PRO/II热力学方程的选择（华南理工）

null热力学方法讲座 热力学方法讲座 华南理工大学化学工程研究所 陆恩锡重点内容重点内容☆热力学方法概述 ☆状态方程模型 ☆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 快递问题件怎么处理流程河南自建厂房流程下载关于规范招聘需求审批流程制作流程表下载邮件下载流程设计 模拟箴言流程模拟箴言热力学方法的用途热力学方法的用途分离过程计算 distillation, stripping, evaporation, extraction Require accurate VLE and LLE calculation 换热器 设计 领导形象设计圆作业设计ao工艺污水处理厂设计附属工程施工组织设计清扫机器人结构设计 和核算 要求焓值及其它性质计算 压缩机、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 要求传递性质计算热力学方法应用步骤热力学方法应用步骤☆ 确定物系的性质：极性或非极性物质 ☆ 选择适合物系的正确的热力学模型. 1、非极性物质－状态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. 估算缺少的其它二元对的相互作用参数. 相平衡基础相平衡基础什么是相平衡常数 ?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（Ideal gas） 理想气体为纯组分气体或气体混合物，凡服从理想气体状态方程(Ideal gas equation of state)的气体为理想气体: PV=RT 理想溶液（Ideal solution）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形成溶液后体积不变，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理想溶液和非理想溶液划分低压下（绝压小于2atm），轻烃类混合物的气相可以认为是理想气体；中压下（绝压15～20atm），轻烃类混合物的气相可以认为是理想溶液，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。 对于理想溶液，相平衡常数K为压力和温度的函数: K=f(P, T) 对于非理想溶液，相平衡常数K为压力、温度和组成的函数： K=f(P, T, Xi) 理想气体和理想溶液相平衡常数的计算 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+…+Pn＝∑Pi Pi=P Yi 理想气体和理想溶液相平衡常数的计算 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相同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： 实际体系相平衡常数计算实际体系相平衡常数计算对于实际体系，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理非理想溶液的气液相平衡关系。 实际体系相平衡常数计算的 三类方法 实际体系相平衡常数计算的 三类方法1、状态方程法 2、活度系数法 3、通用关联式法 状态方程法状态方程法K-values 计算 气液两相的逸度系数均由状态方程计算立方型状态方程立方型状态方程立方型状态方程立方型状态方程Van der Waals (1873) Redlich-Kwong (1949) Soave-Redlich-Kwong (1972) Peng-Robinson (1976)立方型状态方程立方型状态方程☆优点 可用于气液两相； 方程相对较简单，计算快速，省时； 覆盖温度压力范围广； 可用于临界区的K-values计算； 可处理超临界组分； 计算其它热力学性质具有热力学一致性；立方型状态方程立方型状态方程☆局限性: 限于非极性或轻微极性的物系； 液相密度预测准确性较差； 靠近临界区时，液相焓值计算准确性较差； 立方型状态方程立方型状态方程Van der Waals (1873) Redlich-Kwong (1949)立方型状态方程立方型状态方程Soave-Redlich-Kwong (1972) Peng-Robinson (1976)立方型状态方程-Φi计算立方型状态方程-Φi计算PR方程Φi计算立方型状态方程关键计算内容立方型状态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”； 混合规则 – 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 SRK方程分析Soave-Redlich-Kwong equation b 与温度无关 a 是温度的函数 SRK方程分析 SRK方程分析临界点约束 无因次公式ai 与温度相关的 表 关于同志近三年现实表现材料材料类招标技术评分表图表与交易pdf视力表打印pdf用图表说话 pdf 达式 SRK方程分析 SRK方程分析Alpha 函数 Soave SRK方程分析 SRK方程分析混合规则 Amix, Bmix = ???kij －二元相互作用参数(T) Function (T) Function Redlich-Kwong equation (1949): Wilson (1964) was the first to introduce that a is a function of temperature: ALPHA 函数ALPHA 函数 (T) Function (T) FunctionSoave modification to RK equation Regression of 61 components: mostly hydrocarbons Major step in the generalization of CEOS (T) Function (T) FunctionPeng and Robinson (1976) inherited Soave’s (T) Regressed a larger data set Still not completely generalized formProblems With Soave’s (T)Problems With Soave’s (T)Poor vapor pressure prediction at low Tr Becomes zero at finite temperature and then rises again with increasing temperature Not reliable for extrapolation to high acentric factor because of 4th order dependence on w Cannot be applied to polar componentsAdvanced (T) FunctionsAdvanced (T) FunctionsSoave (1979) Boston-Mathias (1980) Mathias-Copeman (1983)Advanced (T) FunctionsAdvanced (T) FunctionsMathias (1983) Twu et al. (1991):Advanced (T) FunctionsAdvanced (T) FunctionsTwu et al. (1995): whereAdvanced (T) FunctionsAdvanced (T) FunctionsSIMSCI (T) Supported by a databank with parameters for over 1100 components. Default for all CEOS EXCEPT SRK & PR. For these, their original form’s the default but SimSci form can be specified.混合规则和二元相互作用参数混合规则和二元相互作用参数 VdW Type Mixing Rules VdW Type Mixing RulesVan der Waals one-fluid mixing rules Used in SRK and PR CEOSBinary Interaction ParametersBinary Interaction Parameters对 VLE 计算十分重要； 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；液体活度系数模型液体活度系数模型活度系数方法活度系数方法液相: 活度系数模型 气相: 状态方程模型 fioL － 标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 态逸度，定义为: 液体活度系数模型液体活度系数模型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 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； 容易使用无限稀释活度系数数据； 可根据基团贡献进行预测； 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Margules 模型 经验 班主任工作经验交流宣传工作经验交流材料优秀班主任经验交流小学课改经验典型材料房地产总经理管理经验 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van Laar 模型另一种经验关联式； 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Wilson 模型局部组成模型； 适用于较广的温度范围； Wilson 模型原型无法预测 LLE；Regular Solution 模型Regular Solution 模型 优点：无需数据库； 缺点：超临界组分无法处理；NRTL 模型NRTL 模型Non-Random Two-Liquid Modelaij = aji b ij = b jiCan use 3-term (a’s, b’s and a), 5-term (a’s, b’s, and a) or 8-term (a’s, b’s, c’s, a and b)UNIFAC模型UNIFAC模型基于基团贡献法； 优点: 根据基团结构进行预测； 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； 能较好的描述含有极性和/或非极性组分体系的VLE and LLE 行为；UNIFAC 模型UNIFAC 模型局限性: 不适于多官能团结构的物质； 分子量大于 400 的物质不适用； 无法预测异构化影响； 活度系数模型活度系数模型需要实验数据支持，用来确定二元相互作用参数 需要气相压力数据 Pisat 亨利定律亨利定律超临界组分不适用于活度系数方法，需采用亨利定律处理: 亨利常数是温度、压力和组成的函数； 亨利定律亨利定律二元亨利常数: 混合物亨利常数: Henry’s LawHenry’s Law当选择亨利定律后，对于组分 Tc < 400 K，会自动使用亨利定律；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，产生缺少的二元相互作用参数； 使用 FILL=UNIFAC (VLE or VLLE)补充缺少的二元相互作用参数. UNIFAC 将给出易于使用的二元相互作用参数；液体活度系数方法液体活度系数方法除 UNIFAC 和 Regular Solution模型,所有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，不能使用活度系数法，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.