Modeling the phase equilibria of asymmetric hydrocarbon mixtures using molecular simulation and equations of state

Monte Carlo simulation (MC) is combined with equations of state (EoS) to develop a methodology for the calculation of the vapor–liquid equilibrium (VLE) of multicomponent hydrocarbon mixtures with high asymmetry. MC simulations are used for the calculation of the VLE of binary methane mixtures with long n-alkanes, for a wide range of temperatures and pressures, to obtain sufficient VLE data for the consistent fitting of binary interaction parameters (BIPs) for the EoS. The Soave-Redlich-Kwong (SRK), Peng-Robinson (PR), and Perturbed Chain - Statistical Associating Fluid Theory (PC-SAFT) EoS are considered. The ability of each EoS to correlate the VLE data is assessed and the selected ones are used to predict the VLE of multicomponent gas condensate mixtures. MC simulations proved to be very accurate in predicting the VLE in all conditions and mixtures considered. The BIPs regressed from the simulation dataset lead to equally accurate modeling results for multicomponent mixtures, compared to those regressed from experimental data. © 2018 American Institute of Chemical Engineers AIChE J, 65: 792–803, 2019     

RG-CPA方程计算超临界CO2-醇体系汽液相平衡

综合考虑缔合作用和密度涨落的影响,将经重整化群修正的CPA方程（RG-CPA方程）扩展到二元体系汽液相平衡的计算。通过一个温度下的汽液相平衡数据回归得到二元交互作用参数,预测其他温度下的相平衡。采用这种方法计算了超临界CO₂与醇二元体系的汽液相平衡性质和临界曲线。结果表明,RG-CPA方程预测超临界CO₂与醇二元体系的气液相组成和密度具有较高的精度,液相组分平均绝对偏差为0.032,气相组分平均绝对偏差为0.019。与原始CPA方程相比,RG-CPA方程能更好地预测气液临界曲线。     

An electrolyte CPA equation of state for mixed solvent electrolytes

Despite great efforts over the past decades, thermodynamic modeling of electrolytes in mixed solvents is still a challenge today. The existing modeling frameworks based on activity coefficient models are data‐driven and require expert knowledge to be parameterized. It has been suggested that the predictive capabilities could be improved through the development of an electrolyte equation of state. In this work, the Cubic Plus Association (CPA) Equation of State is extended to handle mixtures containing electrolytes by including the electrostatic contributions from the Debye–Hückel and Born terms using a self‐consistent model for the static permittivity. A simple scheme for parameterization of salts with a limited number of parameters is proposed and model parameters for a range of salts are determined from experimental data of activity and osmotic coefficients as well as freezing point depression. Finally, the model is applied to predict VLE, LLE, and SLE in aqueous salt mixtures as well as in mixed solvents. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2933–2950, 2015     

多元渗透维里方程通式的表达：双水相系统的液液平衡计算

提出了基于三元系修正Ｐｉｔｚｅｒ模型的多元渗透维里方程通式，并应用于双水相系统液液平衡性质的关联和预测，用汽液平衡数据关联模型参数，预测了聚乙二醇／硫酸镁双水相系统的液液平衡；用汽液平衡数据和尽可能少的液液平衡数据关联模型参数。同时预测了焦点或不含电解质的ＰＥＧ／葡萄糖双水相系统的液液平衡和ＫＣｌ电解质在ＰＥＧ／ＤＥＸ系统中的分配系数。计算结果表明，模型有较好的预测功能。     

Phase equilibria (LLE and VLE) of refining operations for enzymatic biodiesel production via quantum mechanical COSMO‐RS method

