化学反应工程课件

第2章均相反应动力学

Chapter2KineticsofHomogenousReactions2.1反应速率方程

2.1TheRateEquation2．l．1反应速率表示方法

2.1.1TheRateExpressionsTheminussignmeansdisappearingSupposeasingle-phasereactionAPThemostusefulmeasureofrateforAisthen

均相反应速率定义：单位时间内，单位体积反应混合物中某一组分i的反应量（或生成量）。例如，有一简单反应APCaution1&2(-rA)为一整体符号，恒为正值Supposeasingle-phasereactionaA+bBpP+sSTheratesofallmaterialsarerelatedbyCaution3AccordingtotherateequationCaution4OrFortheidealgaseswhereInaconstant-volumesystemthemeasureofreactionrateofcomponentibecomesCaution5TherateofreactioninitsvariousformsisdefinedasfollowsBasedonunitvolumeofreactionfluidBasedonunitmassofsolidinfluid-solidsystemsBasedonunitinterfacialsurfaceintwo-fluidsystemsorbasedonunitsurfaceofsolidingas-solidsystemsBasedonunitvolumeofsolidingas-solidsystemsBasedonunitvolumeofreactorInhomogenoussystems,thevolumeoffluidinthereactorisoftenidenticaltothevolumeofreactor.InsuchcaseVandVRareidenticalandEqs2.1-7and2.1-11areusedinterchangeable.Inheterogeneoussystemsallabovedefinitionsofreactionrateencountered,thedefinitionusedinanyparticularsituationoftenbeingamatterofconvenienceFromEqs2.1-7and2.1-11theseintensivedefinitionsofreactionratearerelatedby

W——固体（催化剂）的重量S——相界面面积VP——固相（催化剂）占体积；V——液相占体积；VR­­——反应器的有效体积，VR＝VP＋V。Theconversion

转化率SupposethatNA0isinitialamountofAinreactorattimet=0,andthatNAtheamountpresentattimet.thentheconversionofAintheconstantvolumesystemisgivenby微分上式fortheconstantvolumesystem

式中CA0——A的初始浓度。2.1.2KineticsofHomogeneousReaction均相反应：反应物系中，所有反应物及生成物（包括催化剂在内）都处于同一相中。影响反应速率的参数：浓度、温度、催化剂等，因此，反应速率与上述这些参数成函数关系。SupposeahomogeneousirreversiblereactionTherateofprogressofthereactioncanbeapproximatedbyanexpressionofthefollowingtypen=α+βWhereα,βarenotnecessarilyrelatedtothestoichiometriccoefficients.Wecallthepowerstowhichtheconcentrationsareraisedtheorderofthereaction.Thus,thereactionis

αthorderwithrespecttoA

βthorderwithrespecttoBnthorderoverall速率常数k

RateConstantkWhentherateexpressionforahomogenouschemicalreactioniswrittenintheformEq.2.1.17,thedimensionsoftherateconstantkfornth-orderreactionare(time)-1(concentration)1-nwhichforafirst-orderreactionbecomessimply(time)-12.1.3Arrhenius’LawFormanyreactions,andparticularlyelementaryreaction,therateexpressioncanbewrittenasaproductofatemperature-dependenttermandacomposition-dependentterm,or(-rA)=f1(temperature)·f2(composition)=k·f2(composition)Forsuchreactionthetemperature-dependentterm,thereactionrateconstant,hasbeenfoundinpracticallyallcasestobewellrepresentedbyArrhenius’Law:k=k0e-E/RTWhere:k0frequencyorpre-exponentialfactorEActivationenergyAttwodifferenttemperatures,Arrhenius’LawindicatesthatActivationenergyandtemperaturedependencyFromArrhenius’Lawaplotoflnkvs1/Tgivesastraightline,withlargeslopeforlargeEandsmallslopeforsmallEReactionswithhighactivationenergiesareverytemperature-sensitive;reactionwithlowenergiesarerelativelytemperature-insensitive.Anygivenreactionismuchtemperature-sensitiveatalowtemperaturethanatahightemperature.FromtheArrhenius’Law,thevalueoffrequencyfactork0doesnotaffectthetemperaturesensitive.Example:Milkispasteurizedifitisheatedto63℃for30min,butifitisheatedto74℃itonlyneeds15sforthesameresult.Findtheactivationenergyofthissterilization.Solutionherewearetoldthatt1=30minataT1=336Kt2=15secataT2=347KNowtherateisinverselyproportiontothereactiontime,orrate∝1/timesoEq2.1-21becomesFromwhichtheactivationenergyE=422000J/mol第8页例题2-1自习2．2单一反应TheSingleReactions

