化學(xué)反應(yīng)過程課件 Chapter 5-new

ChemicalReactionEngineeringChapter5

IdealReactorsforaSingleReaction

ChemicalReactionEngineeringWhatarethethreeidealreactors

(showninFig.5.1)?BasicContents:Theperformanceequations(ordesignequations)ofthethreeidealreactors.ChemicalReactionEngineeringBatchReactorChemicalReactionEngineeringTheBatchReactor,orBR(Fig.5.1a):Atanyinstantthecompositionthroughoutthereactorisuniform;Unsteady-stateoperationwherecompositionchangeswithtime;Hascontinuousmixbutnobackmix.Themixwhichtakesplacebetweentheelementsoffluidhavingdifferentresidencetimeorreactionextent.ChemicalReactionEngineeringThePlugFlowReactor,orPFR(Fig.5.1b)ChemicalReactionEngineeringThePlugFlowReactor,orPFR(Fig.5.1b)ChemicalReactionEngineering1.Theflowoffluidthroughthereactorisorderlywithnoelementoffluidovertakingormixingwithanyotherelementaheadorbehind.2.Theremaybelateral(徑向的)mixingoffluidinaplugflowreactor;however,theremustbenomixingordiffusionalongtheflowpath.3.Thenecessaryandsufficientconditionforplugflowisfortheresidencetimeinthereactortobethesameforallelementsoffluid.Thefirstofthetwoidealsteady-stateflowreactorsisastheplugflowreactor,orPFR(orcalledslugflow,pistonflow,idealtubular,andunmixedflowreactor,etc.)NoBackmix!TheMixedFlowReactor,orMFR(Fig.5.1c)

ChemicalReactionEngineeringItisareactorinwhichthe

contentsarewellstirredanduniformthroughout.Thus,theexitstreamfromthisreactorhasthesamecompositionasthefluidwithinthereactor.Thebackmixingextentismaximumamongalloftheidealreactors.Theother

idealsteady-stateflowreactoriscalledthemixedreactor,orMFR(orthebackmixreactor,theidealstirredtankreactor,theC*(meaningC-star),CSTR,ortheCFSTR(constantflowstirredtankreactor),etc.)Thesteadyandunsteadyoperation間歇操作(Batchreactor,BR)連續(xù)操作(MixedFlowReactor,MFR)

連續(xù)操作(PlugFlowReactor,PFR)Forthesereasons,weoftentrytodesignrealreactorssothattheirflowsapproachtheseidealsituations.Theseidealreactorsarerelativelyeasytotreat.Inaddition,oneorotherusuallyrepresentsthebestwayofcontactingthereactants－nomatterwhattheoperation.ChemicalReactionEngineeringWhydowestudytheidealreactors?

5.1IDEALBATCHREACTOR

Inabatchreactor,sincethecompositionisuniformthroughoutatanyinstantoftime,wemaymakethematerialbalance

aboutthewholereactor.Notingthatnofluidentersorleavesthereactionmixtureduringreaction,Eq.4.1,whichwaswrittenforlimitingcomponentA,becomes

input=output+disappearance+accumulation

orChemicalReactionEngineeringEvaluatingthetermsofEq.1,wefindChemicalReactionEngineeringByreplacingthesetwotermsinEq.1,weobtain

(2)

Rearrangingandintegratingthengives(3)

ThisisthegeneralequationshowingthetimerequiredtoachieveaconversionXAforeitherisothermalornonisothermaloperation.ChemicalReactionEngineeringThisequationmaybesimplifiedforanumberofsituations.Ifthedensityofthefluidremainsconstant,weobtain

(4)

ChemicalReactionEngineeringForallreactionsinwhichthevolumeofreactingmixturechangesproportionatelywithconversion,suchasinsinglegas-phasereactionswithsignificantdensitychanges,Eq.3becomes

(5)

Figure5.2isagraphicalrepresentationofEquation3and4.

ChemicalReactionEngineeringChemicalReactionEngineeringSpace-TimeandSpace-VelocityJustasthereactiontimetisthenatureperformancemeasureforabatchreactor,soarethespace-timeandspace-velocitytheproperperformancemeasureofflowreactors.Thesetermsaredefinedasfollows:

Space-time:

(6)

ChemicalReactionEngineeringSpace-velocity:

(7)

Asexamples:Aspace-velocityof5hr-1meansthatfivereactorvolumesoffeedatspecifiedconditionsarebeingfedintothereactorperhour.Aspace-timeof2minmeansthatevery2minonereactorvolumeoffeedatspecifiedconditionsisbeingtreatedbythereactor.ChemicalReactionEngineeringIfthespecifiedconditionistheactualconditionofthestreamenteringthereactor,therelationbetweenandsandtheotherpertinentvariablesis(8)

ChemicalReactionEngineering5.2STEADY-STATEMIXEDFLOWREACTION

SincethecompositioninaMFRisuniformthroughout,thematerialbalancemaybemadeaboutthereactorasawhole.ByselectingreactantAforconsideration,Eq.4.1becomes

Input=output+disappearancebyreaction+accumulation

(10)

=0ChemicalReactionEngineeringFigure5.3

Notation(符號)foramixedreactor.

