反应精馏塔的优化设计外文文献

（二〇一六年六月外文文献及翻译学校代码：10128学号：201220506019题目：DN1800脱丁烷精馏塔设计学生姓名：袁浩楠学院：化工学院系别：过控系专业：过程装备与控制工程班级：过控12-1班指导教师：耿清OptimalDesignofaReactiveDistillationColumnEdwinZondervan,MayankShah*andAndréB.deHaanEindhovenUniversityofTechnology,DepartmentofChemistryandChemicalEngineering,P.O.Box513,5600MB,Eindhoven,theNetherlands,[e-mail]NLPmodelthatcanbeusedtooptimizethedesignofreactivedistillationcolumn.MINLPmodelisformulatedinGAMSinsuchawaythatitcanbesolvedlocallyandglobally.IntheRDcolumnacomponentAisconvertedintoproductBwhilevapourandliquidareassumedtobeinequilibrium.Theobjectiveistofindadesignforthisprocessthatminimizesthetotalcosts(consistingofcapitalandoperationalcosts).Thedesignvariablesofinterestarethetotalnumberofstages,thenumberofreactivestages,thelocationofthereactivestages,thefeedtraylocationandtherefluxratio.Keywords:Reactivedistillation,Design,Optimization,MINLP1.IntroductionReactivedistillation(RD)isamaturedtechnologythatcombinesreactionandseparationinasingleprocessingunit.RDhasdistinctadvantages;normallytheequipmentismuchsmallerthanconventionalequipment,theenergyrequirementsarelowerandtheconversionoftheproductishigherastheproductsareimmediatelyremovedbydistillation.Krishnaetal.(2002)giveamorecompleteoverviewofreactivedistillationHowever,designandcontrolofRDisacomplexprocess(Al-ArfajandLuyben(2000)).Especiallytheoptimaldesignofsuchasystemrequiresaccurateprocessmodelsthatleadtoacomputationallydemandingmathematicalproblem.Althoughtheproblemhasbeenstudiedinthescientificliterature,mostofthetimetheproposedmodelsarestrongsimplificationsofrealityandmostauthorsagreethatthemorecomplexmodelscannotbesolvedtoglobaloptimality.InJacksonandGrossmann(2001)anoptimizationapproachfortheoptimaldesignofareactivedistillationcolumnisproposed,whichshowsthatdisjunctiveprogrammingcanbeeffectivelyusedtohandletheresultingnonlinearoptimizationproblem.Thedesignofareactivedistillationcolumnisconcernedwithfindingthetotalnumberoftraysofthecolumn,thenumberandlocationofreactivetrays,andthefeedandrefluxlocationsofthecolumn.AlsoSeferlisandGrievink(2001)solveasimilarproblemusingcollocationmodels.Stochasticoptimizationmethodssuchasgeneticalgorithmarealsooftenappliedtodesigntheseprocesses.However,thisapproachiscomputationallyexpensiveandbecauseofaprobabilisticapproach,thereisnoassuranceofglobaloptimality.Thismodelisassociatedwithnonlinearitiesfromreactionkinetics,phaseequilibriumandbilineartermsofthebalanceequations.Gangadwalaetal.(2006)haveformulatedMINLPmodelforRDprocess.However,theycanonlysolvetheproblemlocally.ForglobaloptimalitytheyhaveappliedpolyhedralrelaxationsandconvertedMINLPproblemtoMILPproblem.TheyhaveconcludedthatMINLPproblemforRDprocesscanonlybesolvedlocally.Toovercomethisdesignproblem,inthisworkanRDmodelisformulatedasMINLPinsuchwaythatmodelcanbesolvedglobally.Thismodelcontainscontinuous-aswellasdiscretevariables.Continuousvariablesareusuallyrelatedtooperatingconditionssuchasliquidandvapourflows,feedflows,refluxratio.Discretevariablesarerelatedtonumberandpositionsofreactivestages,refluxlocation,numberandpositionsoffeed,requiredstagestoobtainpureproduct.2.ProblemstatementandproposedmodelInthissectionanMINLPisproposedtooptimizethedesignofareactivedistillationcolumn.Theoptimizationobjectiveistominimizethetotalcostsandtofindoptimalreboilerandcondenserduties,therefluxratio,thenumberofstages,thenumberandlocationofreactivestages,catalystloadingsonreactivestagesandthefeedlocation.InthecolumnareactionABtakesplaceforwhichthereactionkinetics,componentbalancesandmaterialbalancesareknown,alsovapourandliquidareassumedtobeinequilibriumforthesystemofourinterest.Figure1:AschematicviewofRDcolumnandgraphicalviewofdiscretebinaryvariablesAschematicviewofRDcolumnisshowninfigure1whichalsoincludesallimportantdesignvariablestobedeterminedbysolvingtheMINLPmodel.Thestagesarenumberedfromtoptobottom.Thefirststagerepresentscondenserandthelaststagerepresentsthereboiler.Sincethereisonlyoneproductproducedinacolumn,whichisobtainedasdistillate,atotalcondenserisusedtoobtainthedistillateatthetopofacolumn.Areactantisheavycomponentandunreactedreactanthastoberecycledbackcompletelytothecolumnthusatotalreboilerisused,whichresultsRDcolumnwithoutbottomflowrate.ThebinaryvariablessuchasIREAK(J)forreactivestagelocation,IREF(J)forrefluxlocation,ILIN(J)forfeedlocationareintroducedtoknowwhetherastageJisareactivestage(IREAK(J)=1)oratopstagereceivingreflux(IREF(J)=1)orfeedstage(ILIN(J)=1).Liquidisnotpresentonthestagesabovetherefluxstagesothesestageshavenoeffectonthecolumnperformance.Hence,theThesummationofbinaryvariableIREAK(J)givestotalnumberofreactivestages.Theobjectivefunctionwhichrepresentsthetotalcostofreactivedistillationcolumnisbasedonthecolumndimensionsandtheheatduties:WhereNTisthetotalnumberofstages,Histhecolumnlength,DisthecolumndiameterandTaretheheatduties.Thecomponentbalancesateachstagencanbegivenas:WhereLaretheliquidflows,Vthevapourflowsandxandytheliquidandvapourcompositions.Thereactionkineticsholdsthat:Andforthevapour-liquidequilibriumweusearelative