Phase equilibria, both liquid–liquid equilibria (LLE) and vapor‐liquid equilibria (VLE), are equally important in the refining operations of biodiesel production. Equilibrium distributions of components at the down‐processing of enzymatic ethanolysis reaction were investigated through quantum mechanical COnductor‐like Screening MOdel‐Real Solvent method with implemented vapor pressure equations. Due to the composite nature of fatty acid ethyl ester (FAEE) components as the biodiesel fuel, multicomponent predictive phase equilibria approach was applied for a model reaction system of refined soybean oil with 30% molar excess amount of ethanol. Simulation results for the LLE at 303 K were in significant agreement with reported experimental data. Minimum boiling azeotropes were found for FAEE‐glycerol binaries at isothermal (at 423 and 473K) and isobaric (at reduced pressures) VLE simulations. Similar results were also found at the VLE of glycerol purification operations for multicomponent real case simulations. The feasibilities of simple and rigorous unit operations were also pointed up in this study. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

Representation of vapor–liquid and liquid–liquid equilibria for binary systems containing polymers: Applicability of an extended flory–huggins equation

For some binary systems, an extended Flory–Huggins equation is applicable to both vaporliquid equilibria (VLE) and liquid–liquid equilibria (LLE) using the same adjustable parameters. New LLE and VLE data are reported for polystyrene (PS) (MW = 100,000)/cyclohexane and for poly(ethylene glycol) (PEG) (MW = 8,000)/water. Experimental results for the PS/cyclohexane system agree well with the semiempirical model, whereas those for PEG/water do not, probably because, for PEG/water, the temperature range of the VLE data is about 55°C lower than that of the LLE data. Excellent fits were obtained for our previously published experimental results for PS/cyclohexane (upper critical solution temperature, UCST), PS/ethyl acetate (lower critical solution temperature, LCST), PS/tert-butyl acetate and PS/methyl acetate (both UCST and LCST), and PEG/water (closed-loop). The semiempirical model also fits well with new data obtained for the polymer blend PS/poly(vinyl methyl ether). © 1993 John Wiley & Sons, Inc.     

Understanding phase behaviors of multicomponent polymer mixtures based on a molecular thermodynamic framework combined with molecular simulation

A new molecular thermodynamic model based on a closed-packed lattice model is developed for multicomponent systems. Based on Monte-Carlo (MC) simulation results, we introduce new universal functions to consider the chain length dependence of polymers, and are able to obtain more accurate critical volume fraction results in liquid–liquid equilibrium (LLE) calculations. In associated blend systems, specific interactions are used to characterize strongly interacting polymer mixtures with a secondary lattice. To minimize the number of adjustable model parameters, chain length parameters are calculated in a conventional way using molecular weight and specific volume. Our proposed model successfully describes binary LLE for polymer-solvent systems. Furthermore, the model parameters obtained from these binary systems are directly used to predict corresponding LLE ternary systems, and the results were in good agreement with experimental data.     

基于黏滞球模型的CPA状态方程应用于醇胺系统相平衡的计算

考虑到醇胺及其混合物中分子间存在缔合作用的事实,结合立方型PR状态方程,通过引入基于黏滞球模型(SSM)发展起来的缔合流体的分子热力学模型,建立了一个新的CPA(cubic-plus-association)状态方程,即CPA-SSM,并将方程应用到醇胺系统相平衡的计算中。通过关联对比温度0.55～0.90范围下醇胺流体的实验饱和蒸气压和液相体积得到了8种醇胺流体的分子参数。结果表明,CPA-SSM方程可满意地计算出醇胺饱和蒸气压和液体密度,总平均误差分别只有0.57%和1.80%。对醇胺混合物,无论是恒压还是恒温系统,只需引入一个与温度无关的可调参数,CPA-SSM方程即可满意关联二元系统的汽液平衡数据,并可进一步预测多元混合物的汽液平衡。     

