Distillation of a Complex Mixture. Part I High Pre

Entropy,2007,9,58-72entropyISSN1099-4300©2007byMDPI:HighPressureDistillationColumnAnalysis:ModelingandSimulationDouaniMustapha*,OuadjeniaFatimaandTerkhiSabriaDepartmentofChemicalEngineering,UniversityofMostaganem,Mostaganem,AlgeriaE-Mails:[e-mail];[e-mail].*Authortowhomcorrespondenceshouldbeaddressed.E-Mail:[e-mail]:7December2006/Accepted:14April2007/Published:25April2007Abstract:Inthisanalysis,basedonthebubblepointmethod,aphysicalmodelwasestablishedclarifyingtheinteractions(massandheat)betweenthespeciespresentinthestreamsincirculationinthecolumn.Inordertoidentifytheexternallycontrolledoperatingparameters,thedegreeoffreedomofthecolumnwasdeterminedbyusingGibbsphaserule.ThemathematicalmodelconvertedtoFortrancodeandbasedontheprinciplesof:1)Globalandlocalmassconservationbalance,2)Enthalpybalance,and3)Vapour-liquidequilibriumateachtray,wasusedtosimulatethebehaviorofthecolumn,concentrationdistributions,temperatureandstreamsforeachphasealongthecolumnathighpressureineachtray.TheenergyconsumptionatthecondenserandtheboilerwasalsoevaluatedusingtheStarlingequationofstate.Keywords:Highpressuredistillation,complexmixture,modeling,simulation,bubblepointmethod.1.IntroductionNumerousmethodsarecitedintheliteratureregardingtheresolutionofthecomplexmixturesdistillationproblem.However;theengineeroftenresortstotheshortcutmethodwhichenablesthecomputationoftheminimumnumberoftrays(Nmin)[1,2-3]andtotheformalismofUnderwoodtodeterminetheminimumrefluxrateRmin[4,5-6].Asfortheoptimalrefluxrate,theMalkanov‘sequationwhichrequiresthepreliminarydefinitionofthekeycomponents(lightandheavy)iscalledEntropy,2007,959upon[1,4,5-6].Forthecomplexmixtures,otherlightcomponentsarecombinedwiththelightkeycomponentaccordingtothevapour-liquidequilibriumconstantsK.Incrudedistillation,itisclearthatthedefinitionofthekeycomponentvariesfromonetraytoanotheraccordingtothevaluesofK.Obviously,thisremarkcannotbeappliedforstronglynonidealcomplexmixtureswithoutintroducingacertainnumberoferrorswheredistillationwithaminimumrefluxexhibitsapinchingpointinthetwosectionsofthecolumn[7].Thequantityofminimalenergynecessaryforagivenseparationisspecifiedpurelybythermodynamicanalysisoftheprocessanddependsonlyonthequalityofthefeed,thecompositionofthedesiredproductsandthepressureinthecolumn.Althoughrigorous,theshortcutmethodremainsauniversalprocedureofdesignpresentingsufficientpreliminaryinformationtoinitiatecomplexmixturesdistillationsimulation[8].Inexchange,thesimulationprogramsexploitedintheindustryrequireasignificantnumberofiterationscarriedoutmanuallywhichisreflectedbyalongcomputationperiodoftime.Bausaetal[9]proposedageometricalmethodofnon-idealseparationwhilecalculatingtherateofminimumreflux.Inthepetrochemicalfield,therelatedindustriesrequireproductsofspecificqualitymeetingsomestandards.Thecomplexmixturesdistillationdoesrequireaseriesofcolumnswhosearrangementdependsonseveralfactors.Thesynthesisofprocessesofcomplexmixturesdistillationisverysignificantforanoptimaldesign.Indeed,duetothecomplexinteractionsbetweencomponentsinthemixture,theresearchhasbeenfocusedonternarymixtures[10].Reversibledistillationofternarymixturesimpliesaconsequentminimizationofthepotentialdifferenceoftransfer(massandheat)atthetraylevel.Thisminimizationresultsgraphicallyinthereductionofthedifferencebetweentheoperatinglineandtheequilibriumcurveonanx-ydiagram.2.ColumnModelingSchematically,adistillationcolumniscomposedofacascadeoftraysbetweenwhichliquidandvapourphasesflowincounter-currentdirectionsaccordingtohydrodynamicdiagramsdependingontraymodel.Theseinteractionsleadtoamasstransfersothatthelessvolatilecomponentsarerecoverableatthelowertrays,whereasthelightestarerecoveredmainlyinthedistillate.Totakeaccountofphysicalinteractions,weusedtherigorousmethodbasedonthebubblepointcalculationwithoutdefinitionofthelightandheavierkeysinthecolumn.[11]Intheabsenceofachemicalreaction,themostcomplextraywithramifiedinteractionscanbedepictedinFigure1.MjandUjaretheliquidandvapoursidestreamsandFjthefeedflowratefortrayJ.ForacomplexmixturemadeupofCchemicalspecies,themathematicalmodelrelatedtoatrayiswritten:Massbalanceforcomponenti:)2(Ci≤≤:()()0,,,1,11,1=×+−×+−×+×+×++−−jijjjijjjijjijjijYUVXMLZFYVXL(1)Foreachcomponent,thevapour-liquidequilibriumisexpressedby:0,,,=×−jijijiXKY(2)Theconditionrelatedtothecomposition,expressedinmolarfraction,is:Entropy,2007,960011,=−∑=CijiX(3)Figure1.Theoreticaltraywithheatexchange.TheenthalpybalanceforatrayJis:()()01111=−×+−×+−×+×+×++−−jjjjjjjjjjjjjQHvUVHlMLHfFHvVHlL(4)HfjisthefeedenthalpyatthetrayJ.ProceedingbyeliminationofLjandYij,themathematicalmodelforacolumnofNtrayscanbereducedto:jijijijijijijDXCXBXA,1,,,,1,=×+×+×+−(5)where:()111VMUFVAjmmmmjj−−−+=∑−=Nj≤≤2(6)()()×+++∑−−−+−==+jijjjjmmmmjjiKUVMVMUFVB,111,(7)1,1,++×=jijjiKVC11−≤≤Nj(8)jijjiZFD,,×−=Nj≤≤1(9)withmreferstonumberofthetrays.ItisnoticedthatthemassbalancebasedonEquation(5),forthevariouscomponents,takestheCN×formofline