推荐 推荐 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通用关联式模型通用关联式模型Thermodynamic Models before 1972Thermodynamic Models before 1972KDATA BK10 (1960) Chao-Seader (1961) Chao-Seader-Erbar Extension Grayson-Street (1963) Grayson-Street-Erbar Extension Improved Grayson-StreetBraun K-10 (BK10) ABraun K-10 (BK10) AFor natural gas processes, the convergence pressure can usually be used as the parameter that represents the composition of the vapor and liquid phase in equilibrium. The convergence pressure is, in general, the critical pressure of a system at a given temperature. The Braun K-10 charts is the low pressure equilibrium ratio, arbitrarily taken at 10 psia system pressure and at 5,000 psia convergence pressure.Braun K-10 (BK10)Braun K-10 (BK10)For hydrocarbons, the equilibrium K-values are predicted from vapor pressure The K-values at any pressure P are then calculated fromBraun K-10 (BK10)Braun 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 MethodChao-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 mixture Activity coefficient model Liquid fugacity coefficient of pure component i in its standard stateChao-Seader MethodChao-Seader MethodFugacity coefficient in a vapor mixture RK CEOS is used to calculate fugacity coefficient of component i in vapor mixtures. Chao-Seader MethodChao-Seader MethodRegular solution activity coefficient model i 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 MethodChao-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 MethodChao-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 (xi1) at the system temperature and pressure. fioL is well defined asChao-Seader MethodChao-Seader MethodChao-Seader proposed Above terms calculated as a function of reduced temperature and pressure. How to deal with super-critical components?Chao-Seader MethodChao-Seader MethodStrengths Predictive 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 MethodChao-Seader MethodLimitations The extrapolation of pure liquid fugacity coefficient outside recommended ranges for subcritical component may not be reliable Difficult to compute the fugacity of any supercritical “liquid” Chao-Seader correlation does not predict other thermodynamic properties such as enthalpy, entropy, density, etc.Grayson-Streed MethodGrayson-Streed MethodAn enhancement to Chao-Seader Pure component liquid fugacities were re-correlated to extend the temperature range of the Chao-Seader K-values New equations for liquid fugacity for hydrogen, methane and petroleum components have been developedGrayson-Streed MethodGrayson-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-Erbar Grayson-Streed-ErbarChao-Seader-Erbar Grayson-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)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 HANDLINGSPECIAL WATER HANDLINGCalculation with Two Liquid PhasesCalculation with Two Liquid PhasesRigorous VLLE calculationsWater decant optionRigorous VLLE CalculationsRigorous VLLE CalculationsMust enable two-liquid phase calculations.Water Decant OptionWater Decant OptionEnthalpy CalculationsEnthalpy 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 CalculationEnthalpy CalculationBenedict-Webb-Rubin-Starling EOS Use if parameters are available Associating Equations: The Hexamer EOS can be used for systems containing HF, such a refrigerant mixtures Hayden-O’Connell can be used for enthalpies in the vapor phase for systems containing dimerizing componentsDensity MethodsDensity MethodsCEOS (SRK, SRKM, SRKS etc.) Good for vapor density Inaccurate for hydrocarbon liquid density Horrible for liquid density of polar components SIMSCI CEOS systems use API method for the liquid density, which is good for hydrocarbon systems but is not very good for chemicals Associating EOS Good for vapor densities only Density MethodsDensity MethodsNon-cubic EOS BWRS can be used very adequately for the densities of both phases. Rackett Saturated liquid densities using Tc , Pc , and Zc Recommended for defined hydrocarbon components by the API but it works for polar substances as well.Density MethodsDensity MethodsThe Rackett equation is: where:RACKETT (cont)RACKETT (cont)Databank of regressed