热力学方法讲座 华南理工大学化学工程研讨所陆恩锡重点内容热力学方法概述形状方程模型液体活度系数模型通用关联式二元相互作用参数的选用和估算流程模拟箴言热力学方法的用途分别过程计算distillation, stripping, evaporation, extractionRequire accurate VLE and LLE calculation换热器设计和核算要求焓值及其它性质计算紧缩机、膨胀机设计要求熵值及其它性质计算塔水力学计算，管线阻力降、直径计算要求传送性质计算热力学方法运用步骤 确定物系的性质：极性或非极性物质 选择适宜物系的正确的热力学模型. 1、非极性物质形状方程法或通用关联式法； 2、极性物质活度系数法；确定该物系的关键二元对.核实该关键二元对的相互作用参数.估算短少的其它二元对的相互作用参数.相平衡根底什么是相平衡常数 ? K-values 定义为：相平衡常数是温度、压力和气液相组成的函数.理想气体Ideal gas理想气体为纯组分气体或气体混合物，凡服从理想理想气体为纯组分气体或气体混合物，凡服从理想气体形状方程气体形状方程(Ideal gas equation of state)(Ideal gas equation of state)的气的气体为理想气体体为理想气体: : PV=RT PV=RT 理想溶液Ideal solution理想溶液是指构成溶液的各个纯组分在混合前和构成溶液后体积不变，并且无混合热的混合物系统；需指出的是这里所述的溶液系指广义的溶液，它包括气相混合物和液相混合物；理想溶液不一定是理想气体；但理想气体必定是理想溶液；一个气液系统可以气相是理想溶液，而液相是非理想溶液，反之亦然；理想溶液和非理想溶液划分低压下绝压小于低压下绝压小于2atm2atm，轻烃类混合物的气相可，轻烃类混合物的气相可以以为是理想气体；中压下绝压以以为是理想气体；中压下绝压151520atm20atm，轻，轻烃类混合物的气相可以以为是理想溶液，但不是理想烃类混合物的气相可以以为是理想溶液，但不是理想气体；高压下，轻烃类混合物的气相是非理想溶液。气体；高压下，轻烃类混合物的气相是非理想溶液。对于理想溶液，相平衡常数对于理想溶液，相平衡常数K K为压力和温度的函数为压力和温度的函数: : K=f(P, T) K=f(P, T)对于非理想溶液，相平衡常数对于非理想溶液，相平衡常数K K为压力、温度和组成为压力、温度和组成的函数：的函数： K=f(P, T, Xi) K=f(P, T, Xi) 理想气体和理想溶液相平衡常数的计算 道尔顿定律 当气体为理想气体时，气体总压P为各个组分分压的总和： P=P1+P2+PnPi Pi=P Yi 理想气体和理想溶液相平衡常数的计算 拉乌尔定律 当液体为理想溶液时，溶液中i组分的饱和分压等于该纯组分在与气相一样温度时的饱和分压乘以该组分的液相分子分数： Pi=Pi0Xi 理想气体和理想溶液相平衡常数的计算拉乌尔定律和道尔顿定律联立,得到相平衡常数计算公式： 实践体系相平衡常数计算对于实践体系，如高压下烃类混合物为非理想溶液，不服从道尔顿定律和拉乌尔定律，此时以上公式已不适用。需采用逸度、逸度系数和活度系数来处置非理想溶液的气液相平衡关系。 实践体系相平衡常数计算的三类方法1、形状方程法2、活度系数法3、通用关联式法形状方程法K-values 计算气液两相的逸度系数均由形状方程计算立方型形状方程立方型形状方程Van der Waals (1873)Redlich-Kwong (1949)Soave-Redlich-Kwong (1972)Peng-Robinson (1976)立方型形状方程优优点点可用于气液两相；可用于气液两相；方程相方程相对较简单对较简单，计计算快速，省算快速，省时时；覆盖温度覆盖温度压压力范力范围围广；广；可用于可用于临临界区的界区的K-valuesK-values计计算；算；可可处处置超置超临临界界组组分；分； 计计算其它算其它热热力学性力学性质质具有具有热热力学一致性；力学一致性；立方型形状方程局限性:限于非极性或细微极性的物系；液相密度预测准确性较差；接近临界区时，液相焓值计算准确性较差； 立方型形状方程Van der Waals (1873)Redlich-Kwong (1949)立方型形状方程Soave-Redlich-Kwong (1972)Peng-Robinson (1976)立方型形状方程-i计算PRPR方程方程ii计计算算立方型形状方程关键计算内容临界约束；Alpha 函数 纯组分需符合气相压力数据，用于预测和温度相关的方程参数 “a；混合规那么 与混合物符合，确定混合物的相关其它方程参数； SRK方程分析Soave-Redlich-Kwong equationb 与温度无关a 是温度的函数PRTvbaTvvbc=- ()() SRK方程分析临界点约束无因次公式ai ai 与温度相关的表达式与温度相关的表达式 SRK方程分析Alpha 函数Soave SRK方程分析混合规那么 Amix, Bmix = ?kij 二元相互作用参数(T) Function Redlich-Kwong equation (1949):Wilson (1964) was the first to introduce that a is a function of temperature:ALPHA 函数 (T) FunctionSoave modification to RK equationRegression of 61 components: mostly hydrocarbonsMajor step in the generalization of CEOS (T) FunctionPeng and Robinson (1976) inherited Soaves (T)Regressed a larger data setStill not completely generalized form20.2699 1.5422 + 0.3746 mw ww w-=Problems With Soaves (T)Poor vapor pressure prediction at low TrBecomes zero at finite temperature and then rises again with increasing temperatureNot reliable for extrapolation to high acentric factor because of 4th order dependence on wCannot be applied to polar componentsAdvanced (T) FunctionsSoave (1979)Boston-Mathias (1980)Mathias-Copeman (1983)Advanced (T) FunctionsMathias (1983)Twu et al. (1991):Advanced (T) FunctionsTwu et al. (1995):whereAdvanced (T) FunctionsSIMSCI (T) Supported by a databank with parameters for over 1100 components. Default for all CEOS EXCEPT SRK & PR. For these, their original forms the default but SimSci form can be specified.