化學反應工程課件

第2章均相反應動力學

Chapter2KineticsofHomogenousReactions2.1反應速率方程

2.1TheRateEquation2．l．1反應速率表示方法

2.1.1TheRateExpressionsTheminussignmeansdisappearingSupposeasingle-phasereactionAPThemostusefulmeasureofrateforAisthen

均相反應速率定義：單位時間內(nèi)，單位體積反應混合物中某一組分i的反應量（或生成量）。例如，有一簡單反應APCaution1&2(-rA)為一整體符號，恒為正值Supposeasingle-phasereactionaA+bBpP+sSTheratesofallmaterialsarerelatedbyCaution3AccordingtotherateequationCaution4OrFortheidealgaseswhereInaconstant-volumesystemthemeasureofreactionrateofcomponentibecomesCaution5TherateofreactioninitsvariousformsisdefinedasfollowsBasedonunitvolumeofreactionfluidBasedonunitmassofsolidinfluid-solidsystemsBasedonunitinterfacialsurfaceintwo-fluidsystemsorbasedonunitsurfaceofsolidingas-solidsystemsBasedonunitvolumeofsolidingas-solidsystemsBasedonunitvolumeofreactorInhomogenoussystems,thevolumeoffluidinthereactorisoftenidenticaltothevolumeofreactor.InsuchcaseVandVRareidenticalandEqs2.1-7and2.1-11areusedinterchangeable.Inheterogeneoussystemsallabovedefinitionsofreactionrateencountered,thedefinitionusedinanyparticularsituationoftenbeingamatterofconvenienceFromEqs2.1-7and2.1-11theseintensivedefinitionsofreactionratearerelatedby

W——固體（催化劑）的重量S——相界面面積VP——固相（催化劑）占體積；V——液相占體積；VR--——反應器的有效體積，VR＝VP＋V。Theconversion

轉(zhuǎn)化率SupposethatNA0isinitialamountofAinreactorattimet=0,andthatNAtheamountpresentattimet.thentheconversionofAintheconstantvolumesystemisgivenby微分上式fortheconstantvolumesystem

式中CA0——A的初始濃度。2.1.2KineticsofHomogeneousReaction均相反應：反應物系中，所有反應物及生成物（包括催化劑在內(nèi)）都處于同一相中。影響反應速率的參數(shù)：濃度、溫度、催化劑等，因此，反應速率與上述這些參數(shù)成函數(shù)關(guān)系。SupposeahomogeneousirreversiblereactionTherateofprogressofthereactioncanbeapproximatedbyanexpressionofthefollowingtypen=α+βWhereα,βarenotnecessarilyrelatedtothestoichiometriccoefficients.Wecallthepowerstowhichtheconcentrationsareraisedtheorderofthereaction.Thus,thereactionis

αthorderwithrespecttoA

βthorderwithrespecttoBnthorderoverall速率常數(shù)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頁例題2-1自習2．2單一反應TheSingleReactions

2．2．1一級反應

IrreversibleUnimolecular-TypeFirst-OrderReactionConsiderthereactionA

Patconstant-volumeandconstant-temperatureprocesses,thefirst-orderrateequationisForthisreaction.SeparatingandintegratingweobtainAplotofln(1-XA)orln(CA/CA0)vs.t,asshownontheleft,givesastraightlinethroughtheoriginforthisformofrateofequation.2．2．2二級反應

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

WhichonseparationandformalintegrationbecomesAfterbreakdownintopartialfractions,integrationandrearrangement,thefinalresultinanumberofdifferentformisThefiguresshowtwoequivalentwaysofobtainingalinearplotbetweentheconcentrationfunctionandtimeforthissecond-orderratelaw.2.2.3n級反應

Irreversiblenth-orderReaction

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

氣相反應A

3P為一級反應，速度常數(shù)k=0.5min-1，反應在恒容間歇式反應器中進行，求1min后體系的總壓，進料狀況如下：a)純A，0.1Mpa；b)純A，1Mpa；c)10%的A和90%的I（惰性氣體）混合物，1MPa解：對比（1）、（2），得

當t=0，

=

0積分（3），得

2.3可逆反應

ReversibleReaction可逆反應是指正方向、逆方向同時以顯著速度進行的反應，也叫對峙反應。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.,givesastraightline2.3.2二級可逆反應

