復(fù)試復(fù)習(xí)化反新課件章

Chapter13DistributionsofresidencetimesforchemicalreactorsNothinginthelifeistobefeared.Itisonlytobeunderstood.Thereactorstreatedinthebookthusfar-theperfectlymixedbatch,theplug-flowtubular,andtheperfectlymixedcontinuoustankreactors-havebeenmodeledasidealreactors.Unfortunately,intherealworldweoftenobservebehaviorverydifferentfromthatexpectedfromtheexemplar,thisbehavioristrueofstudents,engineer,collegeprofessors,andchemicalreactors.Justaswemustlearntoworkwithpeoplewhoarenotperfect,sothereactoranalystmustlearntodiagnoseandhandlechemicalreactorswhoseperformancedeviatesfromtheideal.Non-idealreactorsandtheprinciplesbehindtheiranalystformthesubjectofthischapterandthenext.AfterstudyingthischapterthereaderwillbeabletodescribethecumulativeF(t),externalageE(t),andinternalageI(t)residence-timedistributionfunctionsandtorecognizethesefunctionsforPFR,CSTR,andlaminar(層流）flowreactions.Thereaderwillalsobeabletoapplythesefunctionstocalculatetheconversionandconcentrationsexitingareactorusingthesegregationmodelandthemaximummixednessmodelforbothsingleandmultiplereactions.Thebasicideasorconceptsusedtocharacterizeandmodelnon-idealreactorsarereallyfewinnumber.Beforeproceedingfurther,afewselectedexamplesofnon-idealmixingandmodelingfromtheauthor’sexperienceswillbepresented.Gas-liquidReactorPackedBedReactor(填充床反應(yīng)器)CSTR連續(xù)攪拌斧反應(yīng)器停留時(shí)間分布函數(shù)測(cè)量方法例題13-1ConstructingC(t)andE(t)curvesAsampleofthetracerhytaneat320Kwasinjectedasapulsetoareactorandtheeffluentconcentrationmeasuredasafunctionoftime,resultinginthefollowingdata:t(min)0123456789101214C(t)(g/m3)0158108643.02.21.50.60Themeasurementsrepresenttheexactconcentrationsatthetimeslistedandnotaveragevaluesbetweenthevarioussamplingtests.ConstructfiguresshowingC(t)andE(t)asfunctionsoftimeDetermineboththefractionofmaterialleavingthereactorthathasspentbetween3and6mininthereactorandthefractionofmaterialleavingthathasspentbetween7.75and8.25mininthereactor3minorless.C(t)~tCurveCalculatedresultst(min)

123456789101214

C(t)(g/m3)

1581086432.21.50.60E(t)(積分面積=50)0.020.10.160.20.160.120.080.060.0440.030.0120=47.4g.min/m3Simpson近似積分發(fā)法，對(duì)于N+1個(gè)點(diǎn)，且N是偶數(shù)時(shí)停留時(shí)間為3到6分鐘之間，流出反應(yīng)器的物料分率為51％。停留時(shí)間為3分鐘以下的物料分率為20%。停留時(shí)間段7.75~8.25分鐘內(nèi)流出的物料為3.0%例13－2平均停留時(shí)間和方差的計(jì)算Example13-2MeanresidencetimeandVariancecalculationCalculatethemeanresidencetimeandthevarianceforthereactorcharacterizedinExample13-1bytheRTDobtainedfromapulseinputat320K.tC(t)E(t)tE(t)t-tma(t-tm)2E(t)a012345678910121401581086432.21.50.6000.020.100.160.200.160.120.080.060.0440.030.012000.020.200.480.800.800.720.560.480.400.300.140-5.15-4.15-3.15-2.15-2.15-0.150.851.852.853.854.856.858.8500.340.9920.740.2650.0040.0870.2740.4870.6520.7060.5630

在0～10min和10～14min時(shí)間內(nèi)進(jìn)行積分σ2σ＝2.4minExample13-5MeanConversioninaPFRandCSTRDerivetheequationofafirst-orderreactionusingthesegregationmodelwhentheRTDisequivalentto(a)anidealPFR,and(b)anidealCSTR.Comparetheseconversionswiththoseobtainedfromthedesignequation(Chapter4).Solution:（a）

ForthePFR,theRTDfunctionis:

（13-35）（13-55）SubstitutingfortheRTDfunctionforaPFRgives

（E13-5.1）UsingtheintegralpropertiesoftheDiracdeltafunction,weobtain

（E13-5.2）RecallthatforaPFRaftercombingthemolebalance,ratelaw,andstoichiometricrelationships(cf.Chapter4),wehad

（E13-5.3）Integratingyields（E13-5.4）Whichisidenticaltotheconversionpredictedbythesegregationmodel.（b）FortheCSTR，theRTDfunctionis

RecallingEquation(13-56),themeanconversionforafirst-orderreactionis

(Chapter4)CombingtheCSTRmolebalance,theratelaw,andstoichiometry,wehave

whichisidenticaltotheconversionpredictedbythesegregationmodel.Example13-6

MeanconversionCalculationsinaRealReactorCalculatethemeanconversioninthereactorwehavecharacterizedbyRTDmeasurementsinExamples13-1and13-2forafirst-order,liquid-phase,irreversiblereactioninacompletelysegregatedfluid:Thespecificreactionrateisk=0.1min-1at320K.SolutionBecauseeachglobuleactsasabatchreactorofconstantvolume,weusethebatchreactordesignequationtoarriveattheequationgivingconversionasafunctionoftime:

（E13-6.1）

Tocalculatethemeanconversionweneedtoevaluatetheintegral:

（13-53）

TheRTDfunctionforthisreactorwasdeterminedpreviouslyandgiveninTableE13-2.1andisrepeatedinTableE13-6.1.ToevaluatetheintegralwemakeaplotofX(t),E(t)asafunctionoftasshowninFigureE13-6.1.anddeterminetheareaunderthecurve.t(min)E(t)(min-1)X(t)X(t)E(t)(min-1)00.0000010.0200.0950.001920.1000.1810.018030.1600.2590.041440.2000.3300.066050.1600.3930.062960.1200.4510.054170.0800.5030.040280.0600.5510.033190.0440.5930.0261100.0300.6320.01896120.0120.6990.0084140.0000.750

Chapter13Homework(第十三章作業(yè)題)p865:P13-8BAnisothermalpulsetestonapieceofreactionequipmentgavethefollowingresults.Theoutputconcentrationsroselinearlyfromzeroto0.5umol/dm3in5min,thenfelllinearlytozeroin10minafterreachingthemaximumvalue.CalculatethevaluesofE(t)andF(t)andgivethecurvesasafunctionoftime(E(t)~t,F(t)~t).（求解析解）Whatisthemeanresidencetime?Whatisthevariance?Iftheflowwere150gal/min,whatwouldbethetotalreactorvolume?

（用解析積分計(jì)算）AsecondorderreactionwithkCA0=1.2min-1at325Kiscarriedoutinthesystem.Answerfollowingquestions.(c)Ifthereactorwereplugflowwiththesameflowrateandvolume,whatwouldbetheconversion?(d)IfthereactorwereaCSTRwiththesameflowrateandvolume,whatwouldbetheconversion?(e)IftheflowwerecompletelysegregatedwiththeE(t)above,whatwouldbetheconversion?(f)Togetmeanresidencetimeusingthreemethods:1)analyticalmethod,and2)numericalmethod(choseSimpsonrule),3)differentialmethodlikeexperimentaldatatreatment)(g)Iftanksinseri