2．2．1一级反应

IrreversibleUnimolecular-TypeFirst-OrderReactionConsiderthereactionA

Patconstant-volumeandconstant-temperatureprocesses,thefirst-orderrateequationisForthisreaction.SeparatingandintegratingweobtainAplotofln(1-XA)orln(CA/CA0)vs.t,asshownontheleft,givesastraightlinethroughtheoriginforthisformofrateofequation.2．2．2二级反应

IrreversibleBimolecular-TypeSecond-OrderReactionConsiderthereactionA+APwithcorrespondingrateequationWhichonintegrationyieldsConsiderthereactionA+BP.Thedefinitionsecond-orderdifferentialequationbecomesNotingthattheamountsofAandBthathavereactedatanytimetareequalandgivenbyCA0xA,wemaywriteaboveequationintermsofxAasLettingM=CB0/CA0betheinitialmolarratioofreaction,weobtain

WhichonseparationandformalintegrationbecomesAfterbreakdownintopartialfractions,integrationandrearrangement,thefinalresultinanumberofdifferentformisThefiguresshowtwoequivalentwaysofobtainingalinearplotbetweentheconcentrationfunctionandtimeforthissecond-orderratelaw.2.2.3n级反应

Irreversiblenth-orderReaction

ConsiderthereactionnAP.Whenthemechanismofreactionisnotknown,weoftenattempttofitthedatawithnth-orderrateequationoftheformWhichonseparationandintegrationyieldsTheorderncannotbefoundexplicitlyfromtheequation,soatrial-anderrorsolutionmustbemade.Thisisnottoodifficult,however.Justselectavaluefornandcalculatek.Thevalueofnwhichminimizesthevariationinkisthedesiredvalueofn.SeeTable2.2-1(Page11)[例题2.2-1]

气相反应A

3P为一级反应，速度常数k=0.5min-1，反应在恒容间歇式反应器中进行，求1min后体系的总压，进料状况如下：a)纯A，0.1Mpa；b)纯A，1Mpa；c)10%的A和90%的I（惰性气体）混合物，1MPa解：对比（1）、（2），得

当t=0，

=

0积分（3），得

2.3可逆反应

ReversibleReaction可逆反应是指正方向、逆方向同时以显著速度进行的反应，也叫对峙反应。2.3.1First-orderReversiblereactionLetusconsidertheopposedunimolecular-typedreactionKC=K=k1/k2equilibriumconstantStartingwithaconcentrationratioM=CR0/CA0therateequationisNowatequilibriumdCA/dt=0.HencefromEq.2.3.1wefindtheequilibriumconstantofAatequilibriumconditionstobeCombiningtheaboveequationsweobtain,intermsoftheequilibriumconversionThismaybelookedonaspseudofirst-orderirreversiblereactionwhichonintegrationgivesAplotof–ln(1-xA/xAe)vs.t,asshownintheFig.,givesastraightline2.3.2二级可逆反应

Second-orderReversibleReaction

Forthebimolecular-typesecond-orderreactionWiththerestrictionthatCA0=CB0andCR0=CS0,theintegratedrateequationforAandBisasfollowsAplotcanthenbeusedtotesttheadequacyofthiskineticsTable2.3.1onpage132．4复合反应

MultipleReactionSinglereactionrequiresonlyonerateexpressiontodescribeitskineticsbehaviorwhereasmultiplereactionsrequiremorethanonerateexpression.Multiplereactionscanbeconsideredtobecombinationsoftwoprimarytypes:parallelreactionsandseriesreactions.收率：Yield,fractionyield得率：Operationyield选择性：Selectivity2.4.l一级平行反应

First-orderParallelReactionConsiderthedecompositionofAbyeitheroneoftwopaths:WithcorrespondingrateequationsIntegratingtheequation(1)att=0,CA=CA0，CP=CP0，CS=CS0

