第三章 管式反应器

第三章管式反应器3.1平推流反应器thePlugFlowReactor平推流反应器（PFR）：反应器中的流动状态是人们设想的一种理想流动，即在反应器内具有严格均匀的速度分布，且轴向没有任何混合。PFRischaracterizedbythefactthattheflowoffluidthroughthereactorisorderlywithnoelementoffluidovertakingormixingwithanyotherelementaheadorbehind.Actually,theremaybelateralmixingoffluidinaPFR;however,theremustbenomixingordiffusionalongtheflowpath.Thenecessaryandsufficientconditionforplugflowisfortheresidencetimeinthereactortobethesameforallelementsoffluid.平推流反应器特点：（1）在正常情况下，它是连续定态操作，故在反应器的各个截面上，过程参数（浓度、温度等）不随时间而变化；（2）反应器内浓度、温度等参数随轴向位置变化，故反应速率随轴向位置变化。（3）由于径向具有严格均匀的速度分布，也就是在径向不存在浓度分布。

PFR的基础设计方程对PFR建立物料衡算式，就可以得到PFR的基础设计方程式。在PFR中进行平推流动时，物料衡算式有如下特点：（1）由于流动处于稳定状态，各点浓度、温度和反应速度均不随时间而变化，故单元时间上t可任取；（2）

由于沿流动方向浓度、温度和（－rA）都在改变，故应取单元体积△V＝dV；（3）稳定状态下，单元时间、单元体积内反应物的积累量为零。Steady-statePlugFlowReactorInaplugflowreactorthecompositionofthefluidvariesfrompointtopointalongflowpath;consequently,thematerialbalanceforareactioncomponentmustbemadeforadifferentialelementofvolumedV.ThusforreactantA,thematerialbalancebecomesinput=output+disappearancebyreaction+accumulation=0ReferringtoFigleft,weseeforvolumedVthat:InputofA,moles/time=FAOutputofA,moles/time=FA+dFADisappearanceofAbyreaction,moles/time=(-rA)dVFig5.5onpage101LevIntroducingthesethreetermsinthematerialbalanceequationweobtainFA=(FA+dFA)+(-rA)dVNotingthatdFA=d[FA0(1-xA)]=-FA0dxAWeobtainonreplacementFA0dxA=(-rA)dVThis,then,istheequationwhichaccountsforAinthedifferentialsectionofreactorofvolumedV.Forthereactorasawholetheexpressionmustbeintegrated.NowFA0,thefeedrate,isconstant,but(-rA)iscertainlydependentontheconcentrationorconversionofmaterials.Groupingthetermsaccordingly,weobtainEquation3.2-5allowsthedeterminationofreactorsizeforagivenfeedrateandrequiredconversion.Asamoregeneralexpressionforplugreactors.Ifthefeedonwhichconversionisbased,subscript0,entersthepartiallyconverted,subscripti,andleavesataconversiondesignatedbysubscriptf,wehaveForthespecialcaseofconstant-densitysystemsxA=1-CA/CA0ordxA=-dCA/CA0Inwhichcasetheperformanceequationcanbeexpressedintermsofconcentrations,orTheseperformanceequationscanbewritteneitherintermsofconcentrationorconversion.Whateveritsform,theperformanceequationsinterrelatetherateofreaction,theextentofreaction,thereactorvolume,andthefeedrate,andifanyoneofthesequantitiesisunknownitcanbefoundfromtheotherthree.Fig.Belowdisplaystheseperformanceequationsandshowsthatthespace-timeneededforanyparticulardutycanalwaysbefoundbynumericalorgraphicalintegration.However,forcertainsimplekineticformsanalyticintegrationispossible–andconvenient.Someofthesimplerintegratedformsforplugflowareastable3.2-1.Fig5.6onpage103Bycomparingthebatchexpressionswiththeseplugflowexpressionswefind:Forsystemsofconstantdensity(constant-volumebatchandconstant-densityplugflow)theperformanceequationsareidentical,τforplugflowisequivalenttotforthebatchreactor,andtheequationscanbeusedinterchangeable.Forsystemsofchangingdensitythereisnodirectcorrespondencebetweenthebatchandplugflowequationsandthecorrectequationmustbeusedforeachparticularsituation.Inthiscasetheperformanceequationscannotbeusedinterchangeable.Example3.2-2PlugFlowReactorperformanceAhomogenousgasreactionA3Phasareportedrateat215℃,(-rA)=0.01CA1/2,(mol/liter·sec).Findthespace-timeneededfor80%conversionofa50%A-50%inertfeedtoaplugflowreactoroperatingat215℃and5atm(CA0=0.0625mol/liter).SolutionForthisstoichiometryandwithinerts,InwhichcasetheplugflowperformanceequationbecomesTheintegralcanbeevaluatedinanyoneofthreeways:graphically,numerically,oranalytically.LetusillustratethesemethodsGraphicalIntegration.Firstevaluatethefunctiontointegratedatselectedvalues(seetable)andplotthisfunction(seeFig).CountingsquaresorestimatingbyeyewefindNumericalIntegration.UsingSimpson’srule,applicabletoanevennumberofuniformlyspacedintervalsonthexAaxis,wefindAnalyticalIntegration.FromatableintegralsThemethodofintegrationrecommendeddependsonthesituation.Inthisproblemprobablythenumericalmethodisthequickestandsimplestandgivesagoodenoughanswerformostpurposes.Sowiththeintegralevaluated,Eq.BecomesThehomogenousgasdecompositionofphosphine4PH3(g)→P4+6H2Proceedsat649℃withthefirst-orderrate(-rPH3)=(10/hr)CPH3

