Chapter03IdealReactorsBATCHREACTORDESIGN1CONTINUOUS-FLOWREACTORS2PLUG-FLOWREACTORS313idealreactorsStirredtanksturbularorpacked-bedreactorsthecriterionforidealityintankreactorsisthattheliquidbeperfectlymixed,whichmansnogradientsintemperatureorconcentrationinthevessel.inplug-flowreactors,orPFRs,thereareaxialgradientsofconcentrationandperhapsalsoaxialgradientsoftemperatureandpressure,butintheidealPFRthereisnoaxialdiffusionorconduction.2BatchReactorDesign

First-orderreactions1Second-orderreactions2ConsecutiveReactions3ParallelReactions4SemibatchReactions53First-orderreactionsForanirreversiblefirst-orderreationofthetype(3.2)4First-orderreactionsTheresultisoftengivenintermsofthefractionconverted:(3.3)5Second-orderreactionsforaunimolecularsecond-orderreation,(3.6)(3.5)(3.4)or6Second-orderreactionsbimolecularreationWhereR>1(3.7)SinceandwithAthelimitingreactant.Let7Second-orderreactions

(3.8)Integrationbetweenlimitsgives(3.10)8大家有疑問(wèn)的，可以詢問(wèn)和交流可以互相討論下，但要小聲點(diǎn)9大家有疑問(wèn)的，可以詢問(wèn)和交流可以互相討論下，但要小聲點(diǎn)10Second-orderreactionsR=2.011ConsecutiveReactionsTheratesofreactiondependontheconcentrationofBintheliquidphase,whichisafunctionofgassolubility,pressure,andagitationconditions.weareoftenconcernedwiththerelativereactionratesandtheselectivity,whichdonotdependontheconcentrationofB,ifthereactionordersarethesameforbothreactions.Thereactionsaretreatedaspseudo-first-order,andequationsaredevelopedforanidealbatchreactorwithirreversiblefirst-orderkinetics:12ConsecutiveReactions(3.13)(3.12)TheconcentrationofAfallsexponentially,aswasshownearlierinEq.(3.2):(3.11)13ConsecutiveReactionsThematerialbalanceforproductCisCombiningtheseequationsgives(3.15)(3.14)14ConsecutiveReactionsIfnoCispresentatthestart,integrationofEq.(3.15)givesTheconcentrationofCgoesthroughamaximumwithtime,canbefoundbydifferentiatingEq.(3.16)andsettingthederivativetozero:(3.16)(3.17)15ConsecutiveReactionsTheconcentrationofDisobtainedbyamaterialbalance:(3.18)(3.19)(3.20)16ConsecutiveReactionsmaximumof67%conversionofAis86.5%

andtheselectivityis77%.theconversionis63%andtheyieldofCis56%foraselectivityof89%.17ParallelReactionsSelectivityeffectscanalsobeimportantwithparallelreactionshavingdifferentreactionorders.Considerthecasewherethemainreactionisfirstordertobothreactantsandthebyproductreactionissecondordertooneofthereactants:byproductformationmainreaction18ParallelReactionsThelocalorinstantaneousselectivityistheratiooftothetotalrateofconsumptionofA:(3.21)(3.22)19ParallelReactionsHigherselectivitycouldbeachievedbydecreasingtheconcentrationofAintheinitialcharge,butthiswouldgivealowerconcentrationofCinthefinalproductandincreaseseparationcosts.20SemibatchReactionsThereactormightbetwo-thirdstothree-quartersfullatthestart,andthefluidvolumeincreasesasAisaddedandnoproductwithdrawn.Figure3.4showsthecalculatedconcentrationcurvesforthesamekineticsandasforFigure3.3,withthefeedofAataslow,constantratefor14hours21SemibatchReactionstheinitialselectivityisveryhighbutdecreasesasdecreasesandincreasesslightly.Afterthefeedisstopped,theselectivityagainincreases22CONTINUOUS-FLOWREACTORSReactorsinSeries2TemperatureOptimization3CONTINUOUS-FLOWREACTORS123CONTINUOUS-FLOWREACTORSOperatingastirred-tankreactorwithcontinuous-flowofreactantsandproducts(aCSTR)hassomeadvantagesoverbatchoperation.Thereactorcanmakeproducts24hoursadayforweeksatatime,whereasforatypicalcycle,thebatchreactorisproducingonlyabouthalfthetime.IntheCSTR,temperaturecontroliseasierbecausethereactionrateisConstant,andtherateofheatreleasedoesnotchangewithtime,asitdoesinabatchreactor.24CONTINUOUS-FLOWREACTORSFinally,conversionandselectivitymayvaryfromdaytodaywithabatchreactor,andtheyaremorelikelytobeconstantwithaCSTRandagoodcontrolsystem.Themaindisadvantageofcontinuousoperationisthatthereactionrateisnearlyalwayslowerthantheaveragerateforabatchreaction.Inmostcases,thebatchreactionratedecreasesastheconversionincreases,andintheCSTRthereactionrateisthesameasthefinalreactionrateinthebatchreactor.Forhighconversions,thefinalratemaybeseveral-foldlowerthantheaveragerateandtheaverageresidencetimeintheCSTRmustthenbeseveral-foldgreaterthanthereactiontimeinabatchreactor.TheaverageresidencetimeintheCSTRist=V/F.TheratioofCSTRresidencetimetobatchresidencetimeisreadilyderivedforsimplekineticmodels.ForafirstorderreactioninaCSTR,thesteady-statematerialbalanceis25CONTINUOUS-FLOWREACTORSIntermsoffractionconverted,in-out(3.23)(3.24)(3.25)(3.26)(3.27)In-out=amountreacting26CONTINUOUS-FLOWREACTORSorEquations(3.26),(3.27),and(3.28)areequivalent,andtheyareusedwhensolvingfor,t,orx.TocomparethebatchandCSTRtimes,theequationforabatchfirst-orderreaction,Eq.(3.3)orEq.(3.29),isusedwithEq.(3.27):(3.28)(3.29)(3.30)27CONTINUOUS-FLOWREACTORS28CONTINUOUS-FLOWREACTORS29CONTINUOUS-FLOWREACTORSFortheCSTRFromFigure3.5,or(3.31)(3.32)(3.33)(3.34)30CONTINUOUS-FLOWREACTORS31ReactorsinSeries32ReactorsinSeriesCSTR-1CSTR-2CSTR33ReactorsinSeriesWhenthetworeactorsareusedinseries,thetotalvolumeisproportionaltothesumoftherectangularareaebgfandcdhginFigure3.8.Withseveralreactorsinseries,thetotalvolumewouldapproachthatforaplugflowreactor.(3.36)(3.35)(3.37)(3.38)34ReactorsinSeriesWhenthereactorsareequalinsizeandoperateatthesametemperature,theequationis(3.39)(3.40)35ReactorsinSeriesForaverylargenumberoftanks,theconversionapproachesthatforaplug-flowreactororabatchreactor.Withthreetanksinseries,thetotaltimeis50%morethanforplugflowifthedesiredconversionis90%andforfivetanksthetimeisonly25%greater.36ReactorsinSeries

Itiseasytoshowthatforafirst-orderreactionandtwotanks,thevolumeshouldbeequal:Taking,forexample,:Anyothercombinationwiththesametotaltimegiveshigher.Forexample,ifand;37TemperatureOptimizationWhenasequenceofreactionsproducesamixtureofproducts,theselectivityforthemainproductisamajorfactorinchoosingreactionconditions.Wehaveshownthattheratioofreactantconcentrationsandtheconversioncanaffecttheselectivity,particularlywhenthemainandbyproductreactionshavedifferentreactionorders.Whenthereactionshavedifferentactivationenergies,theselectivitywillalsodependonthetemperature.Ifthemainreactionhasthehigheractivationenergy,raisingthetemperaturewillincreasetheselectivityandalsodecreasethetimeneededtoreachthedesiredconversion.Thebestoperatingtemperaturecannotbechosenfromjustthekineticsbutdependsonotherfactors,suchasthecostofsupplyingorremovingheat,vaporizationlosses,corrosionrate,andsafetyconsiderations.38TemperatureOptimizationWhenthebyproductreactionhasahigheractivationenergythanthemainreaction,theselectivityisimprovedbyreducingthetemperature.However,thismeansagreaterreactiontimeforabatchreactororalargerreactorforaflowsystem.Thetemperaturechosenisagainacompromisebasedonthereactorsize,rawmaterialcosts,andthecostofproductseparation.However,foranexistingCSTRandafixedfeedrate,anoptimumtemperaturecanbedefinedasthetemperaturethatgivesthegreatestyieldofthemainproduct.Increasingthetemperatureincreasestheconversionbutdecreasestheselectivity,sotheyieldgoesthroughamaximum,asshowninthefollowingexample.39TemperatureOptimization40TemperatureOptimization41TemperatureOptimization42TemperatureOptimization43PLUG-FLOWREACTORSHeterogeneousReactions2HomogeneousReactions1AdiabaticReactors3OptimumReactionTemperature4OptimumFeedTemperature544PLUG-FLOWREACTORSelementsofthefluidareassumedtopassthroughthereactorwithnomixingallelementsspendthesametimeinthereactor.Withapacked-bedreactor,thevelocityprocomplexandchangingwithdistance,asthefluidflowsaroundandbetweentheparticles.However,whenthebeddepthismanytimestheparticlediameter(L/dp>40),theresidencetimedistributionofthefluidisquitenarrow,andplugflowcanbeassumed.45HomogeneousReactions(3.41)TocomparetheequationsforthePFRwithabatchreactor,themolarfeedrateisexpressedasthevolumefeedrateFtimestheconcentrationofA:(3.42)46HomogeneousReactions(3.43)Equation(3.42)canthenbepresentedusingthespacevelocitySVorthespacetime,whichisthereciprocalofthespacevelocity:wherevolumetricfeedratereactorvolume(3.44)47HeterogeneousReactionsForaheterogeneouscatalyticreactioninanidealpacked-bedreactor,thematerialbalanceiswrittenforadifferentialmassofcatalyst,dW.ThebasicequationfortheconversionofthekeyreactantAisthesameasforanytypeofreaction,orcombinationofreactions,includingreversiblereactions.FororAB+COr48HeterogeneousReactionswhereMolesAfed/hrr=totalmolesAconsumed/hr,kgW=massofcatalystIntegrationoftherateequationgivesthemassofcatalystneededperunitfeedrateofAforaspecifiedconversion.