Second-orderReversibleReaction

Forthebimolecular-typesecond-orderreactionWiththerestrictionthatCA0=CB0andCR0=CS0,theintegratedrateequationforAandBisasfollowsAplotcanthenbeusedtotesttheadequacyofthiskineticsTable2.3.1onpage132．4復合反應

MultipleReactionSinglereactionrequiresonlyonerateexpressiontodescribeitskineticsbehaviorwhereasmultiplereactionsrequiremorethanonerateexpression.Multiplereactionscanbeconsideredtobecombinationsoftwoprimarytypes:parallelreactionsandseriesreactions.收率：Yield,fractionyield得率：Operationyield選擇性：Selectivity2.4.l一級平行反應

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

Integratingtheequation(2)Integratingtheequation(3)2.4.2一級連串反應

IrreversibleFirst-orderReactioninseriesWeconsiderconsecutiveunimolecular-typefirst-orderreactionsuchasWhoserateequationsforthethreecomponentsareLetusstartwithaconcentrationCA0ofA,noPandSpresent,andseehowtheconcentrationsofthecomponentschangewithtime.ByintegrationofEq.(1)wefindtheconcentrationofAtobeTofindthechangeconcentrationofP,substitutetheconcentrationofAfromEq.(4)intothedifferentialequationgoverningtherateofchangeR,Eq.(2);thusWhichisafirst-orderlineardifferentialequation(一階線形微分方程）oftheformBymultiplyingthroughwiththeintegratingfactor(積分因子)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自催化反應

AutocatalyticReactionAreactioninwhichoneoftheproductsofreactionactsascatalystiscalledanautocatalyticreaction.ThesimplestsuchreactionisA+PP+PforwhichtherateequationisBecausethetotalnumberofmolesofAandPremainunchangedasAisconsumed,wemaywritethatatanytimeC0=CA+CP=CA0+CP0=constantThus,therateequationbecomesRearrangingandbreakingintopartialfraction,weobtainForanautocatalyticreactioninbatchreactorsomeproductPmustbepresentifthereactionistoproceedatall.StartingwithaverysmallconcentrationofP,weseequalitativelythattheratewillriseasPisformed.Atotherextreme,whenAisjustaboutuseduptheratemustdroptozero.Thisresultisgiveninfig.below,whichshowsthattheratefollowsaparabola,whichamaximumwheretheconcentrationsofAandPareequal.2.6反應前后分子數(shù)變化的氣相反應

IsothermalGas-phaseReactionwithvarying-molecular變?nèi)莘磻到y(tǒng)：反應前后分子數(shù)發(fā)生變化，如果過程恒壓，則為變?nèi)莘磻到y(tǒng);恒容變壓過程：分于數(shù)發(fā)生變化的氣相反應，如果反應器的容積恒定，其結(jié)果使反應系統(tǒng)的總壓變化，稱之為恒容變壓過程。2.6.1膨脹因子δ和膨脹率εA

膨脹因子δA的意義是反應物A每消耗lmol時，引起整個物系總物質(zhì)的量的增加或減少值。

aA+bBpP+sSδA的大小只取決于化學計量式本身，與是否存在惰性氣體無關(guān)；δA表示反應過程中mol數(shù)的變化，與體系體積變化無關(guān)；對于復雜反應，其數(shù)值大小隨轉(zhuǎn)化率而變化，沒有明確意義；δA數(shù)值可正可負，可以為分數(shù)。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等溫等壓變?nèi)葸^程Isothermalconstantpressurevarying-volumeprocesses例題：設(shè)有一級氣相反應A2P，分別在等容、等壓條件下進行到xA=0.5，求二者的殘余A組分濃度及反應速度。等容：體積不變，壓力增加50%CA=CA0(1-xA)=CA0/2(-rA)=kCA=kCA0/2等壓：壓力不變，體積增加50%CA=CA0/3(-rA)=kCA=kCA0/3NotingthatnA=nA0(1-xA).Wehavewhichistherelationshipbetweenconversionandconcentrationforisothermalvarying-volumesystemssatisfyingthelinearityassumptionTherateofnth-orderreaction(disappearanceofcomponentA),isForthefirst-orderreactionn=12.6.3等溫等容變壓過程IsothermalConstant-VolumeVarying-pressureprocesses

AtIsothermalConstant-Volume,εA=0,δAmaynotbeequalto0[例題2.6-1](p19)總壓法測定氣相反應的速度常數(shù)。設(shè)在一間歇反應器內(nèi)進行等溫等容反應

