Separation-Process-Principles-2

Chapter2Thermodynamicsofseparationoperations•Thermodynamicpropertiesandequationsplayamajorroleinseparationoperations,particularlywithrespecttoenergyrequirements,phaseequilibria,andsizingequipment.•Thischapterdiscussesappliedthermodynamicsforseparationprocesses.Equationsforenergybalances,entropyandavailabilitybalances,andfordeterminingphasedensitiesandphasecompositionsatequilibriumaredeveloped.Theseinvolvethermodynamicproperties,includingspecificvolumeordensity,enthalpy,entropy,availability,andfugacitiesandactivitiestogetherwiththeircoefficients,allasfunctionsoftemperature,pressure,andphasecomposition.•Methodsforestimatingpropertiesforidealandnon-idealmixturesaresummarized.2.1Energy,entropy,andavailabilitybalances*Mostcommercialseparationoperationsutilizelargequantitiesofenergyintheformofheatand/orshaftwork.Forexample,theenergyconsumptionbydistillationintheUSisapproximately$10trillionperyear(1991).Thus,itisofconsiderableinteresttoknowtheextentofenergyconsumptioninaseparationprocess,andtowhatdegreeenergyrequirementsmightbereduced.Suchenergyestimatescanbemadebyapplyingthefirstandsecondlawsofthermodynamics.•Considerthecontinuous,steady-stateflowsystemforageneralseparationprocessinFig.2.1.•Oneormorefeedstreamsflowingintothesystemareseparatedintotwoormoreproductstreamsthatflowoutofthesystem.n-molarflowrates,zi-thecomponentmolefractionsT-temperature,b-molaravailabilitiesh-molarenthalpies,s-molarentropiesP-pressure,Q-heatflowsinorout,W-shaftworkcrossingtheboundaryofthesystemStreamsoutn,zi,T,P,h,s,b,vStreamsinn,zi,T,P,h,s,b,vHeattransferinandoutQin,TsQout,Ts(Ws)in(Ws)outShaftworkinandout(Surroundings)T0SeparationProcess(system)Sirr,LW•Atsteadystate,ifkinetic,potential,andsurfaceenergychangesareneglected,thefirstlawofthermodynamics(alsoreferredtoastheconservationofenergyortheenergybalance),statesthatthesumofallformsofenergyflowingintothesystemequalsthesumoftheenergyflowsleavingthesystem:(streamenthalpyflows+heattransfer+shaftwork)leavingsystem-(streamenthalpyflows+heattransfer+shaftwork)enteringsystem=0•Allseparationprocessesmustsatisfytheenergybalance.Inefficientseparationprocessesrequirelargetransferofheatand/orshaftworkbothintoandoutoftheprocess;efficientprocessesrequiresmallerlevelsofheattransferand/orshaftwork.Thefirstlawofthermodynamicsprovidesnoinformationonenergyefficiency,butthesecondlawofthermodynamics(alsoreferredtoastheentropybalance)does.•Theentropybalanceis(streamentropyflows+entropyflowsbyheattransfer)leavingsystem-(streamentropyflows+entropyflowsbyheattransfer)enteringsystem=productionofentropybytheprocessNotethattheentropybalancecontainsnotermsrelatedtoshaftwork.*Althoughtheproductionofentropy,Sirr,isameasureofenergyinefficiency,itisdifficulttorelatetothismeasurebecauseitdoesnothavetheunitsofenergy/time(power).•AlthoughQandWshavethesamethermodynamicworthinEq.(1)ofTable2.1,heattransferhaslessworthinEq.(3).Thisisbecauseshaftworkcanbeconvertedcompletelytoheat(byfriction),butheatcannotbeconvertedcompletelytoshaftworkunlesstheheatisavailableataninfinitetemperature.•Availability,likeentropy,isnotconservedinareal,irreversibleprocess.Thetotalavailability(i.e.,abilitytoproduceshaftwork)passingintoasystemisalwaysgreaterthanthetotalavailabilityleavingaprocess.Thedifferenceisthelostwork,LW,whichisalsocalledthelossofavailability(orenergy),andisdefinedbyLW=T0Sirr•Lostworkisalwaysapositivequantity.Thegreateritsvalue,thegreateristheenergyinefficiency.Inthelowerlimit,asareversibleprocessisapproached,lostworktendstozero.•Theavailabilitybalanceis(streamavailabilityflows+availabilityofheat+shaftwork)enteringsystem-(streamavailabilityflows+availabilityofheat+shaftwork)leavingsystem=lossofavailability(lostwork)*Foranyseparationprocess,lostworkcanbecomputedfromEq.(3)inTable2.1.Itsmagnitudedependsontheextentofprocessirreversibilities,whichincludefluidfriction,heattransferduetofinitetemperature-drivingforces,masstransferduetofiniteconcentrationoractivity-drivingforces,chemicalreactionsproceedingatfinitedisplacementsfromchemicalequilibrium,mixingofstreamsatdifferingconditionsoftemperature,pressure,and/orcomposition,andsoon.Thus,toreducethelostwork,drivingforcesformomentumtransfer,heattransfer,masstransfer,andchemicalreactionmustbereduced.Practicallimitstothisreductionexistbecause,asdrivingforcesaredecreased,equipmentsizesincrease,tendingtoinfinitelylargesizesasdrivingforcesapproachedzero.•Foraseparationprocessthatoccurswithoutchemicalreaction,thesummationofthestreamavailabilityfunctionsleavingtheprocessisusuallygreaterthanthesamesummationforstreamsenteringtheprocess.•Inthelimitforareversibleprocess(LW=0),Eq.(3)ofTable2.1reducestoEq.(4),whereWministheminimumworkrequiredtoconducttheseparationandisequivalenttothedifferenceintheheattransferandshaftworktermsinEq.(3).Thisminimumworkisindependentofthenature(orpath)oftheseparationprocess.•TheworkofseparationforanactualirreversibleprocessisalwaysgreaterthantheminimumvaluecomputedfromEq.(4).•Thesecond-lawefficiencyisdefinedas(fractionalsecond-lawefficiency)=(minimumworkofseparation)