A MODEL FOR THE DISTRIBUTION OF ACID GASES BETWEEN AN AQUEOUS ALKANOLAMINE SOLUTION AND LPG

The model of Deshmukh and Mather (1981) is a popular method for correlating and predicting the vapor-liquid equilibria in systems containing acid gases (hydrogen sulfide and carbon dioxide) and aqueous solutions of alkanolamines. The model includes phase equilibrium between an aqueous liquid and a gas as well as chemical equilibrium in the aqueous phase. A recent review by Weiland et al. (1993) demonstrated the accuracy of the correlation. Presented here is a model based on that of Deshmukh and Mather (1981) for calculating the distribution of acid gases between two liquid phases - an aqueous phase and a non-aqueous liquid (typically a propane- or butane-rich liquid)

In the new model the phase equilibrium is modeled using a modified Henry's law approach. Fugacities of the components in the non-aqueous phase are calculated using the Peng and Robinson (1976a) equation of state. All of the parameters in the model are taken from the literature. Thus the model represents a prediction of the behavior. It is demonstrated that the predictions are in good agreement with the available experimental data     

基于无限稀释活度系数模型的状态方程

发展了一种从纯物质的性质参数预测混合物汽液平衡的方法,它是以立方状态方程的过量吉布斯自由能 g~E结合型混合规则和无限稀释活度系数 MOSCED模型为基础,由MOSCED模型预测得到活度系数方程的相互作用参数,从而得到混合规则中的g~E,使得状态方程能在较大温度和压力范围内预测汽液平衡.用此法预测了含极性组分体系常压到较高压力的汽液平衡,结果良好,与UNIFAC基团贡献状态方程的结果相当.     

Mutual solubility study for 94.2:5.8 of ethanol to octane with supercritical carbon dioxide solvent

Solubility data of a mixture containing 94.2% ethanol and 5.8% octane was measured in carbon dioxide solvent using a high-pressure type phase equilibrium apparatus at pressures up to 103.5 bar and at temperature of 75 °C. The results showed that considerable separation was not achieved in this ethanol and octane ratio. However, the experimental data were then compared with the theoretical data which were obtained from two models which are regular solution theory and Redlich-Kwong equation of state. Regular solution theory is employed to each phase by applying activity coefficient expressions. Redlich-Kwong equation of state is employed to the vapor phase and then with applying fugacity coefficient, liquid phase data is obtained. The regular solution theory as a novel model approach has been found to be encouraging for the prediction of phase equilibria solubilities. It concluded that the regular solution theory model could predict two phases equilibrium data better than Redlich-Kwong equation of state.     

Multiphase equilibria calculation by direct minimization of Gibbs free energy with a global optimization method

This paper presents a new method for multiphase equilibria calculation by direct minimization of the Gibbs free energy of multicomponent systems. The methods for multiphase equilibria calculation based on the equality of chemical potentials cannot guarantee the convergence to the correct solution since the problem is non-convex (with several local minima), and they can find only one for a given initial guess. The global optimization methods currently available are generally very expensive. A global optimization method called Tunneling, able to escape from local minima and saddle points is used here, and has shown to be able to find efficiently the global solution for all the hypothetical and real problems tested. The Tunneling method has two phases. In phase one, a local bounded optimization method is used to minimize the objective function. In phase two (tunnelization), either global optimality is ascertained, or a feasible initial estimate for a new minimization is generated. For the minimization step, a limited-memory quasi-Newton method is used. The calculation of multiphase equilibria is organized in a stepwise manner, combining phase stability analysis by minimization of the tangent plane distance function with phase splitting calculations. The problems addressed here are the vapor–liquid and liquid–liquid two-phase equilibria, three-phase vapor–liquid–liquid equilibria, and three-phase vapor–liquid–solid equilibria, for a variety of representative systems. The examples show the robustness of the proposed method even in the most difficult situations. The Tunneling method is found to be more efficient than other global optimization methods. The results showed the efficiency and reliability of the novel method for solving the multiphase equilibria and the global stability problems. Although we have used here a cubic equation of state model for Gibbs free energy, any other approach can be used, as the method is model independent.     