状态方程模拟醇胺系统的密度和汽液相平衡

通过考虑醇胺分子间的缔合作用,结合先前开发的非缔合变阱宽链流体状态方程(SWCF-VREOS)建立了一个缔合方阱链流体状态方程,并利用方程模拟了醇胺系统的密度和汽液相平衡。通过关联不同温度下醇胺的饱和蒸气压和液体体积得到了18种醇胺流体的分子参数,新方程计算的饱和蒸气压和液体密度总的平均误差分别为0.94%和0.88%。结合简单的混合规则,将此方程扩展到混合系统。研究发现,建立的方程可预测二元和三元醇胺混合物的密度。当引入一个与温度无关的可调参数时,方程能满意关联二元系统的汽液相平衡数据,并可进一步预测多元混合系统的汽液相平衡,预示着新方程可模拟醇胺系统的相行为。     

基于MPHC活度系数模型关联烃－水体系液－液平衡

基于普遍化范德华配分函数理论，应用由局部组成概念导出的方阱流体配位数模型导出了链状分子混合物的配位数模型，并由此建立了一个新的活度系数模型；将其应用于高度非理想体系汽－液平衡活度系数的关联，结果与Ｗｉｌｓｏｎ方程相当，但方程参数随温度变化较小；其于Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ－Ｇａｕｓｓ液－液平衡算法，应用新模型对烃－水体系的液－液平衡进行了关联计算，结果优于ＮＲＴＬ方程     

基于MPHC活度系数模型关联烃－水体系液－液平衡

基于普遍化范德华配分函数理论，应用由局部组成概念导出的方阱流体配位数模型导出了链状分子混合物的配位数模型，并由此建立了一个新的活度系数模型；将其应用于高度非理想体系汽－液平衡活度系数的关联，结果与Ｗｉｌｓｏｎ方程相当，但方程参数随温度变化较小；其于Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ－Ｇａｕｓｓ液－液平衡算法，应用新模型对烃－水体系的液－液平衡进行了关联计算，结果优于ＮＲＴＬ方程     

Description of the thermodynamic properties and fluid-phase behavior of aqueous solutions of linear,branched, and cyclic amines

The SAFT-γ Mie group-contribution equation of state is used to represent the fluid-phase behavior of aqueous solutions of a variety of linear, branched, and cyclic amines. New group interactions are developed in order to model the mixtures of interest, including the like and unlike interactions between alkyl primary, secondary, and tertiary amine groups (NH₂, NH, N), cyclic secondary and tertiary amine groups (cNH, cN), and cyclic methine-amine groups (cCHNH, cCHN) with water (H₂O). The group-interaction parameters are estimated from appropriate experimental thermodynamic data for pure amines and selected mixtures. By taking advantage of the group-contribution nature of the method, one can describe the fluid-phase behavior of mixtures of molecules comprising those groups over broad ranges of temperature, pressure, and composition. A number of aqueous solutions of amines are studied including linear, branched aliphatic, and cyclic amines. Liquid–liquid equilibria (LLE) bounded by lower critical solution temperatures (LCSTs) have been reported experimentally and are reproduced here with the SAFT-γ Mie approach. The main feature of the approach is the ability not only to represent accurately the experimental data employed in the parameter estimation, but also to predict the vapor–liquid, liquid–liquid, and vapor–liquid–liquid equilibria, and LCSTs with the same set of parameters. Pure compound and binary phase diagrams of diverse types of amines and their aqueous solutions are assessed in order to demonstrate the main features of the thermodynamic and fluid-phase behavior.     

Isobaric Vapor-Liquid-Liquid Equilibria for 1-Butanol + Water + 2,3-Butanediol at 101.3 kPa

Vapor-liquid-liquid equilibria (VLLE) data were determined for the ternary system 1-butanol + water + 2,3-butanediol at 101.3 kPa. A binary heterogeneous minimum boiling azeotrope was found at 365.95 K with mass fractions of 0.526 and 0.474 for 1-butanol and water, respectively. A modified UNIQUAC model was used to predict VLLE by using experimental data, including VLE of 1-butanol + 2,3-butanediol, VLE of water + 2,3-butanediol, LLE of 1-butanol + water, and one LLE tie-line of 1-butanol + water + 2,3-butanediol. The experimental data were compared with the calculated values. The absolute average relative deviations (AARD) are 1.65%, 1.72%, and 2.22% for organic liquid phase, aqueous liquid phase, and vapor phase, respectively. It demonstrates an appropriate fit of the modified UNIQUAC model.     

