第十講 平衡級分離過程

Firstpage傳遞過程與分離技術全日制專業(yè)碩士研究生學位課程面向應用的專業(yè)基礎課程第十講—平衡級分離過程SeparationByEquilibriumStagesi10.1

單級分離過程FlashCalculationSingleEquilibriumStageandIntroductionTheseparationprocessbysingleequilibriumstageisoneinwhichtwophaseincontactarebroughttophysicalequilibriumandfollowedbyphaseseparation.Thecalculationsofsinglestageseparationaremadebycombiningmaterialbalanceandenergybalancewithphaseequilibriarelations.DegreesofFreedomThevariablestodescribethephysicalequilibriumofasystemareclassifiedasintensivevariables,whichareindependentofthesizeofthesystem,andextensivevariables,whichdependonsystemsize.Onlyafewofthevariablesareindependenttodeterminethestateofsystem.Thenumberoftheindependentvariablesiscalledthedegreesoffreedom.GibbsPhaseRuleForasystematphysicalequilibrium,thenumberofindependentintensivevariablestodescribeitsthermodynamicstateisgivenbyGibbsphaseruleas(4-1)Forthevapor-liquidequilibriumofaternarysystem,inwhichCisthenumberofcomponents,Pthenumberofphases.Degrees-of-FreedomAnalysis(1)Forasystemwithfeedstreamsandextensivevariables,thephaseruleshouldbeextendedbyangeneralanalysisofdegreesoffreedomasfollowsinwhichVisthenumberofvariables,Ethenumberofindependentequations.ItshouldbepointedoutthatVdoesnotcountthethermodynamicfunctionswhichcanbecalculatedfromtheintensivevariables.Degrees-of-FreedomAnalysis(2)Forasingleequilibriumstageshownintherightfigure,thereare(CP

+2)

intensivevariablestodeterminethephaseequilibrium,and(C+P+4)

additionalvariables(zi,TF,PF,F,Q,V,L)todescribetheprocessstate.AndthereshouldbeindependentequationsforP

molarnormalizations,C(P

-1)

K-values,Ccomponentmaterialbalancesand1energybalance.Degrees-of-FreedomAnalysis(3)Therefore,(4-4)Forexample,ifvariables(zi,TF,PF,F,T,P)arespecified,alltheremainingvariablescanbecalculatedfromtheequations.BinaryVapor-LiquidSystems(1)Forbinaryvapor-liquidsystems,Gibbsphaserulegives(4-4)ThenifTandParespecified,thephasecompositions(xi,yi)shouldbecompletelydetermined.Andtherelativevolatility

A,B

(separationfactor)isalsodetermined.BinaryVapor-LiquidSystems(2)WhilePhasbeenspecified,T

andzicanchangefreelyinsinglephaseregionsbutxiandyibotharefixedifTisspecifiedin2-phaseregion.VandLarealsodeterminedbytheleverrule.BinaryVapor-LiquidSystems(3)Forvaporization,theplotintherightfigureismoreconvenient.Theequationofq-lineisAzeotropicSystems(1)Azeotropesareformedbyliquidmixturesexhibitingmaximumorminimumboilingpoints,whichrepresent,respectively,negativeorpositivedeviationsfromRaoults’law.Ifthereisonlyoneliquidphase,themixtureformsahomogeneousazeotrope;ifmorethanoneliquidphasearepresent,theazeotropeisheterogeneous.AzeotropicSystems(2)Minimumboilingpointsazeotrope.PartialpressuresshowpositivedeviationfromRaoults’law.ThereisamaximuminitsP-xcurve.AzeotropicSystems(3)Correspondingly,thereisaminimuminitsT-x-ycurve,whichstandsforthecompositionofazeotrope.AzeotropicSystems(4)Iny-xplot,equilibriumlinehasanintersectionwiththey=xline.AzeotropicSystems(5)Maximumboilingpointsazeotrope.PartialpressuresshownegativedeviationfromRaoults’law.ThereisaminimuminitsP-xcurve.AzeotropicSystems(6)Correspondingly,thereisamaximuminitsT-x-ycurve,whichstandsforthecompositionofazeotrope.AzeotropicSystems(7)Iny-xplot,equilibriumlinehasanintersectionwiththey=xline.AzeotropicSystems(8)Heterogeneousazeotropearealwaysminimumboilingmixtures.Theactivitycoefficientsmustbemuchgreaterthan1tocauseliquidphasesplit.AzeotropicSystems(9)In2-Lregion,temperature,totalpressure,partialpressures,andphasecompositionskeepconstantastherelativeamountsofthe2liquidphaseschange.AzeotropicSystems(10)In2-Lregion,thecompositionsofvaporphasekeepsconstantThoughthetotalcompositionofliquidphaseschange.Thepointsa,brepresentthecompositionsof2liquidphases.FlashCalculationsFlashisasingle-equilibrium-stageseparationprocesswithpartialvaporizationorcondensationofafeedstream.Arealflashprocessisalwaysaccompaniedbytemperatureandpressurechangeandheatexchange.Theisothermalandadiabaticflashesaretwoidealizedsituationsdiscussedmostcommonly.IsothermalFlash&AdiabaticFlashInanisothermalflash,heatingorcoolingarenecessarytokeepTVatthespecifiedvalue.Inanadiabaticflash,thepressureisreducedadiabaticallythatTVwillalsoreducetoprovidetheheatofvaporization.FlashCalculations