Rackett parameters is available for many components. For other components, Zc is used Two versions of Rackett method available RACKETT calculates density of each component from the equations and then adds them together assuming no volume of mixing change RCK2 uses a mixing rule for Tc , Pc , and Zc to get mixture values, then uses the equations for the mixture densityDensity MethodsDensity MethodsCOSTALD: Comparable to Rackett for liquid densities Uses modified Vc and w for each componentCOSTALD (cont.)COSTALD (cont.)Correction for higher pressures The ai, bi, B and C are non-component specific Costald parameters.Density MethodsDensity MethodsLibrary Method For 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 isn't recommended except at VERY low pressures. DATA REGRESSIONDATA REGRESSIONData RegressionData RegressionUses of Data Regression Types of Data Some Helpful hints for Data Regression Uses of Data RegressionUses of Data RegressionFit Property vs. Temperature Correlation Fit EOS “Alpha” coefficients to vapor-pressure data Fit EOS or LACT binary parameters to phase-equilibrium dataUses of Data RegressionUses of Data RegressionFit LACT binary parameters to activity-coefficient data Fit excess enthalpies to Redlich-Kister correlation Verify calculated results for a given set of parameters Data FormatsData FormatsPT (Property vs. Temperature PTX (Bubble points, gas solubility) PTXY (Complete VLE data) PTXXY (Complete VLLE data) TXX (LLE data) HTX (Enthalpy of mixing)Example - Water/NMP DataExample - Water/NMP DataSelect Components Regression of Water/NMP DataRegression of Water/NMP DataSelect Thermodynamic Method(s) for Regression. Regression of Water/NMP DataRegression of Water/NMP DataEnter Data Regression Program Regression of Water/NMP DataRegression of Water/NMP DataModify General Options Select Regression Type Equation Format, Data Type, Number of Components in Data SetnullRegression of Water/NMP DataRegression of Water/NMP DataEnter Experimental Data Regression of Water/NMP DataRegression of Water/NMP DataSelect Units of Measurement Enter Pressure, Temperature and Composition Data Use Propagate check box for Isobaric or Isothermal dataRegression of Water/NMP DataIf necessary, set Objective Function, Print Options or View Equation Initial Estimates can be used to Generate Initial Estimates or Use the built-in Initial Estimates Generator Run Regress, View Results, Store Results Regression of Water/NMP DataHintsHintsDon’t 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).HintsHintsRegress your data based on how you will use the resulting parameters. Beware of large volatility differences. Verify pure component properties.HintsHintsWith 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 PROPERTY MANIPULATIONComponent PropertiesComponent PropertiesViewing existing component properties Predicting pure component properties Manipulating SIMSCI library properties Building component property libraries Viewing Component PropertiesViewing Component PropertiesFixed properties Temperature dependent propertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesViewing Component PropertiesPredicting Component PropertiesPredicting Component PropertiesPredicting Component PropertiesPredicting Component PropertiesPredicting Component PropertiesPredicting Component PropertiesComponent Property LibrariesComponent Property LibrariesPure-component and mixture databanks Pure component databanks: Process (Default) SimSci (Contains DIPPR data when available) DIPPR OLI (Electrolytes) User (Created using Dataprep and/or LIBMGR) Default is BANK=PROCESS, SIMSCIComponent Property LibrariesComponent Property LibrariesMixture databanks NRTL/UNIQUAC Azeotrope UNIFAC Henry’s Law (includes priority pollutants) Alcohol (dehydration) User (created using LIBMGR)CONCLUSIONCONCLUSIONConclusionsConclusionsVery important to choose the correct thermodynamic method Even more important to insure that binary interaction parameters are availableConclusionsConclusionsAdvanced Equations of State Model hydrocarbon behavior Advanced Alpha forms Advanced mixing rules Databank of regressed binary interaction coefficientConclusionsConclusionsLiquid Activity Coefficient methods Model non-ideal behavior Databank of regressed binaries Databank of azeotropes Fill options for binariesConclusionsConclusionsGeneralized Correlation Typically designed for a specific application Do a good job for heavier hydrocarbonsConclusionsConclusionsEnthalpy, Entropy and Density Library correlation for enthalpy No Library correlation for entropy Library correlation for density Rackett parameters in LibraryClosingClosingHow can we improve this course Thank You for having us