已知速率方程：由式（2.6-16）得代入速率式

將上式積分，得

2.7動力學的實驗和數(shù)據(jù)處理

KineticsExperimentandits

Data

AnalysisArateequationcharacterizestheratereaction,anditsformmayeitherbesuggestedbytheoreticalconsiderationorsimplytheresultofanempiricalcurve-fittingprocedure.Inanycase,thevalueoftheconstantsoftheequationcanonlybefoundbyexperiment;predictivemethodsareinadequateatpresent.Thedeterminationoftherateequationisusuallyatwo-stepprocedure;firsttheconcentrationdependencyisfoundatfixedtemperatureandthenthetemperaturedependenceoftherateconstantsisfound,yieldingthecompleterateequation.Equipmentbywhichempirical(經(jīng)驗)informationisobtainedcanbedividedintotwotypes,thebatchandflowreactors.Thebatchreactor（釜式反應器或間歇式反應器）issimplyacontainertoholdthecontentswhiletheyreact.Theexperimentalbatchreactorisusuallyoperatedisothermallyandatconstantvolumebecauseitiseasytointerpret(解釋)theresultsofsuchruns.Thisreactorisarelativelysimpledeviceadaptable（能適應的）tosmall-scalelaboratoryset-ups（裝置）,anditneedsbutlittleauxiliary（輔助設(shè)施）equipmentorinstrumentation.Thus,itisusedwheneverpossibleforobtaininghomogenouskineticdata.Theflowreactor(連續(xù)式反應器)isusedprimarilyinthestudyofthekineticsofheterogeneous(非均相)reactions.Planningofexperimentsandinterpretationofdataobtainedinflowreactorsareconsideredinlaterchapters.Therearetwoproceduresforanalyzingkineticdata,theintegralandthedifferentialmethods(積分法和微分法).2.7.1用積分法分析實驗數(shù)據(jù)

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用微分法分析實驗數(shù)據(jù)

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用微分法分析實驗數(shù)據(jù)

微分法求動力學方程是直接利用某一類動力學方程的微分式，以反應速度對濃度的函數(shù)作圖，然后與實測的數(shù)據(jù)相擬合的一種方法。一般也是設(shè)法把圖形線性化，把實驗數(shù)據(jù)代人。若得出一直線，便認為所假設(shè)的動力學方程是正確的。否則，重新選定另一個動力學方程進行猜算，直到得出一條直線為止。在處理實驗數(shù)據(jù)時，最小二乘法特別適用于如下形式的方程式：

(2.7-6)

k,α,β是待測定的，為此，可對式（2.7-6）取對數(shù)：寫成：根據(jù)最小二乘法法則：

當a0、a1、a2取得最佳值時，有：也就是用分別對a0,a1,a2求偏導數(shù)并令其為零，可以得到方程組|：這是一個三元一次方程組，可以用行列式求解第3章均相等溫反應器

Chapter3HomogeneousIsothermalReactors3．1概述

GeneralIntroduction

Inreactordesignwewanttoknowwhatsizeandtypeofreactorandmethodofoperationarebestforagivenjob.Becausethismayrequirethattheconditionsinthereactorvarywithpositionaswellastime,thisquestioncanonlybeansweredbyaproperintegrationoftherateequationfortheoperation.Thismaypose(造成)difficultiesbecausethetemperatureandcompositionofthereactingfluidmayvaryfrompointtopointwithinthereactor,dependingontheendothermic(吸熱的)orexothermic(放熱的)characterofthereaction,therateofheatadditionorremovalfromthesystem,andtheflowpatternoffluidthroughthevessel.Ineffect,thenmanyfactorsmustbeaccountedforinpredictingtheperformanceofareactor.Howbesttotreatthesefactorsisthemainproblemofreactordesign.Operationtypes:thebatch(間歇)thesteady-stateflow(連續(xù))theunsteady-statefloworsemibatchreactor(半連續(xù))Flowpattern:IdealflowandNon-idealflowHeatTransferMethods:isothermaloperation,adiabaticoperation,heatexchangeandheatproducingfromreactionitself.1、反應時間與停留時間ReactionTimeandResidenceTime

反應時間：從反應物料加人反應器后實際進行反應時算起至反應到某一時刻所需的時間，稱為反應時間，以符號t表示。停留時間：而所謂停留時間則是指從反應物料進人反應器時算起至離開反應器時為止所經(jīng)歷的時間。