多元流体相平衡的统计回归及相互推算

本文应用普遍化最大似然原理及其他统计回归判据、由21套三元液液、汽液及汽液液平衡数据、分别求得三种局部组成模型(NRTL、FHW、UNIQUAC)的配偶参数并比较其拟合精度.结果证实、应用最大似然原理可以提高多元流体相平衡的关联与推算精度.其次由所得的配偶参数来探讨在液液、汽液及汽液液平衡之间进行相互推算的可靠性与局限性、从而阐明液液平衡与汽液平衡的差异与内在联系.     

含盐多元体系汽液相平衡数据测定及预测

对甲醇／乙醇/水／NH_4NO_3四元体系中的有关含盐二元汽液相平衡数据进行了测定及关联．提出用化学滴定──色谱分析联合法确定含盐液相组成．关联所得的最佳参数用于该体系三元及四元汽液相平衡数据的预测,并与实验值作了比较．结果表明,预测值与实验值符合良好．     

AN NEW GROUP-CONTRIBUTION EQUATION OF STATE AND ITS APPLICATION TO PHASE EQUILIBRIUM CALCULATIONS(Ⅲ)Application to Liquid-Liquid Equilibria

Based on the group interaction parameters determined from binary VLE data,the VDW-GC EOS developedin Part I~[13] is extended to binary and multicomponent liquid-liquid equilibrium calculations.Equilibrium phasecompositions and the temperature effects on LLE can be predicted with reasonable accuracy.     

Recovery of Formic Acid and Acetic Acid from Waste Water Using Reactive Distillation

Processing of biobased feedstock materials may lead to formation of multicomponent azeotropic mixtures. Reactive separations provide an opportunity to circumvent azeotropes by changing the substance properties through chemical reactions. Exemplarily several effluents from black liquor processing contain aqueous mixtures of low molecular weight fatty acids such as formic acid and acetic acid. These mixtures form inseparable azeotropes. Separation of the system formic acid–acetic acid–water by esterification with methanol was investigated. Reactive distillation experiments in batch and continuous mode confirmed complete removal of formic acid in a first step. Acetic acid may then be isolated by distillation or by reactive distillation.     

盐效分离作用理论预测

研究了盐效分离基本原理,采用选择性溶剂化模型,利用定标粒子理论计算盐在含水体系中的标准摩尔迁移自由能。提出了将迁移自由能与相平衡中盐效应的大小结合起来,用迁移自由能理论解释相平衡中的盐效应。文中计算了盐在6种含水体系的标准摩尔迁移自由能,并与其盐效应进行了对比,研究发现在含水体系中盐效应随盐的标准摩尔迁移自由能增大而增大,因此在盐效分离过程中可以采用标准摩尔迁移自由能模型选择有效的盐作分离剂。     

Effect of dissolved inorganic salts on the isothermal vapor–liquid equilibrium of the propionic acid–water mixture

Propionic acid–water is one of the minimum boiling point azeotropic binary mixtures. Alteration of the vapor–liquid equilibrium (VLE) by addition of inorganic salts is of interest, since it allows bypassing the azeotropic point due to salt-in and salt-out effects. The effect of NaCl, NH₄Cl, CaCl₂, and AlCl₃ at salt concentrations of 1 m and the effect of NaCl molality (0.5–3 m) on the VLE of the binary propionic acid–water mixture has been experimentally investigated at 60 °C using the headspace gas chromatography (HSGC) technique. The alteration in the VLE of the system was salt type and salt concentration dependent. Salting out of the propionic acid was observed when salts were added and was most obvious in the case of AlCl₃ salt. The salt effect parameter, determined from the Furter's equation was a function of the liquid concentration.