ChemicalReactionEngineeringAsshowninFig.5.3,ifisthemolarfeedrateofcomponentAtothereactor,thenconsideringthereactorasawholewehave

inputofA,moles/time=FA0(1-XA0)=FA0outputofA,moles/time=FA=FA0(1-XA)

=ChemicalReactionEngineeringwhichonrearrangementbecomes

or(11)

WhereXA0=0,soXA=XA-XA0=

XA.XA

and-rA

aremeasuredatexitstreamconditions,whicharethesameastheconditionswithinthereactor.IntroducingthesethreetermsintoEq.10,weobtain

ChemicalReactionEngineeringMoregenerally,ifthefeedonwhichconversionisbased,subscript0,entersthereactorpartiallyconverted,subscript

i,andleavesatconditionsgivenbysubscriptf,wehave

or(12)

ChemicalReactionEngineeringForthespecialcaseofconstant-densitysystems

XA=1-CA/CA0,inwhichcasetheperformanceequationformixedreactorscanalsobewrittenintermsofconcentrationsoror(13)

Figure5.4isagraphicalrepresentationofthesemixedflowperformanceequations.ChemicalReactionEngineeringFigure5.4

Graphicalrepresentationofthedesignequationsformixedflowreactor.0XAXAGeneralcaseArea==FromEq.11Constant-densitysystemsonlyCA0CA0CAArea==FromEq.13ConditionsWithinreactorandatexit

ChemicalReactionEngineeringEXAMPLE5.1REACTIONRATEINAMIXEDFLOWREACTOR

OneliterperminuteofliquidcontainingAandB(CA0=0.10mol/liter,CB0

=0.01mol/liter)flowintoamixedreactorofvolumeV=1liter.Thematerialsreactinacomplexmannerforwhichthestoichiometryisunknown.TheoutletstreamfromthereactorcontainsA,BandC(CAf=0.02mol/liter,CBf=0.03mol/liter,CCf=0.04mol/literasshowninFig.E5.1.FindtherateofreactionofA,BandCfortheconditionswithinthereactor.ChemicalReactionEngineeringFigureE5.1

ChemicalReactionEngineeringSOLUTION

ForaliquidinamixedflowreactorA=0andEq.13appliestoeachofthereactingcomponents,givingfortherateofdisappearance:ThusAisdisappearingwhileBandCarebeingformed.

ChemicalReactionEngineeringEXAMPLE5.2KINETICSFROMAMIXEDFLOWREACTOR

PuregaseousreactantA(CA0=100millimol/liter)isfedatasteadyrateintoamixedflowreactor(V=0.1liter)whereitdimerizes(2AR).Fordifferentgasfeedratesthefollowingdataareobtained:Runnumber123410.03.01.20.5millimol/liter85.766.75033.4

Findarateequationforthisreaction.ChemicalReactionEngineeringSOLUTION

Forthisstoichiometry,2AR,theexpansionfactoris

andthecorrespondingrelationbetweenconcentrationandconversionisorChemicalReactionEngineeringTheconversionforeachrunisthencalculatedandtabulatedincolumn4ofTableE5.2.TableE5.2logCA

log(-rA)

23.066.70.5015001.8243.17631.2500.6678001.6992.93040.533.30.804001.5222.602

CalculatedChemicalReactionEngineeringFromtheperformanceequation,Eq.11,therateofreactionforeachrunisgivenbyThesevaluesaretabulatedincolumn5ofTableE5.2.

Havingpairedvaluesof-rAandCA

(seeTableE5.2),letustestdirectlyfornth-orderkinetics.Forthistakelogarithmsof,giving

ChemicalReactionEngineering021234log（-rA）Slope=3.398-2.6021.933-1.522Fitthelowestpoint400=k(33.3)2∴k=0.36logCAFigureE5.2=1.93≈2ChemicalReactionEngineeringFornth-orderkineticsthisdatashouldgiveastraightlineonalog(-rA)vs.logCAplot.Fromcolumns6and7ofTableE5.2andasshowninFig.E5.2,thefourdatapointsarereasonablyrepresentedbyastraightlineofslope2,sotherateequationforthisdimerizationisChemicalReactionEngineeringEXAMPLE5.3MIXEDFLOWREACTORPERFORMANCE

Theelementaryliquid-phasereactionA+2BRwithrateequationistotakeplaceina6-litersteady-statemixedflowreactor.Towfeedstreams,onecontaining2.8molA/literandtheothercontaining1.6molB/liter,aretobeintroducedatequalvolumetricflowratesintothereactor,and75%conversionoflimitingcomponentisdesired(seeFig.E5.3).Whatshouldbetheflowrateofeachstream?Assumeaconstantdensitythroughout.

