传质分离过程的热力学基础

传质分离过程第二章传质分离过程的热力学基础?Chapter2ThermodynamicsofSeparationOperationFormasstransferseparationprocesses,theseparationisachievedbyenhancingtherateofmasstransferbydiffusionofcertainspeciesrelativetomasstransferofallspeciesbybulkmovementwithinaparticularphase.Chapter2ThermodynamicsofSeparationOperationThedrivingforceanddirectionofmasstransferbydiffusionisgovernedbythermodynamics,withtheusuallimitationsofequilibrium.Thus,bothtransportandthermodynamicsconsiderationsarecrucialinseparationoperations.Therateofseparationisgovernedbymasstransfer,whiletheextentofseparationislimitedbythermodynamicsequilibrium.极限程度------热力学分离速率------动力学Extent=ThermodyanmicsRate=TransportContents2.1相平衡基础2.1.1气液平衡2.1.2液液平衡2.2多组分物系的泡点和露点计算2.2.1泡点温度和压力的计算2.2.2露点温度和压力的计算2.3多组分闪蒸计算2.3.1等温闪蒸和部分冷凝过程2.3.2绝热闪蒸过程2.4液液平衡过程的计算2.5多相平衡过程2.6共沸系统和剩余曲线2.1PhaseEquilibria2.1.1Vapor-LiquidEquilibrium2.1.2Liquid-LiquidEquilibrium2.2Bubble-point,andDew-pointCalculationforMulticomponentMixtures2.2.1Bubble-pointTemperatureandPressureCalculation2.2.2Dew-pointTemperatureandPressureCalculation2.3FlashCalculation2.3.1IsothermalFlashandPartialCondensation2.3.2AdiabaticFlash知识点1.相平衡常数计算：状态方程法，活度系数法2.泡点、露点计算（1）泡点计算：在一定P（或T）下，已知xi，确定Tb（或Pb）和yi。（2）露点计算3.等温闪蒸和绝热闪蒸计算：给定物料的量与组成，计算在一定P和T下闪蒸得到的汽相量与组成，以及剩余的液相量与组成。2.1相平衡基础（PhaseEquilibria）一、相平衡关系二、相平衡常数的计算常见的化工单元操作，如精馏、吸收、萃取、结晶等都是有相变化的过程，其研究和设计基础是相平衡、物料平衡和传递速率。相平衡在传质分离过程中占有重要地位，实际系统与平衡状态的差距是相间传质过程的推动力。相平衡是阐述混合物分离原理和计算传质推动力的基础数据。一、相平衡关系（1）什么是相平衡？混合物所形成的若干相保持物理平衡而共存的状态。热力学：整个物系的自由能最小。Atequilibrium,thetotalGibbsfreeenergy(G)forallphasesisaminimum.动力学：相间表观传递速率为零。Theapparentrateofmasstransferacrossthephaseinterfaceiszero.一、相平衡关系（2）相平衡条件（准则）：各相的温度相等、压力相等，每个组分的化学位相等。......TTT......''''''iii......PPPRTCfiiexpˆChemicalpotentialcannotbeexpressedasanabsolutequantity,andthenumericalvaluesofchemicalpotentialaredifficulttorelatetomoreeasilyunderstoodphysicalquantities.Furthermore,thechemicalpotentialapproachesaninfinitenegativevalueaspressureapproacheszero.Forthesereasons,thechemicalpotentialisnotfavoredforphaseequilibriacalculations.Instead,fugacity,inventedbyG.N.Lewisin1901,isemployedasasurrogate.Chemicalpotential一、相平衡关系（2）相平衡条件（准则）：各相的温度相等、压力相等，每个组分的逸度相等。......TTT......PPP......ˆˆˆiiifff相平衡关系的表示方法：1.相图2.相平衡常数：yixi0iiixyK/3.