2．空時與空速

Space-TimeandSpace-Velocity空時：為在規(guī)定條件下，進入反應器的物料通過反應器體積所需的時間，用符號

表示Space-Time:Timerequiredtoprocessonereactorvolumeoffeedmeasuredatspecifiedconditions空速:為在規(guī)定條件下，單位時間內(nèi)進入反應器的物料體積相當于幾個反應器的容積，用符號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簡單反應器3．2.1間歇反應器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恒容過程Forallreactionsinwhichthevolumeofreactingmixturechangesproportionatelywithconversion,suchasinsinglegas-phasereactionswithsignificantdensitychanges,theEq.Abovebecomes變?nèi)莘磻獀olume-varyingreactionsIftheequationsmentionedabovecannotbeintegrateddirectly,thegraphicalmethodcanbeused間隙反應器的體積計算由BR設(shè)計式求得每批操作的反應時間t后，可以根據(jù)經(jīng)驗選取兩批操作之間必須有的輔助時間τ’，根據(jù)物料處理量求得每批操作總時間內(nèi)物料的平均體積處理量υ0，求得反應器的有效體積VR，再根據(jù)物料的起泡特性，在0.4-0.85之間選取一個裝料系數(shù)φ，而求得反應器總體積VBVR=(t+τ’)υ0

VB=VR/φ如果算得的VB太大，則可以分成若干個小間隙釜并列操作，起效果相同，但設(shè)備造價提高。[例題3.2-1]某廠生產(chǎn)醇酸樹脂是使己二酸和己二醇以等摩爾比在70℃用間隙釜并以H2SO4作催化劑進行縮聚反應而生產(chǎn)的，實驗測得反應的動力學方程式為：(-rA)=kCA2kmol/(L·min)k=1.97L/(kmol·min)CA0=0.004kmol/L求己二酸轉(zhuǎn)化率分別為xA=0.5、0.6、0.8、0.9所需的反應時間為多少？

若每天處理2400kg己二酸，轉(zhuǎn)化率為80%，每批操作的非生產(chǎn)時間為1hr，計算反應器體積為多少？設(shè)反應器的裝料系數(shù)為0.75。

解：（1）達到所需要求的轉(zhuǎn)化率所需的反應時間為：

可見隨著轉(zhuǎn)化率的增加，所需的反應時間將急劇增加，因此，在確定最終轉(zhuǎn)化率時應該考慮這一因素。

（2）反應器體積的計算：最終轉(zhuǎn)化率為0.80時，每批所需的反應時間為8.50hr，

每小時己二酸進料量

每批生產(chǎn)總時間=反應時間+非生產(chǎn)時間=9.5hr反應器體積VR=ν0t總=171×9.5=1630L=1.63m3考慮裝料系數(shù)，故實際反應器體積3.2.2平推流反應器

thePlugFlowReactor平推流反應器（PFR）：反應器中的流動狀態(tài)是人們設(shè)想的一種理想流動，即在反應器內(nèi)具有嚴格均勻的速度分布，且軸向沒有任何混合。PFRischaracterizedbythefactthattheflowoffluidthroughthereactorisorderlywithnoelementoffluidovertakingormixingwithanyotherelementaheadorbehind.Actually,theremaybelateralmixingoffluidinaPFR;however,theremustbenomixingordiffusionalongtheflowpath.Thenecessaryandsufficientconditionforplugflowisfortheresidencetimeinthereactortobethesameforallelementsoffluid.平推流反應器特點：（1）在正常情況下，它是連續(xù)定態(tài)操作，故在反應器的各個截面上，過程參數(shù)（濃度、溫度等）不隨時間而變化；（2）反應器內(nèi)濃度、溫度等參數(shù)隨軸向位置變化，故反應速率隨軸向位置變化。（3）由于徑向具有嚴格均勻的速度分布，也就是在徑向不存在濃度分布。

PFR的基礎(chǔ)設(shè)計方程對PFR建立物料衡算式，就可以得到PFR的基礎(chǔ)設(shè)計方程式。在PFR中進行平推流動時，物料衡算式有如下特點：（1）由于流動處于穩(wěn)定狀態(tài)，各點濃度、溫度和反應速度均不隨時間而變化，故單元時間上t可任??；（2）

由于沿流動方向濃度、溫度和（－rA）都在改變，故應取單元體積△V＝dV；（3）穩(wěn)定狀態(tài)下，單元時間、單元體積內(nèi)反應物的積累量為零。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