Integratingtheequation(2)Integratingtheequation(3)2.4.2一级连串反应

IrreversibleFirst-orderReactioninseriesWeconsiderconsecutiveunimolecular-typefirst-orderreactionsuchasWhoserateequationsforthethreecomponentsareLetusstartwithaconcentrationCA0ofA,noPandSpresent,andseehowtheconcentrationsofthecomponentschangewithtime.ByintegrationofEq.(1)wefindtheconcentrationofAtobeTofindthechangeconcentrationofP,substitutetheconcentrationofAfromEq.(4)intothedifferentialequationgoverningtherateofchangeR,Eq.(2);thusWhichisafirst-orderlineardifferentialequation(一阶线形微分方程）oftheformBymultiplyingthroughwiththeintegratingfactor(积分因子)R=thesolutionisApplyingthisgeneralproceduretotheintegrationofEq.(5),wefindthattheintegratingfactoris.Theconstantofintegrationisfoundtobe–k1CA0/(k2-k1)fromtheinitialconditionsCR0=0att=0,andthefinalexpressionforthechangingconcentrationofP(6)Notingthatthereisnochangeintotalnumberofmoles,thestoichiometryrelatestheconcentrationsofreactingcomponentsbywhichwithEqs.(4)and(6)givesThus,wehavefoundhowtheconcentrationsofcomponentsofA,P,andSvarywithtime.Ifk2ismuchlargerthank1,Eq.(7)reducestoInotherwords,therateisdeterminedbyk1orthefirststepofthetwo-stepreaction.Ifk1ismuchlargerthank2,thenWhichisafirst-orderreactiongovernedbyk2,theslowerstepinthetwo–stepreaction.Thus,ingeneral,foranynumberofreactionsinseriesitisthesloweststepthathasthegreatestinfluenceontheoverallreactionrate(7)toptAsmaybeexpected,thevalueofk1andk2alsogovernthelocationandmaximumconcentrationofP.ThismaybefoundbydifferentiatingEq.(6)andsettingdCP/dt=0.ThetimeatwhichthemaximumconcentrationofPoccursisthusThemaximumconcentrationofPisfoundbycombiningEqs.(6)andtheabovetogiveIfk1=k2,theconcentrationofPandSshouldbere-foundPage16figure2.4.32.5自催化反应

AutocatalyticReactionAreactioninwhichoneoftheproductsofreactionactsascatalystiscalledanautocatalyticreaction.ThesimplestsuchreactionisA+PP+PforwhichtherateequationisBecausethetotalnumberofmolesofAandPremainunchangedasAisconsumed,wemaywritethatatanytimeC0=CA+CP=CA0+CP0=constantThus,therateequationbecomesRearrangingandbreakingintopartialfraction,weobtainForanautocatalyticreactioninbatchreactorsomeproductPmustbepresentifthereactionistoproceedatall.StartingwithaverysmallconcentrationofP,weseequalitativelythattheratewillriseasPisformed.Atotherextreme,whenAisjustaboutuseduptheratemustdroptozero.Thisresultisgiveninfig.below,whichshowsthattheratefollowsaparabola,whichamaximumwheretheconcentrationsofAandPareequal.2.6反应前后分子数变化的气相反应

IsothermalGas-phaseReactionwithvarying-molecular变容反应系统：反应前后分子数发生变化，如果过程恒压，则为变容反应系统;恒容变压过程：分于数发生变化的气相反应，如果反应器的容积恒定，其结果使反应系统的总压变化，称之为恒容变压过程。2.6.1膨胀因子δ和膨胀率εA

膨胀因子δA的意义是反应物A每消耗lmol时，引起整个物系总物质的量的增加或减少值。

aA+bBpP+sSδA的大小只取决于化学计量式本身，与是否存在惰性气体无关；δA表示反应过程中mol数的变化，与体系体积变化无关；对于复杂反应，其数值大小随转化率而变化，没有明确意义；δA数值可正可负，可以为分数。Acapillarytubereactorcanbeusedforisothermalconstantpressureoperation,ofreactionshavingasinglestoichiometry.Forsuchsystemthevolumeislinearlyrelatedtotheconversion,orV=V0(1+εAxA)whereεAisthefactionalchangeinvolumeofthesystembetweennoconversionandcompletelyconversionofreactantA.AsanexampleoftheuseofεAandδA,considertheisothermalgas-phasereactionA4R,(a)bystartingwithpurereactantA,εA=(4-1)/1=3δA=(4-1)/1=3(b)Butwith50%inertspresentatthestart,twovolumesofreactantmixtureyield,oncompletelyconversion,fivevolumesofproductmixture.InthiscaseεA=(5-2)/2=1.5δA=(4-1)/1=32.6.2等温等压变容过程Isothermalconstantpressurevarying-volumeprocesses例题：设有一级气相反应A2P，分别在等容、等压条件下进行到xA=0.5，求二者的残余A组分浓度及反应速度。等容：体积不变，压力增加50%CA=CA0(1-xA)=CA0/2(-rA)=kCA=kCA0/2等压：压力不变，体积增加50%CA=CA0/3(-rA)=kCA=kCA0/3NotingthatnA=nA0(1-xA).Wehavewhichistherelationshipbetweenconversionandconcentrationforisothermalvarying-volumesystemssatisfyingthelinearityassumptionTherateofnth-orderreaction(disappearanceofcomponentA),isForthefirst-orderreactionn=12.6.3等温等容变压过程IsothermalConstant-VolumeVarying-pressureprocesses