(3.46)49HeterogeneousReactionsThereactorvolumeisdeterminedfromthemassofcatalystandthebeddensity:(3.47)Thedimensionsofthereactorarenotfixedbytheseequations,Thereactordimensionsareselectedtogivereasonableproportionsandatolerablepressuredrop.Oftenthemassvelocityischosenfirst,whichgivesthecross-sectionalarea,andthebedlengthisdeterminedfromtherequiredvolume.50HeterogeneousReactionsTorelatetheconversiontothespacevelocity,thefeedconcentrationandthebeddensityareintroducedintoEq.(3.46):where(3.48)Itisnotreallynecessarytousetheconceptofspacevelocityindesigningareactor,sincethemassofcatalystneededandthebedvolumearedetermineddirectlyfromEqs.3.46and3.47.However,somepatentsandtechnicalreportsgivetheconversionasafunctionofspacevelocityandtemperatureratherthanpresentingfundamentalkineticdata.Tousesuchdata,thespacevelocitymustbecarefullydefinedandinterpreted.51HeterogeneousReactionsInEq.(3.48),thespacevelocityisdefinedusingthevolumetricflowrateattheentrancetothereactor,butitcouldbebasedonthevolumeofgasatstandardconditions:Anotherdefinitionisbasedonthevoidvolumeofthereactor[2],whichcorrespondstoAlthoughisclosertothegasresidencetimethanis,thereisnoadvantageinusingforalculations,andEq.(3.50)incorrectlyimpliesthatraisingwouldincreasetheconversion.(3.49)(3.50)52HeterogeneousReactionsOthertermsthatareusedwhenfeedingliquidstoareactoraretheweighthourlyspacevelocity(WHSV)andtheliquidhourlyspacevelocity(LHSV)[3].Bothhaveunitsofbutaredefineddifferently:poundsoffeed/hrpoundsofcatalyst=WHSVvolumeofliquid/hrvolumeofreactor=LHSVTheLHSVissometimesusedwhenfeedingliquidsthatarevaporizedinapreheaterbeforeenteringthereactor,andofcoursetheLHSVismuchlowerthantheSVbasedontheactualvaporflowtothereactor.SometimesWHSVisbasedonthefeedrateofonereactantratherthanthetotalfeedrate53HeterogeneousReactionsEvenwhenthespacevelocityisclearlydefined,theremaybeproblemsinscaleupordesign.Itmightbethoughtthatiftemperature,pressure,andspacevelocityarekeptconstantonscaleup,theconversionwillbeconstant.However,asEq.(3.48)shows,achangeinormayaffecttheconversion.Asmall-diameterlaboratoryreactormayhavealowerbeddensitythanalargereactor,inwhichcasethelargereactormighthaveahigherconversionforthesameSV.Doublingwoulddoublerifthereactionisfirstorder,andtheconversionwouldnotchange;butforotherorderstheeffectsofwouldnotcancel,andtheconversioncouldchange.54AdiabaticReactorsReactionsonsolidcatalystsareoftencarriedoutinadiabaticreactorsifthereislittlechangeinselectivityortherateofcatalystagingwithtemperature.Thereactorisgenerallyalarge-diametercylindricalvesselcontainingoneormorebedsofcatalyticparticlessupportedongridsorheavyscreens,asshowninFigure3.12a.Anothertypeofreactorhasoneormoreannularbedsofcatalystwithradialflowofgaseitherinwardoroutward,asshowninFigure3.12b.55AdiabaticReactors56AdiabaticReactorsThefirststepinreactordesignistocalculatetheequilibriumconversionasafunctionoftemperatureforagivenpressureandfeedratio.Forabimolecularreversiblereactionsuchas(3.54)57AdiabaticReactorsAtsteadystate,theenergyreleasedisequaltotheincreaseinsensibleheatofthefeedstream,sincethereisnoheatlosstothesurroundingsinanadiabaticreactor.Theheatcapacityofthecatalystandthereactorwallarenotincludedintheheatbalance,sinceoncethesteady-statetemperatureproestablished,thesolidscannotstoreanymoreenergy,andalltheheatreleasedmustbeabsorbedbytheflowinggas.FromEqs.(3.55)and(3.36),(3.56)(3.55)58A