ChemicalReactionEngineeringFigureE5.3

ChemicalReactionEngineeringSOLUTIONTheconcentrationofcomponentsinthemixedfeedstreamisThesenumbersshowthatBisthelimitingcomponent,sofor75%conversionofBand,thecompositioninthereactorandintheexitstreamisChemicalReactionEngineeringWritingtherateandsolvingtheproblemintermsofBwehaveattheconditionswithinthereactorFornodensitychange,theperformanceequationofEq.13givesChemicalReactionEngineeringHencethevolumetricflowrateintoandoutofthereactorisor

ChemicalReactionEngineering5.3STEADY-STATEPLUGFLOWREACTORInaplugflowreactorthecompositionofthefluidvariesfrompointtopointalongaflowpath,sothematerialbalanceforareactioncomponentmustbemadeforadifferentialelementofvolume

dV.ThusforreactantA,Eq.4.1becomesInput=output+disappearancebyreaction+accumulation

(10)

=0ChemicalReactionEngineeringFigure5.5Notationforaplugflowreactor.

ChemicalReactionEngineeringReferringtoFig.5.5,weseeforvolumethat

ChemicalReactionEngineeringIntroducingthesethreetermsinEq.10,weobtain

Notingthat

Weobtainonreplacement(16)

=

ChemicalReactionEngineeringThis,then,istheequationwhichaccountsforAinthedifferentialsectionofreactorofvolumedV.Forthereactorasawholetheexpressionmustbeintegrated.So,Thusorany(17)

ChemicalReactionEngineeringAsamoregeneralexpressionforplugflowreactor,ifthefeedonwhichconversionisbased,subscript0,entersthereactorpartiallyconverted,subscripti,andleavesataconversiondesignatedbysubscriptf,wehave

or(18)

ChemicalReactionEngineering

Forthespecialcaseofconstant-densitysystems

inwhichcasetheperformanceequationcanbeexpressedintermsofconcentrations,oror(19)

ChemicalReactionEngineeringFigure5.6displaytheseperformanceequationsandshowsthatthespace-timeneededforanyparticulardutycanalwaysbefoundbynumericalorgraphicalintegration.ChemicalReactionEngineeringFigure5.6Graphicalrepresentationoftheperformanceequationsforplugreactors.

ChemicalReactionEngineering(1)

Forsystemsofconstantdensity(constant-volumebatchandconstant-densityplugflow)theperformanceequationsareidentical,forplugflowisequivalenttotforthebatchreactor,andtheequationscanbeused

interchangeably.(2)

Forsystemsofchangingdensity

thereisnodirectcorrespondencebetweenthebatchandtheplugflowequationsandthecorrectequationmustbeusedforeachparticularsituation.Inthiscasetheperformanceequationscannotbeusedinterchangeably.BycomparingthebatchexpressionsofChapter3withtheseplugflowexpressionswefind:ChemicalReactionEngineeringEXAMPLE5.4PLUGFLOWREACTORPERFORMANCEAhomogeneousgasreactionA3Rhasareportedrateat215℃Findthespace-timeneededfor80%conversionofa50%A-50%inertfeedtoaplugflowreactoroperatingat215℃and5atm(CA0=0.0625mol/liter).ChemicalReactionEngineeringFigureE5.4a

ChemicalReactionEngineeringSOLUTIONForthisstoichiometryandwith50%inerts,twovolumesoffeedgaswouldgivefourvolumesofcompletelyconvertedproductgas;thusinwhichcasetheplugflowperformanceequation,Eq.17,becomes(i)

ChemicalReactionEngineeringTheintegralcanbeevaluatedinanyoneofthreeways:graphically(做圖地),numerically(數(shù)值地),oranalytically(解析地).Letusillustratethesemethods.

TableE5.4

0110.21.22280.6420.893ChemicalReactionEngineeringGraphicalintegration.Firstevaluatethefunctiontobeintegratedatselectedvalues(seeTableE5.4)andplotthisfunction(seeFig.E5.4b).

Fig.E5.4bChemicalReactionEngi