分离因子：jijijiijKK/xx/yy二、相平衡常数相平衡常数（Ki）---EquilibriumRatioiiixyK/EquilibriumRatioistheratioofmolefractionsofaspeciespresentintwophasesatequilibrium.iiixyKEquilibriumRatioForthevapor-liquidcase（egDistillationandAbsorption）,theconstantisreferredtoastheK-value（K值）orvapor-liquidequilibriumratio（气液平衡常数）.yi---Concentrationofanycomponentinvaporxi---ConcentrationofanycomponentinliquidFortheliquid-liquidcase（eg.Extraction）,theconstantisreferredtoasthedistributioncoefficient（分配系数）orliquid-liquidequilibriumratio（液液平衡常数）.xi(1)---Concentrationofanycomponentinextractxi(2)---Concentrationofanycomponentinraffinate)2()1(/iiDixxKiiixyKCalculationofEquilibriumRatioKi的计算：Case1---理想体系的吸收过程：亨利定律（Henry’sLaw）Case2---理想体系的精馏过程拉乌尔定律（Raoult’sLaw）Case3---非理想体系用气相逸度和液相活度系数来计算。三、分离因子SeparationFactor平衡分离过程，常采用分离因子表示平衡关系。jijijiijKK/xx/yyrelativevolatility（相对挥发度）forDistillation相对挥发度对温度和压力变化不敏感，常视为常数，简化计算。DjDiijKKFortheliquid-liquidcase,relativeselectivityis分离因子与1的偏离程度表示组分间分离的难易程度。Forthevapor-liquidcase,separationfacorisAtvapor-liquidequilibrium,LiViffˆˆCase2---理想气体混合物Forapureidealgas,fugacityisequaltothepressure,andforacomponentinanidealgasmixture,thepartialfugacityisequaltoitspartialpressure,.pypiiDalton’slaw2.1.1汽液平衡Vapor-liquidequilibriaCase1—纯组分Forapurecomponent,thepartialfugacity,,becomesthepure-componentfugacity,.ifˆif逸度等于纯组分的逸度逸度等于组分的分压2.1.1汽液平衡Vapor-liquidequilibriaViLiiiixyKˆˆpxfiLiLiˆˆCase3---真实混合物Forarealmixture,partialfugacitycoefficientsaredefinedbyandTherefore,pyfiViViˆˆpxpyiLiiViˆˆ(2-7)(2-8)(2-10)aso-calledequation-of-stareformoftheK-valueisobtained:LiViffˆˆ应用状态方程分别计算汽、液两相的逸度系数。用逸度系数或活度系数计算逸度Atvapor-liquidequilibrium,LiViffˆˆaso-calledactivitycoefficientformoftheK-valueisobtained:Activitycoefficientofispeciesinaliquidphaseisdefinedby:pfxyiVioLiiiiKˆLiiLiifxf0ˆˆ(2-9)Fugacityunderstandardstate通常取纯组分i的液体在系统温度和压力下的逸度。2.1.1汽液平衡Vapor-liquidequilibria应用状态方程计算汽相逸度系数，应用活度系数方程计算活度系数。相平衡常数计算的两种方法：状态方程法活度系数法2.1.1汽液平衡Vapor-liquidequilibriaViLiiiixyKˆˆpfxyiVioLiiiiKˆPPnpTitiiidpPRTnVRTpyfnnj0])[(1ˆˆ,,VmttnVTiiiinZdVVRTnpRTpyfnnj])[(1ˆˆ,,(2-13)(2-14):;:;:molesnfactorilitycompressibZvolumetotalVimtViLiiiixyKˆˆ一、状态方程法（PVTequation-of-statemodel）以V和T为独立变量：以P和T为独立变量：适合于气相、液相和固相溶液状态方程法的关键选择一个既适用于气相，又适用于液相的状态方程。UsefulEquationsofStateNameEquationEquationconstantsandfunctionIdealgaslawNoneGeneralizedRedlich-Kwong(R-K)Soave-Redlich-Kwong(SRKorRKS)Peng-Robinson(P-R)VRTp)176.0574.1480.0)(1(125.05.0rTVZRTpccccpRTbpTRa0867.04278.0252datefromderivedasorZTpzZcrr,,ccccpRTbpTRa0867.04278.0252ccpRTb07780.0)(bVVabVRTpRTbVbVVTap)()(5.0222bbVVabVRTp226992.054226.137464.0fcrcpTfTRa5.0221145724.0思考对常用的状态方