AtIsothermalConstant-Volume,εA=0,δAmaynotbeequalto0[例题2.6-1](p19)总压法测定气相反应的速度常数。设在一间歇反应器内进行等温等容反应

已知速率方程：由式（2.6-16）得代入速率式

将上式积分，得

2.7动力学的实验和数据处理

KineticsExperimentandits

Data

AnalysisArateequationcharacterizestheratereaction,anditsformmayeitherbesuggestedbytheoreticalconsiderationorsimplytheresultofanempiricalcurve-fittingprocedure.Inanycase,thevalueoftheconstantsoftheequationcanonlybefoundbyexperiment;predictivemethodsareinadequateatpresent.Thedeterminationoftherateequationisusuallyatwo-stepprocedure;firsttheconcentrationdependencyisfoundatfixedtemperatureandthenthetemperaturedependenceoftherateconstantsisfound,yieldingthecompleterateequation.Equipmentbywhichempirical(经验)informationisobtainedcanbedividedintotwotypes,thebatchandflowreactors.Thebatchreactor（釜式反应器或间歇式反应器）issimplyacontainertoholdthecontentswhiletheyreact.Theexperimentalbatchreactorisusuallyoperatedisothermallyandatconstantvolumebecauseitiseasytointerpret(解释)theresultsofsuchruns.Thisreactorisarelativelysimpledeviceadaptable（能适应的）tosmall-scalelaboratoryset-ups（装置）,anditneedsbutlittleauxiliary（辅助设施）equipmentorinstrumentation.Thus,itisusedwheneverpossibleforobtaininghomogenouskineticdata.Theflowreactor(连续式反应器)isusedprimarilyinthestudyofthekineticsofheterogeneous(非均相)reactions.Planningofexperimentsandinterpretationofdataobtainedinflowreactorsareconsideredinlaterchapters.Therearetwoproceduresforanalyzingkineticdata,theintegralandthedifferentialmethods(积分法和微分法).2.7.1用积分法分析实验数据

Analyzingtheexperimentdatabyintegralmethod

Intheintegralmethodofanalysisweguessaparticularformofrateequationand,afterappropriateintegrationandmathematicalmanipulation,predictthattheplotofacertainconcentrationfunctionversustimeshouldyieldastraightline.Thedataareplotted,andifareasonablygoodstraightlineisobtained,thentherateequationissaidtosatisfactorilyfitthedataHalf-timet1/2method半衰期法Forasinglenth-orderreactionIntegratingforn1givesDefiningthehalf-timeofreaction,t1/2,asthetimeneededfortheconcentrationofreactantstodroptoone-halftheoriginalvalue,weobtainThisexpressionshowsthataplotoflogt1/2vs.logCA0givesastraightlineofslope1-n,asshowninFig2.7.1Thehalf-timemethodrequiresaseriesofruns,eachatadifferentinitialconcentration,andshowsthatthefractionalconversioninagiventimeriseswithincreasedconcentrationforordersgreaterthanone,dropswithincreasedconcentrationfororderslessthanone,andisindependentofinitialconcentrationforreactionsoffirstorder.2.7.2用微分法分析实验数据

Analyzingtheexperimentdatabydifferentialmethod

Thedifferentialmethodofanalysisdealsdirectlywiththedifferentialrateequationtobetested,evaluatingalltermsintheequationincludingthederivativedCi/dt,andtestingthegoodnessoffitoftheequationwithexperiment.Theprocedureisasfollows.1)PlottheCAvs.tdata,andthenbyeyecarefullydrawasmoothcurvetorepresentthedata.Thiscurvemostlylikelywillnotpassthroughalltheexperimentalpoints/2)Determinetheslopeofthiscurveatsuitablyselectedconcentrationvalues.Theseslopes-dCA/dt=(-rA)aretheratesofreactionatthesecompositions3)Nowsearchforarateexpressiontorepresentthis(-rA)vs.CAdata,eitherbya)pickingandtestingaparticularrateform,(-rA)=kf(CA)b)testingannth-orderform(-rA)=kCAnbytakinglogarithmsoftherateequation2.7.2用微分法分析实验数据

