第十讲 平衡级分离过程

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讲—平衡级分离过程SeparationByEquilibriumStagesi10.1

单级分离过程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