Phase equilibria of associating fluid mixtures using the perturbed-hard-sphere-chain equation of state combined with the association model

For developing the equation of state which can be applicable to associating fluids, the Perturbed-Hard-Sphere-Chain-Association (PHSC-AS) equation of state is proposed by incorporating the association term of the SAFT model into the PHSC equation of state which has been widely used to describe phase equilibria for the fluid system containing a large molecule such as polymer. In this work, two different types of PHSC models have been examined. One is the original model proposed by Song et al., and the other is the modified model by Kim and Bae whose chain term was replaced with that of the SAFT model. As a result, two types of PHSC-AS models are obtained, and applied to the calculation of phase equilibria for the binary system containing a self-associating compound such as alcohol, amine and carboxylic acid, etc. The calculated results of vapour-liquid equilibria are in good agreement with the experimental data. The proposed models (PHSC-AS) are also compared to the PC-SAFT model.     

A new semiempirical equation of state for fluids—III Application to phase equilibria in binary mixtures

The equation of state derived in a previous publication [1] is used to correlate vapour-liquid, liquid-liquid, and gas-gas equilibria in binary mixtures. Special mixing rules for the parameters of the equation of state are derived from a quasichemical lattice model. It is possible to describe phase equilibria at very high pressures (beyond 1000 bar) with reasonable accuracy. The unlike interaction potential parameters, which are used as adjustable data to obtain a good fit, have physically reasonable values.     

Vapor-liquid equilibrium correlations for systems containing amines using a lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of vapor-liquid equilibria (VLE) for binary amine and hydrocarbon mixture at various temperatures. For these mixtures, the consideration of hydrogen bondings in the lattice equation of state clearly improves the prediction for VLE. The amines were divided into four groups due to the different strength of the hydrogen bonding. For all groups, different hydrogen bonding parameters were obtained and evaluated. The effects of varying hydrogen bonding energies for NLF-HB EOS are discussed. For systems containing lower amines, the NLF-HB EOS showed excellent agreement with the experimental data. For the correlation of systems containing tertiary amine molecules, binary interaction parameter had to be involved instead of hydrogen bonding parameters.     

Thermodynamic studies related to emulsion polymerization

Liquid–liquid and vapor–liquid phase equilibria for the binary, ternary, and quaternary systems of vinyl acetate, surfactant, water, and poly(vinyl acetate) (PVAc) were obtained using liquid–liquid equilibria, inverse gas chromatography, and the headspace methods. The Flory–Huggins interaction parameters for the different species in the emulsion polymerization of PVAc latices are reported. These parameters could not be used to predict the phase equilibria because of their strong dependence on concentration. The UNIFAC‐vdW‐FV model was applied to predict the vapor–liquid equilibria in the binary and ternary systems containing vinyl acetate, 4‐nonylphenol polyethoxilate surfactant, and PVAc. The predicted results compare favorably with the experimental data for all systems. Diffusion coefficients were also measured for the solvents in the PVAc. Analysis confirmed that the diffusion in the latex particles was so fast compared to the reaction that the assumption of uniform monomer composition through the particles was valid. On the other hand, the results indicate that the complex thermodynamic interactions will lead to changes with time in the monomer concentration in the reacting polymer phase. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci 2007     

On the predictive capabilities of CPA for applications in the chemical industry: Multicomponent mixtures containing methyl-methacrylate,dimethyl-ether or acetic acid

