第十二讲 基于传递速率的精馏计算模型

Firstpage传递过程与分离技术全日制专业硕士研究生学位课程面向应用的专业基础课程第十二讲基于传递速率的精馏计算模型Introduction(1)Inarealcolumn,thevaporandliquidphasearenotatequilibriumbecauseofthelimitedratesoftransportprocesses.Fordealingwithsuchsituations,itisthemostcommonlyusedmethodtointroducethestageefficiency,whichrepresents,bydefinition,theextentofapproachingphaseequilibriuminastage.Introduction(2)Forexample,theMurphreeefficiencyforvaporphaseisdefinedas,,1*,,,1MVijijijijijyyEyy,,1,,,,1MVijijijijijijyyEKxy(12-2)(12-3)Introduction(3)Forbinarysystems,thetheoreticalvaluesofMurphreeefficienciesarebetween0and100%.0.65%to4.2%forabsorptionintoandstrippingfrom,ofcarbondioxide,waterandglycerinesolutions;4.7%to24%forabsorptionofolefinsintooils;and69%to92%forabsorptionofammoniaintowater,humidificationofair.Introduction(4)Formulticomponentsystems,itismuchmorecomplicatedbecauseofthecouplingeffectsbetweencomponents.Whenthevapormole-fractiondrivingforceofcomponentAissmallcomparedtotheothercomponentsinthemixture,thetransportrateofAiscontrolledbytheothercomponents,withtheresultthatEMVforAisanywhereintherangefromminusinfinitytoplusinfinity.Introduction(5)Thistheoreticalpredictionhasbeenconfirmedbyconductingexperimentswiththeethanol/tert-butanol/watersystem.TheobtainedvaluesofEMVfortert-butanolrangedfrom-2,978%to+527%.Inaddition,valuesofEMVforethanolandwatersometimesdifferedfromthebinarysystemsignificantly.Introduction(6)In1979,KrishnaandStandartshowedthepossibilityofapplyingrigorousmulti-componentmass-andheat-transfertheorytocalculationsofsimultaneoustransport.ThetheorywasfurtherdevelopedbyTaylorandKrishna.Theavailabilityofthistheoryledtothedevelopmentin1985byKrishnaMurthyandTaylorofthefirstgeneralrate-based,computer-aidedmodelforapplicationtotrayedandpackedcolumnsfordistillationandothercontinuous,countercurrentvapor-liquidseparationoperations.THEORETICALMODELFORANEQUILIBRIUMSTAGE(1)Feedsenteringstagejaretreatedasaliquidandavaporstreamwithmolarflowratefi,Lj,fi,VjandmolarenthalpyHLFj,HVFjrespectively.THEORETICALMODELFORANEQUILIBRIUMSTAGE(2)Alsoleavingfrom(+)orenteringto(-)theliquidand/orvaporphasesinthestageareheattransferratesQjVandQjL,respectively.THEORETICALMODELFORANEQUILIBRIUMSTAGE(3)AlsoenteringthestagefromthestageaboveisliquidmolarftowrateLj-1attemperatureTLj-1andpressurePj-1,withmolarenthalpyHLj-1andcomponentmolefractionsxi,j-1;THEORETICALMODELFORANEQUILIBRIUMSTAGE(4)AndenteringthestagefromthestagebelowisvapormolarflowrateVj+1attemperatureTVj+1andpressurePj+1,withmolarenthalpyHVj+1andcomponentmolefractionsyi,j+1.THEORETICALMODELFORANEQUILIBRIUMSTAGE(5)AndenteringthestagefromthestagebelowisvapormolarflowrateVj+1attemperatureTVj+1andpressurePj+1,withmolarenthalpyHVj+1andcomponentmolefractionsyi,j+1.THEORETICALMODELFORANEQUILIBRIUMSTAGE(6)Withinthestage,masstransferofcomponentsoccursacrossthephaseboundaryatmolarratesNi,jfromthevaporphasetotheliquidphase(+)orviceversa(-),andheattransferoccursacrossthephaseboundaryatratesejfromthevaporphasetotheliquidphase(+)orviceversa(-).THEORETICALMODELFORANEQUILIBRIUMSTAGE(7)LeavingthestageisliquidattemperatureTjandpressurePj,withmolarenthalpyHLjandvaporattemperatureTjandpressurePjwithmolarenthalpyHVj.THEORETICALMODELFORANEQUILIBRIUMSTAGE(8)Afraction,rLj,oftheliquidexitingthestagemaybewithdrawnasaliquidsidestreamatmolarflowrateUj,leavingthemolarflowrateLjtoenterthestagebelowortoexitthecolumn.THEORETICALMODELFORANEQUILIBRIUMSTAGE(9)Afraction,rVj,ofthevaporexitingthestagemaybewithdrawnasavaporsidestreamatmolarflowrateWj,leavingthemolarflowrateVjtoenterthestageaboveortoexitthecolumn.THEORETICALMODELFORANEQUILIBRIUMSTAGE(10)Ifdesired,entrainment,occlusion,interlinkflows,asecondimmiscibleliquidphase,andchemicalreaction(s)canbeaddedtothemodel.THEORETICALMODELFORANEQUILIBRIUMSTAGE(11)Recallthattheequilibrium-stagemodelofChapter10utilizesthe2C+3MESHequationsforeachstage:•Cmassbalancesforcomponents•Cphaseequilibriarelations•2summationsofmolefractions•1energybalanceTHEORETICALMODELFORANEQUILIBRIUMSTAGE(12)Intherate-basedmodel,themassandenergybalancesaroundeachequilibriumstageareeachreplacedbyseparatebalancesforeachphasearoundastage,whichcanbeatray,acollectionoftrays,orasegmentofapackedsection.Inresidualform,theequationsareasfollows,wheretheresidualsareontheleft-handsidesandbecomezerowhenthecomputationsareconverged.Whennotconverged,theresidualsareusedtodeterminetheproximitytoconvergence.THEORETICALMODELFORANEQUILIBRIUMSTAGE(13)Liquid-phasecomponentmaterialbalance:,,1,1,,10LLLLijjjijjijijijMrLxLxfNVapor-phasecomponentmaterialbalance:,,1,1,,10VVVVijjjijjijijijMrVxVyfNLiquid-phaseenergybalance:11,10LLLLLLFLLjjjjjjijjjjiErLHLHfHQeVapor-phaseenergybalance:11,10VVVVVVFVVjjjjjjijjjjiErVHVHfHQe(12-4)(12-5)(12-6)(12-7)THEORETICALMODELFORANEQUILIBRIUMSTAGE(14)whereatthephaseinterface,I,0IVLjjjEeeEquations(12-4)and(12-5)arecoupledbythecomponentmass-transferrates:,,,0,1,2,,1LLijijijRNNiCTheequationsforthemole-fractionsummationforeachphaseareappliedatthevapor-liquidinterface:,,,0,1,2,,1V