereaction PressuredropneglectedPureAenters Molebalance Ratelaw with Stoichiometry Combine Energybalance IfpureAentersandif Cp 0 then Optimumoperatingtemperatureforexothermicreversiblereaction Whyisthereamaximumintherateofreactionwithrespecttoconversion hencewithrespecttotemperatureandreactorvolume foranadiabaticreactor RateLaw CurveA Reactionrateslow conversiondictatedbyrateofreactionandreactorvolume Astemperatureincreasesrateincreasesandthereforeconversionincreases CurveB Reactionrateveryrapid Virtualequilibriumreachedinreactionconversiondictatedbyequilibriumconversion Forfixedvolumeofcatalyst thereisanTopt intogivemaximumXForfixedconversion thereisanTopt intouseminimumvolumeofcatalystIfVcat 1 Vcat 2 Topt in 1 Topt in 2 FixedVolumeExothermicReactor Optimumfeedtemperatureforexothermicreversiblereaction in 14 3 3Stagedadiabaticpackedbedreactors 33 Optimizationoftheoperationsofstagedpackedbed 34 T0 T1 x1 x1 T1 x3 Togettheminimum thefollowingconditionsshouldbefulfilled T2 x2 x2 T2 优化变量 Ti为i 1级入口温度 xi为i级出口转化率 以上条件的物理含义 第i级出口反应速率与第i 1级反应速率相等第i级入口温度是第i级出口转换率的最优温度 35 Two stageadiabaticpackedbedreactors 36 Optimumtwo stagepackedbedreactor Theoptimizationofoperationsreducestominimizingthetotalamountofcatalystneededtoachieveagivenconversion Threevariables 1 theincomingtemperatureTa 2 theamountofcatalystusedinthefirststage 3 theamountofinter coolingProceduresGuessTa Movealongtheadiabaticlineuntilthefollowingconditionissatisfied Cooltopointcwhichhasthesamerateofreactionaspointb thusMovealongtheadiabaticfrompointcuntilthecriterionofEq 1issatisfied givingpointd Repeatuntilpointdisatthedesiredfinalconversion 37 Eq 1 Coldshotcoolingmultistagefixed bedreactor 38 Optimumtwo stagemixedflowreactorsetup 39 Infiniterecycleforstagedpackedbeds Optimumtwo stagepackedbedreactorwithrecycle 40 TheconversionsshownrepresentarecycleratioR 1inbothstages 14 4Fixed bedreactorwithheatingorcooling Heattransferinthefixed bedreactorHeattransferbetweentheparticleandfluidEffectiveheatconductanceofthebedHeattransferbetweenthebedandwall 41 42 14 4 1Heattransferbetweentheparticleandfluid Heatflux Forforcedconvection theheattransfercoefficientisnormallycorrelatedintermsofthreedimensionlessgroups amisthesurfaceareaperunitweightofcatalyst isafactorrelatedtothecatalystshape 14 4 2Effectivethermalconductivityofpackedbed Theprinciplemechanismsofheattransferinpackedbedsareasfollows ConductionthroughthegasandsolidphasesRadiationbetweenparticlescombinedwithconductionConvectiveflowoffluidelements 43 ktdistheturbulentdiffusionthermalconductivitykt fisthethermalconductivityofthefluidkteistheeffectivethermalconductivityofthebedkristheradiationconductivity 1 Conductionthroughthegasandsolidparticles 44 45 2 Radiantheattransfer Theradialfluxbetweentwosurfacesis hristheradialheattransfercoefficient bisthebedvoidage RadiationbetweenparticlesandconductionthoughthesolidareaccountedforinthemodelofSchotte For3 mmcatalystparticlesinair krisabout1 2kt fat300oCand2 0kt fat500oC 3 Convectiveflowoffluidelements 46 TakingthePecletnumberas10 then 14 4 3Heattransferbetweenbedandwall 47 Tm TheaveragebedtemperatureTR Thetemperaturethatwouldbereachedbyextendingtheparabolatothewall Tw ThewalltemperatureTc Thetemperatureinthecenter Whichtemperaturedifferenceisusedtocalculatetheheattransferrate 14 4 3Heattransferbetweenbedandwall 48 一维模型 二维模型 Theaveragebedtemperature Tm isusedtocalculatethetemperaturedifference andtheheattransfercoefficientish0 Thebedtemperatureattheboundarylayer TR isusedtocalculatethetemperaturedifference andtheheattransfercoefficientusedishw Usingtheoverallheattransfercoefficient U where Torelatektetohb thebedgeometryandshapeofthetemperatureprofileareneeded Ifq therateofheatgenerationperunitvolumeofbed isassumedtobeindependentofthebedradius aheatbalanceforaunitlengthofcylindricalbedis 49 Thetotalheatgeneratedisequatedtotheheatconductedfromthebed usingthedrivingforce Tm TR hb的定义式 热量平衡 50 Integrationleadsto Asaresult AccordingtothedefinitionofTm thereis 51 Insummary theheattransferratecanbecalculatedbasedondifferentdrivingforce T butthecorrespondingheattransfercoefficientmustbeproperlyused hb h0 hw hj U 14 5Designequationforthepackedbedreactor 52 Assumptions 1 Plugflow 2 OverallheattransfercoefficientisU Molarbalance Energybalance Boundaryconditions 自换热固定床反应器 53 Iso thermalreactor Thereactionrate Tmisthetemperatureofthecooling heatingfluid 54 Adiabaticpackedbed Adiabatictemperatureincreaseis 55 Non isothermalandnon adiabaticfixedbed Thenumericalschemes 1 2 Iteration 2 1 2 1 untilconvergence 56 Typicalresults 14 62Dmodelofthepackedbedreactor 57 In Out Generation Accumulation 2Dmodelofthepackedbedrea