混合规那么和二元相互作用参数 VdW Type Mixing RulesVan der Waals one-fluid mixing rulesUsed in SRK and PR CEOSBinary Interaction Parameters对 VLE 计算非常重要；对烃类混合物，组分分子大小相类似， k12 = k21 不能用于含强极性或缔合组分的非对称系统；液体活度系数模型活度系数方法液相: 活度系数模型气相: 形状方程模型 fioL 规范态逸度，定义为:液体活度系数模型Margules (1895)van Laar (1910)Wilson (1964)Non-random Two-Liquid (NRTL) (1968)Regular Solution (1970)UNIQUAC (1975)UNIFAC (1975) 液体活度系数模型优点:有效的关联化学品系统在低压下的性质；容易运用无限稀释活度系数数据；可根据基团奉献进展预测；许多物系的二元相互作用参数可从 DECHEMA 丛书中查出；液体活度系数模型局限性:只能用于液相；可用的温度压力范围很窄；对超临界组分需采用亨利常数；无法计算接近或在临界点时的 K-values；计算其它热力学性质时无一致性；Margules 模型阅历关联式；二元相互作用参数与温度无关；无数据库；Redlich, O. and Kister, A. T., Algebraic Representation of Thermodynamic Properties and the Classification of Solutions, Ind. Eng. Chem., 1948, 40, 345348.van Laar 模型另一种阅历关联式；二元相互作用参数与温度无关；无数据库；van Laar, J. J., The Vapor Pressure of Binary Mixtures, Z. Phys. Chem.,1910, 72, 723-751.Wilson 模型部分组成模型；适用于较广的温度范围； Wilson 模型原型无法预测 LLE；Regular Solution 模型优点：无需数据库；缺陷：超临界组分无法处置；NRTL 模型Non-Random Two-Liquid ModeltjijijijiabTcT=+2tijijijijabTcT=+2()GTijijijij=-+expbtij = ji b ij = b jiCan use 3-term (as, bs and a), 5-term (as, bs, and a) or 8-term (as, bs, cs, a and b)UNIFAC模型基于基团奉献法；优点:根据基团构造进展预测； 当缺乏混合物数据时, UNIFAC 模型对化学品和烃类物质可提供有效的预测； 能较好的描画含有极性和/或非极性组分体系的VLE and LLE 行为；UNIFAC 模型局限性:不适于多官能团构造的物质；分子量大于 400 的物质不适用；无法预测异构化影响；活度系数模型需求实验数据支持，用来确定二元相互作用参数需求气相压力数据 Pisat 亨利定律超临界组分不适用于活度系数方法，需采用亨利定律处置:亨利常数是温度、压力和组成的函数； 亨利定律二元亨利常数:混合物亨利常数:Henrys Law中选择亨利定律后，对于组分 Tc 400 K，会自动运用亨利定律；用户可定义溶质组分；数据库中包括许多水中的污染物质；需检查有无亨利系数；液体活度系数方法Pro/II 包括了NRTL 和 UNIQUAC 方程的大量的二元相互作用参数的数据库，是从 DECHEMA 数据库回归而得；Pro/II 还包括了恒沸物质的数据库，它可用于采用 “fill-in 功能，产生短少的二元相互作用参数；运用 FILL=UNIFAC (VLE or VLLE)补充短少的二元相互作用参数. UNIFAC 将给出易于运用的二元相互作用参数；液体活度系数方法除 UNIFAC 和 Regular Solution模型,一切其它方法均需二元相互作用参数，这些参数是从实验数据回归而得；当组分是超临界组分时，不能运用活度系数法，需采用亨利定律；当超临界组分含量较大时，缺省的焓值计算方法为理想气体方法.引荐 非理想体系: NRTL (VLE or VLLE) with FILL=AZEOTROPE, UNIFAC含离子系统: Electrolytes强酸 (95+%) : NRTL环保气提塔: Henrys with NRTL or CEOSUse the on-line Reference Manual in PROvision通用关联式模型Thermodynamic Models before 1972KDATABK10 (1960)Chao-Seader (1961)Chao-Seader-Erbar ExtensionGrayson-Street (1963)Grayson-Street-Erbar ExtensionImproved Grayson-StreetBraun K-10 (BK10) AFor natural gas processes, the convergence For natural gas processes, the convergence pressure can usually be used as the parameter pressure can usually be used as the parameter that represents the composition of the vapor and that represents the composition of the vapor and liquid phase in equilibrium.liquid phase in equilibrium.The convergence pressure is, in general, the The convergence pressure is, in general, the critical pressure of a system at a given critical pressure of a system at a given temperature.temperature.The Braun K-10 charts is the low pressure The Braun K-10 charts is the low pressure equilibrium ratio, arbitrarily taken at 10 psia equilibrium ratio, arbitrarily taken at 10 psia system pressure and at 5,000 psia convergence system pressure and at 5,000 psia convergence