Whatsizeofplugflowreactoroperatingat649℃and460kPacanproduce80%conversionoffeedconsistingof40molofpurephosphineperhour?Fig5.5onpage106Solution:

letA=PH3,R=P4,S=H2,thenthereactionbecomes4A→R+6Swith(-rA)=(10/hr)(CA)Thevolumeofplugflowreactorisgivenby3.2-5

EvaluatingtheindividualtermsinthisexpressiongivesFA0=40mol/hrCA0=PA0/RT=460000/(8.314×922)=60mol/m3

εA=(7-4)/4*1=0.75xA=0.8hencethevolumeofreactor3.2变温平推流反应器

平推流反应器能量方程的推导，与间歇反应器相似。对于定常流动的PFR，系对微元反应体积作热量衡算，而不是对微元反应时间。1）

基础设计式：作PFR中微元段dl的物料衡算FtFt+dFtdlTmLFA0xAxA+dxATT+dT0(1)作热量衡算FtCptT=(Ft+dFt)Cpt(T+dT)±（-rA）(-△HA)T0S·dl+UA（T-Tm）dl+0FtCpt≈(Ft+dFt)Cpt（2）（1）代入（2）式，得联立（1）、（3）式得：这是非线性常微分方程组，可以用数值法求解，如改进欧拉法等。（3）0LTT0xA2）绝热PFR设计式绝热平推流反应器得热量衡算式中，对外传热项为零，故（2）式变为：式中λ近似为常数，称为变温绝热PFR的绝热温升于是：T-T0=λ(xA-xA0)，从PFR进口处状态T0，xA开始，由各点xA可得相应的反应温度T，结合起来计得（-rA）之值，再代入3）作图法求解变温PFR：xA1.00T0,xA0T0xAfVP/FA0(-rA)斜率=1/λ3.3组合反应器

Multiple-ReactorSystem

3.3.1(a)PlugFlowReactorsinSeriesand/orinParallelConsiderNplugflowreactorconnectedinseries,andletx1,x2,…,xNbethefractionalconversionofcomponentAleavingreactor1,2,…,N.BasingthematerialbalanceonthefeedrateofAtothefirstreactor,wefindfortheithreactorfromEq.3.2-6

OrfortheNreactorsinseriesHence,NplugflowreactorsinserieswithatotalvolumeVgivesthesameconversionasasingleplugflowreactorofvolumeFortheoptimumhookup(连接)ofplugflowreactorsconnectedinparallelorinanyparallel-seriescombination,wecantreatthewholesystemasasingleplugflowreactorofvolumeequaltothetotalvolumeoftheindividualunitsifthefeedisdistributedinsuchamannerthatfluidstreamsthatmeethavethesamecomposition.Thus,forreactorsinparallelV/Forτmustbethesameforeachparallelline.Anyotherwayoffeedingislessefficient.Example:ThereactorsetupshowninFig.Consistsofthreeplugflowreactorsintwoparallelbranches.BranchDhasareactorofvolume50litersfollowedbyareactorofvolume30liters.BranchEhasareactorofvolume40liters.WhatfractionofthefeedshouldgotobranchD?Solution:BranchDconsistsoftworeactorsinseries;hence,itmaybeconsideredtobeasinglereactorofvolumeVD=50+30=80litersNowforreactorsinparallelV/Fmustbeidenticaliftheconversionistobethesameineachbranch.Therefore,Therefore,two-thirdsofthefeedmustbefedtobranchD.3.4循环反应器RecycleReactorIncertainsituationsitisfoundtobeadvantageoustodividetheproductstreamfromaplugflowreactorandreturnaportionofittotheentranceofthereactor.LettherecycleratioβbedefinedasThisrecycleratiocanbemadetovaryfromzerotoinfinity.Reflectionsuggeststhatastherecycleratioisraised