Degrees-of-freedomAnalysis(1)Thereare3C+10variablesinflash:and2C+5equations:EquationPhysicalSignificanceNo.ofEqs.(1)PV=PLMechanicalequilibrium1(2)TV=TLThermal

equilibrium

1(3)yi=KixiPhase

equilibrium

C(4)Fzi=Vyi+LxiComponentmaterial

equilibrium

C(5)F=V+LTotalmaterial

equilibrium

1(6)hF+Q=hVV+hLLEnergybalance1(7)

yi-

xi=0Summations1Ifthefeedconditionsaregiven,only2variablescanbespecified.FlashCalculations

Degrees-of-freedomAnalysis(2)ThedegreesoffreedomareC+5.SpecifiedVariablesTypeofcalculationsTV,PVIsothermalFlashV/F=0,PLBubble-pointtemperatureV/F=1,PVDew-pointtemperatureTL,V/F=0Bubble-pointpressureTV,V/F=1Dew-pointpressureQ=0,PVAdiabaticflashQ,PVNonadiabaticflashV/F,PVPercentvaporizationFlashFlashCalculations

IsothermalFlashTheequationsofcomponentmaterialbalancearenonlinear,sonumericalmethodsarenecessarytocarryoutflashcalculations.Table4.4Rachford-RiceProcedure

FlashCalculations

Bubble&DewpointsThebubblepointismathematicallydescribedby

=0.FromEq.(4)inTable4.4,Thedewpointismathematicallydescribedby

=1.Then,thedewpointequationisTherefore,thebubblepointequationis(4-12)(4-13)FlashCalculations

AdiabaticFlashAdiabaticflashiscalculatedbyiterationofTV

basedonthecalculatingprocedureofisothermalflash.SingleEquilibriumStages

TernaryLiquid-LiquidSystems(1)ForsystemswithA&Cmutuallyinsoluble,thesolute(B)

materialbalanceisandthedistributionofBatequilibriumisThentheratioofBinraffinateis

(4-23)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(2)Inmostsystems,AandCarepartiallysoluble.Severaltypesofphasediagramsareutilizedcommonlytofindtheequilibriumcompositions,fiveofwhichareillustratedasfollows.Theequilateraltriangularandrighttriangulardiagramsareutilizedmostcommonly.SingleEquilibriumStages

TernaryLiquid-LiquidSystems(3)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(4)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(5)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(6)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(7)SingleEquilibriumStages

TernaryLiquid-LiquidSystems(8)SingleEquilibriumStages

MulticomponentLiquid-LiquidSystemsFormulticomponentliquid-liquidsystems,manualcalculationsbasedonphasediagramsareimpossible.Thecomputationoftheequilibriumphasecompositionsisbestmadebyacomputer-assistedalgorithmusingactivitycoefficientequationssuchasNRTLorUNIQUAC

equations.AneffectivealgorithmisamodifiedRachford-Riceprocedure.MulticomponentLiquid-LiquidSystemsSolid-LiquidSystems