The predictive performance of the CPA (Cubic-Plus-Association) equation of state for applications relevant to the chemical industry is illustrated in this work. Three such applications inspired by industrial requests/interest are illustrated here, all of which involve aqueous multicomponent mixtures exhibiting vapor–liquid (VLE) and/or liquid–liquid (LLE) equilibrium. The first two cases include mixtures of methyl-methacrylate with acetone or methanol and dimethyl-ether with ethanol, respectively. In these two cases, the classical form of CPA is used. The third case involves aqueous mixtures with acetic acid, esters, ethers and alcohols, and in this case for water–acetic acid the CPA-Huron Vidal (CPA-HV) version of the model is used. For the latter binary mixture, new CPA-HV binary parameter sets are estimated using, among others, data for activity coefficients at infinite dilutions. The modeling approach is similar in all three cases, i.e. the binary parameters are solely fitted to binary data and thus all multicomponent calculations are considered predictions.It is shown that CPA correlations for binary systems are excellent in all cases using temperature independent parameters except for the acetic acid–water system for which different parameter sets at different temperatures can be recommended. Even with the use of CPA-HV mixing rules, modeling of the acetic acid–water system with few interaction parameters remains a challenging task. Excellent simultaneous VLE and LLE correlation is obtained for complex systems such as aqueous mixtures with ethers and esters. The multicomponent results are, with a few exceptions, very satisfactory, especially for the vapor–liquid equilibrium cases. For the demanding aqueous acetic acid–water containing systems, one parameter set is recommended at the end for modeling ternary or multicomponent mixtures containing acetic acid and water.     

Application of cubic equation of state models in prediction of vapor–liquid equilibria for binary polyvinyl acetate/solvent solutions

The cubic equation of state (CEoS) is a powerful method for calculation of (vapor + liquid) equilibrium (VLE) in polymer solutions. Using CEoS for both the vapor and liquid phases allows one to calculate the non‐ideality of polymer solutions based on a single EoS approach. In this research, vapor–liquid equilibria calculations of polyvinyl acetate (PVAc)/solvent solutions were performed. In this approach, eight models containing PRSV and SRK CEoS separately combined with four mixing rules namely vdW1, vdW2, Wong–Sandler (WS), and Zhong–Masuoka (ZM) were applied to calculations of bubble point pressure. For the better prediction, the adjustable binary interaction parameters existing in any mixing rule were optimized. The results were very acceptable and satisfactory. Absolute average deviations (%AAD) between predicted results and experimental bubble point pressure data were calculated and presented. The capability of two cubic equations of state had a good agreement with experimental data and predict the correct type of phase behavior in all cases, but the performance of the PRSV + vdW2 was more reliable than the other models with 2.65% in AAD for total of solution systems. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014 , 131, 40651.     

Phase equilibria of mixtures containing CO2 and organic acids using the UMR-PRU model

The UMR-PRU model, which has been successfully tested in the past to the predictions of different type of phase equilibrium and thermodynamic properties in binary and multicomponent systems, is applied in this work to phase equilibria in mixtures containing CO₂ and organic acids. New interaction parameters are determined by fitting only binary vapor–liquid equilibrium data and then they are used to predict the vapor–liquid, solid–gas and solid–liquid–gas equilibria in CO₂/organic acid systems. Furthermore, the UMR-PRU model with the newly derived interaction parameters is applied to the prediction of the phase equilibrium in ternary mixtures consisting of CO₂, organic acids and water. Satisfactory results are obtained in all cases.     

Prediction of liquid–liquid equilibrium from the Peng–Robinson+COSMOSAC equation of state

An approach combining the Peng–Robinson equation of state and novel solvation free energy calculation is developed here to describe the liquid–liquid equilibria for highly nonideal mixtures. This method has been previously shown to provide reliable vapor–liquid equilibria of pure and mixture fluids. The hydrogen-bonding interaction in this model is refined in order to properly describe the variation in the strength of hydrogen bond between different types of species. This method contains only 15 global parameters and 3 element-specific parameters (one atomic radius and two for the dispersion energy), and can be used to predict the miscibility gap of liquid mixtures and its temperature variations without sacrificing its capability in predicting vapor–liquid equilibria. The overall root-mean-square error in the mutual solubility of 68 binary mixtures predicted from PR+COSMOSAC is 0.0689, compared to those from the Modified UNIFAC 0.0822 and UNIFAC-LLE 0.0697, respectively.     