pressure.pressure.Braun K-10 (BK10)For hydrocarbons, the equilibrium K-values are predicted from vapor pressureThe K-values at any pressure P are then calculated fromBraun K-10 (BK10)K-values are not functions of composition.The BK10 applies to hydrocarbon mixtures that behave ideally at low pressures or vacuum tower.Good for mixtures of one molecular type.Applies to mixtures of paraffins and olefins.Chao-Seader MethodThe K-values of Chao-Seader method are based on the gamma/phi approach:This method consists of three parts:Fugacity coefficient in a vapor mixtureActivity coefficient modelLiquid fugacity coefficient of pure component i in its standard stateChao-Seader MethodFugacity coefficient in a vapor mixtureRK CEOS is used to calculate fugacity coefficient of component i in vapor mixtures.Chao-Seader MethodRegular solution activity coefficient modeli and viL at reference temperature of 25oC.How about i and viL for super-critical components such as H2, C1, C2, and C2H4 ?Chao-Seader MethodLiquid fugacity coefficient of pure component i in its standard state A standard state is like a point of reference on a map. If someone asks “Where is Berkeley ? a helpful reply is “About 10 miles east of San Francisco. The person asking the question knows where San Francisco is: it serves as his standard state. Chao-Seader MethodThe quantity fioL is the fugacity of i in its standard state. The most frequently used standard state for fioL is the pure liquid (xi1) at the system temperature and pressure. fioL is well defined asChao-Seader MethodChao-Seader proposedAbove terms calculated as a function of reduced temperature and pressure.How to deal with super-critical components?Chao-Seader MethodStrengthsPredictive method for the calculation of K-values for hydrocarbon and light gas systems. The regular solution theory gives a good representation of activity coefficients for many solutions containing nonpolar components.In the absence of any mixture data, the regular solution equations provide useful results for nonpolar systems.Chao-Seader MethodLimitationsThe extrapolation of pure liquid fugacity coefficient outside recommended ranges for subcritical component may not be reliableDifficult to compute the fugacity of any supercritical “liquidChao-Seader correlation does not predict other thermodynamic properties such as enthalpy, entropy, density, etc.Grayson-Streed MethodAn enhancement to Chao-SeaderPure component liquid fugacities were re-correlated to extend the temperature range of the Chao-Seader K-valuesNew equations for liquid fugacity for hydrogen, methane and petroleum components have been developedGrayson-Streed MethodLin, Greenkorn, and Chao (AIChE J., 1995, 41(6):1602-1604) developed another new equation for the standard state liquid fugacity of hydrogen based on the expanded database.Chao-Seader-ErbarGrayson-Streed-ErbarA new set of constants for the Chao-Seader liquid fugacity coefficient specifically for N2, H2S, and CO2 were developed to improve the prediction of the K-values of these gases.New values of the solubility parameter and molar volume.Improved