微分法求动力学方程是直接利用某一类动力学方程的微分式，以反应速度对浓度的函数作图，然后与实测的数据相拟合的一种方法。一般也是设法把图形线性化，把实验数据代人。若得出一直线，便认为所假设的动力学方程是正确的。否则，重新选定另一个动力学方程进行猜算，直到得出一条直线为止。在处理实验数据时，最小二乘法特别适用于如下形式的方程式：

(2.7-6)

k,α,β是待测定的，为此，可对式（2.7-6）取对数：写成：根据最小二乘法法则：

当a0、a1、a2取得最佳值时，有：也就是用分别对a0,a1,a2求偏导数并令其为零，可以得到方程组|：这是一个三元一次方程组，可以用行列式求解第3章均相等温反应器

Chapter3HomogeneousIsothermalReactors3．1概述

GeneralIntroduction

Inreactordesignwewanttoknowwhatsizeandtypeofreactorandmethodofoperationarebestforagivenjob.Becausethismayrequirethattheconditionsinthereactorvarywithpositionaswellastime,thisquestioncanonlybeansweredbyaproperintegrationoftherateequationfortheoperation.Thismaypose(造成)difficultiesbecausethetemperatureandcompositionofthereactingfluidmayvaryfrompointtopointwithinthereactor,dependingontheendothermic(吸热的)orexothermic(放热的)characterofthereaction,therateofheatadditionorremovalfromthesystem,andtheflowpatternoffluidthroughthevessel.Ineffect,thenmanyfactorsmustbeaccountedforinpredictingtheperformanceofareactor.Howbesttotreatthesefactorsisthemainproblemofreactordesign.Operationtypes:thebatch(间歇)thesteady-stateflow(连续)theunsteady-statefloworsemibatchreactor(半连续)Flowpattern:IdealflowandNon-idealflowHeatTransferMethods:isothermaloperation,adiabaticoperation,heatexchangeandheatproducingfromreactionitself.1、反应时间与停留时间ReactionTimeandResidenceTime

反应时间：从反应物料加人反应器后实际进行反应时算起至反应到某一时刻所需的时间，称为反应时间，以符号t表示。停留时间：而所谓停留时间则是指从反应物料进人反应器时算起至离开反应器时为止所经历的时间。

2．空时与空速

Space-TimeandSpace-Velocity空时：为在规定条件下，进入反应器的物料通过反应器体积所需的时间，用符号

表示Space-Time:Timerequiredtoprocessonereactorvolumeoffeedmeasuredatspecifiedconditions空速:为在规定条件下，单位时间内进入反应器的物料体积相当于几个反应器的容积，用符号SV表示Space-velocity:NumberofreactorvolumesoffeedatspecifiedconditionswhichcanbetreatedinuinttimeWemayarbitrarilyselectthetemperature,pressure,andstateatwhichwechoosetomeasurethevolumeofmaterialbeingfedtothereactor.Certainlythevalueforspace-velocityorspace-timedependsontheconditionsselected.Iftheyareofthestreamenteringthereactor,therelationbetweensVand

andtheotherpertinentvariablesisTherelationbetweenthespace-velocityandspace-timeforactualfeedconditions(unprimedsymbols)andatstandardconditionsisgivenbyInmostofwhatfollows,wedealwiththespace-velocityandspace-timebasedonfeedatactualenteringconditions;however,thechangetoanyotherbasisiseasilymade.Thestartingpointforalldesignisthematerialbalanceexpressedforanyreactant(orproduct).Thus,asillustratedinfigurebelow,wehaveWherethecompositionwithinthereactorisuniform(independentofposition),theaccountingmaybemadeoverthewholereactor.Wherethecompositionisnotuniform,itmustbemadeoveradifferentialelement(微元)ofvolumeandthenintegratedacrossthewholereactorfortheappropriateflowandconcentrationconditions.Forthevariousreactortypesthisequationsimplifiesonewayoranother,andtheresultantexpressionwhenintegratedgivesthebasicperformanceequationforthattypeofunit.Thus,inthebatchreactorthefirsttwotermsarezero,inthesteady-stateflowreactorthefourthtermdisappears;forthesemibatchreactorallfourtermsmayhavetobeconsidered.