超临界二氧化碳和醇类体系的相平衡计算

应用Peng-Robinson(P-R)状态方程对超临界CO2系统进行了相平衡模拟。对超临界CO2和醇类二元系统进行了汽液相平衡计算,结果表明,P-R状态方程模拟高压下CO2系统的相平衡具有较高的精度。     

含醇系统的汽液平衡的缔合模型

本文将无限线性缔合模型和ＲＫ方程式相结合建立了含醇系统的热力学模型，对含醇系统进行了相平衡计算。结果表明：对于纯物质，本模型在广阔的温度、压力范围内能描述ＰＶＴ关系；对于醇－醇系统和醇－烃系统，该模型仅需要一个物理作用参数就能获得与活度系数法大致相当的结果。     

Molecular thermodynamics for fluid-phase equilibria in aqueous two-protein systems

With saline water as the continuous medium, a two-component McMillan-Mayer equation of state is used to describe liquid–liquid phase equilibria in a two-protein system. The equation of state is based on a hard-sphere reference with perturbations introduced through a potential of mean force to account for electrostatic forces and for attraction between protein particles. To illustrate the thermodynamic framework, one parameter each is fitted to experimental precipitation data for aqueous saline one-protein systems containing either lysozyme or ovalbumin. A lysozyme–ovalbumin interaction parameter is then introduced to calculate phase behavior in the aqueous two-protein system. These calculations are remarkably similar to classic vapor–liquid equilibrium calculations using an equation of state. For the aqueous two-protein system, calculations give the light-phase composition as well as the lysozyme and ovalbumin partition coefficients for a given dense-phase composition. Agreement with sparse experimental data is reasonable over a range of pH and high ionic strength provided by the common precipitant ammonium sulfate.     

Liquid–liquid equilibrium correlations using lattice fluid equation of state with hydrogen bonding

The nonrandom lattice equation of state with hydrogen bonding (NLF-HB EOS) was examined for the correlation of liquid–liquid equilibria (LLE) for binary alcohol and hydrocarbon mixture in a wide pressure range. For hydrocarbon + alcohol mixtures the consideration of a hydrogen-bonding term in the lattice equation of state clearly improves the prediction for vapor–liquid equilibrium (VLE) as shown in previous works, but the prediction of LLE is still in question. In this paper, LLE data for alcohols (methanol and ethanol) + hydrocarbons (n-hexane to n-hexadecane) were correlated by NLF-HB EOS and results were compared with a cubic equation of state (Peng–Robinson EOS with the T–K Wilson based G^E model). Both equations of state showed similar degree of accuracies but with different number of adjustable parameters. The Peng–Robinson EOS based approach requires six temperature dependent coefficients for accurate calculation whereas NLF-HB EOS requires only two temperature dependent coefficients. The effects of varying hydrogen-bonding energies for NLF-HB EOS are discussed.     

CO_2在MDEA-MEA-H_2O混合溶剂中的溶解度关联和预测

通过简化Clegg-Pitzer方程无需增添调节参数,将甲基二乙醇胺（MDEA）-水、一乙醇胺（MEA）-水二元体系,CO_2-MDEA-H_2O、CO_2-MEA-H_2O三元体系气液平衡数据回归得到的相互作用参数用于预测CO_2-MDEA-MEA-H_2O四元体系的气液平衡数据。所预测四元体系中含有3种中性溶剂（MDEA、MEA和水）和4种离子（MDEAH~+、MEAH~+、HCO_3~-和RNHCOO_-）,并同时考虑了4个化学反应。     

Peng-Robinson状态方程及保形溶液混合规则用于汽-液平衡计算

Peng-Robinson状态方程式用于推算三组二元系统的汽-液平衡:甲烷、二氧化碳及氢与烃类.对含甲烷及二氧化碳的二元系统.推荐了经过关联的相互作用参数.将保形溶液(Conformal Solu-tion)混合规则及本文提出的对温度有关的系数α的修正式应用于高度非对称的含氢二元系统,较Peng-Robinson的原始工作更为精确地表述了汽-液平衡.