Grayson-Streed(IGS)Additional fugacity correlation for CO, O2, and H2O.Allow rigorous modeling of hydrocarbon-water VLLE.Re-tune the to match prediction from the Wagner generalized vapor pressure correlation to improve the vapor pressure prediction for heavy hydrocarbons.SPECIAL WATER HANDLINGCalculation with Two Liquid PhasesRigorous VLLE calculationsWater decant optionL1L2VLWVRigorous VLLE CalculationsVaporLiquid 2Liquid 1VLE K-valuesVLE K-valuesLLE K-valuesMust enable two-liquid phase calculations.Water Decant OptionVaporPure WaterLiquidWater VaporPressureVLE K-valuesWater SolubilityEnthalpy CalculationsSRK & PR (original):Not particularly good for predicting heats of vaporization for polar components.Advanced CEOS (SRKM, SRKS, etc.) New alpha function improve predictions for the heats of vaporization of polar systems.Advanced mixing rules generally give better predictions for the heats of mixing.Enthalpy CalculationBenedict-Webb-Rubin-Starling EOSUse if parameters are availableAssociating Equations:The Hexamer EOS can be used for systems containing HF, such a refrigerant mixturesHayden-OConnell can be used for enthalpies in the vapor phase for systems containing dimerizing componentsDensity MethodsCEOS (SRK, SRKM, SRKS etc.)Good for vapor densityInaccurate for hydrocarbon liquid densityHorrible for liquid density of polar componentsSIMSCI CEOS systems use API method for the liquid density, which is good for hydrocarbon systems but is not very good for chemicalsAssociating EOSGood for vapor densities onlyDensity MethodsNon-cubic EOSBWRS can be used very adequately for the densities of both phases.RackettSaturated liquid densities using Tc , Pc , and Zc Recommended for defined hydrocarbon components by the API but it works for polar substances as well.Density MethodsThe Rackett equation is:where:RACKETT (cont)Databank of regressed Rackett parameters is available for many components. For other components, Zc is usedTwo versions of Rackett method availableRACKETT calculates density of each component from the equations and then adds them together assuming no volume of mixing changeRCK2 uses a mixing rule for Tc , Pc , and Zc to get mixture values, then uses the equations for the mixture densityDensity MethodsCOSTALD:Comparable to Rackett for liquid densitiesUses modified Vc and w for each componentCOSTALD (cont.)Correction for higher pressuresThe ai, bi, B and C are non-component specific Costald parameters.Density MethodsLibrary MethodFor liquid densities, temperature dependent correlation from databank are used Component densities are combined assuming NO excess volume.For vapor densities, gives ideal gas values and isnt recommended except at VERY low pressures.DATA REGRESSIONData Regression Uses of Data RegressionTypes of DataSome Helpful hints for Data RegressionUses of Data RegressionFit Property vs. Temperature CorrelationFit EOS “Alpha coefficients to vapor-pressure dataFit EOS or LACT binary parameters to phase-equilibrium dataUses of Data RegressionFit LACT binary parameters to activity-coefficient dataFit excess enthalpies to