Innonisothermaloperationsenergybalancesmustbeusedinconjunctionwithmaterialbalances.Thus,asillustratedinFigbelow,wehaveFig4.3onpage85LevAgain,dependingoncircumstances,thisaccountingmaybemadeeitheraboutadifferentialelementofreactororaboutthereactorasawhole.Thematerialbalanceandenergybalancearetiedtogetherbytheirthirdtermsbecausetheheateffectisproducedbythereactionitself.Sincethematerialbalanceandenergybalancearethestartingpointsforalldesign,weconsidertheirintegrationforvarietyofsituationsofincreasingcomplexityinthechapter.3．2简单反应器3．2.1间歇反应器BatchReactor(BR)Inbatchreactor,orBR,ofFig.3.2-1thereactantsareinitiallychargedintoacontainer,arewellmixed,andarelefttoreactforacertainperiod.Theresultantmixtureisthendischarged.Thisisanunsteady-stateoperationwherecompositionchangeswithtime;however,atanyinstantthecompositionthroughoutthereactorisuniform.MakeamaterialbalanceforanycomponentA.Forsuchanaccountingweusuallyselectthelimitingcomponent.Inabatchreactor,sincethecompositionisuniformthroughoutatanyinstantoftime,wemaymaketheaccountingaboutthewholereactor.Notingthatnofluidentersorleavesthereactionmixtureduringreaction,materialbalanceequationwhichwaswrittenforcomponentA,becomes=0=0input=output+disappearance+accumulationEvaluatingthetermsofEq.1,wefind(1)ByreplacingthesetwotermsinEq.1,weobtainRearrangingandintegratingthengivesThisisthegeneralequationshowingthetimerequiredtoachieveaconversionxAforeitherisothermalornonisothermaloperation.Thevolumeofreactingfluidandthereactionrateremainundertheintegralsign,foringeneraltheybothchangeasreactionproceeds.Thisequationmaybesimplifiedforanumberofsituations.Ifthedensityofthefluidremainsconstant(恒容),weobtainFig.belowisagraphicalrepresentationoftheseequations.Fig5.2onpage92Lev恒容过程Forallreactionsinwhichthevolumeofreactingmixturechangesproportionatelywithconversion,suchasinsinglegas-phasereactionswithsignificantdensitychanges,theEq.Abovebecomes变容反应volume-varyingreactionsIftheequationsmentionedabovecannotbeintegrateddirectly,thegraphicalmethodcanbeused间隙反应器的体积计算由BR设计式求得每批操作的反应时间t后，可以根据经验选取两批操作之间必须有的辅助时间τ’，根据物料处理量求得每批操作总时间内物料的平均体积处理量υ0，求得反应器的有效体积VR，再根据物料的起泡特性，在0.4-0.85之间选取一个装料系数φ，而求得反应器总体积VBVR=(t+τ’)υ0

VB=VR/φ如果算得的VB太大，则可以分成若干个小间隙釜并列操作，起效果相同，但设备造价提高。[例题3.2-1]某厂生产醇酸树脂是使己二酸和己二醇以等摩尔比在70℃用间隙釜并以H2SO4作催化剂进行缩聚反应而生产的，实验测得反应的动力学方程式为：(-rA)=kCA2kmol/(L·min)k=1.97L/(kmol·min)CA0=0.004kmol/L求己二酸转化率分别为xA=0.5、0.6、0.8、0.9所需的反应时间为多少？

若每天处理2400kg己二酸，转化率为80%，每批操作的非生产时间为1hr，计算反应器体积为多少？设反应器的装料系数为0.75。

解：（1）达到所需要求的转化率所需的反应时间为：

可见随着转化率的增加，所需的反应时间将急剧增加，因此，在确定最终转化率时应该考虑这一因素。

（2）反应器体积的计算：最终转化率为0.80时，每批所需的反应时间为8.50hr，

每小时己二酸进料量

每批生产总时间=反应时间+非生产时间=9.5hr反应器体积VR=ν0t总=171×9.5=1630L=1.63m3考虑装料系数，故实际反应器体积3.2.2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)dVFig5.5onpage101LevIntroducingthesethreetermsinthematerialbalanceequationweobtain

FA=(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.Forsystemsofchangingdensitythereisnodirectcorrespondencebetweenthebatchandplugflowequationsandthecorrectequ