Redlich-Kister correlationVerify calculated results for a given set of parametersData FormatsPT(Property vs. TemperaturePTX(Bubble points, gas solubility)PTXY(Complete VLE data)PTXXY (Complete VLLE data)TXX(LLE data)HTX(Enthalpy of mixing)Example - Water/NMP DataSelect ComponentsRegression of Water/NMP DataSelect Thermodynamic Method(s) for Regression.Regression of Water/NMP DataEnter Data Regression ProgramRegression of Water/NMP DataModify General OptionsSelect Regression TypeEquation Format, Data Type, Number of Components in Data SetRegression of Water/NMP DataEnter Experimental DataRegression of Water/NMP DataSelect Units of MeasurementEnter Pressure, Temperature and Composition DataUse Propagate check box for Isobaric or Isothermal dataIf necessary, set Objective Function, Print Options or View EquationInitial Estimates can be used to Generate Initial Estimates or Use the built-in Initial Estimates GeneratorRun Regress, View Results, Store ResultsRegression of Water/NMP DataHintsDont try to do too much at once.If you give initial estimates, make thoughtful choices.Look at the results.Look at the data (as reprinted).HintsRegress your data based on how you will use the resulting parameters.Beware of large volatility differences.Verify pure component properties.HintsWith nonlinear models, correlation between parameters can produce initial estimate dependence.Use VERIFY=3 (an undocumented Keyword) to run the NLS regression but not the ODR regression.COMPONENT PROPERTY MANIPULATIONComponent PropertiesViewing existing component propertiesPredicting pure component propertiesManipulating SIMSCI library propertiesBuilding component property librariesViewing Component PropertiesFixed propertiesTemperature dependent propertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesPredicting Component PropertiesPredicting Component PropertiesPredicting Component PropertiesComponent Property LibrariesPure-component and mixture databanksPure component databanks: Process (Default)SimSci (Contains DIPPR data when available)DIPPROLI (Electrolytes)User (Created using Dataprep and/or LIBMGR)Default is BANK=PROCESS, SIMSCIComponent Property LibrariesMixture databanksNRTL/UNIQUACAzeotropeUNIFACHenrys Law (includes priority pollutants)Alcohol (dehydration)User (created using LIBMGR)CONCLUSIONConclusionsVery important to choose the correct thermodynamic methodEven more important to insure that binary interaction parameters are availableConclusionsAdvanced Equations of StateModel hydrocarbon behaviorAdvanced Alpha formsAdvanced mixing rulesDatabank of regressed binary interaction coefficientConclusionsLiquid Activity Coefficient methodsModel non-ideal behaviorDatabank of regressed binariesDatabank of azeotropesFill options for binariesConclusionsGeneralized CorrelationTypically designed for a specific applicationDo a good job for heavier hydrocarbonsConclusionsEnthalpy, Entropy and DensityLibrary correlation for enthalpyNo Library correlation for entropyLibrary correlation for densityRackett parameters in LibraryClosingHow can we improve this courseThank You for having us