Predicting the thermodynamic properties and dielectric behavior of electrolyte solutions using the SAFT‐VR+DE equation of state

We extend the SAFT‐VR+DE equation of state to describe 19 aqueous electrolyte solutions with both a fully dissociated and a partially dissociated model. The approach is found to predict thermodynamic properties such as the osmotic coefficient, water activity coefficient, and solution density, across different salt concentrations at room temperature and pressure in good agreement with experiment using only one or two fitted parameters. At higher temperatures and pressures, without any additional fitting, the theory is found to be in qualitative agreement with experimental mean ionic activities and osmotic coefficients. The behavior of the dielectric constant as a function of salt concentration is also reported for the first time using a statistical associating fluid theory (SAFT)‐based equation of state. At high salt concentrations, the stronger electrostatic interactions between the ionic species due to the dielectric decrement, is captured through the inclusion of ion association. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3053–3072, 2015     

Study of solubility and swelling ratio in polymer‐CO2 systems using the PC‐SAFT equation of state

We use the PC‐SAFT equation of state to model the solubility of CO₂ in various homopolymers. We also model the swelling ratio of the PP (polypropylene)‐CO₂ mixture using PC‐SAFT and then compare the results with Sanchez‐Lacombe (S‐L) and Simha‐Somcynsky (S‐S) equations. The results show that PC‐SAFT can describe the solubility of CO₂ in polymers very well. We compare two sets of parameters in the PC‐SAFT equation, Gross et al.'s and Chen et al.'s. As for the swelling ratio, PC‐SAFT using Chen et al. parameters is better than S‐L equation, which is commonly used by early researchers in studying the solubility of CO₂ in polymers. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44804.     

An isomorphic Peng-Robinson equation for phase-equilibria properties of hydrocarbon mixtures in the critical region

The principle of isomorphism of critical phenomena asserts that the equation of state of fluid mixtures in the critical region has the same form as that of the pure components, provided that the mixture is not considered at a fixed composition but at a fixed value of a constant field variable related to the chemical potentials of the components of the mixtures. This principle has been successfully applied by various investigators to formulate nonclassical equations of state for fluid mixtures in the critical region. In this paper we show how the same principle can be applied to simple classical equations of state using the Peng-Robinson equation as a representative example. The isomorphic Peng-Robinson equation thus obtained is applied to represent phase equilibria properties of some binary mixtures of methane, butane and decane.     

Predicting phase behavior in aqueous systems without fitting binary parameters II: Gases and non‐aromatic hydrocarbons

This investigation continues a series of studies evaluating the capability of the recently proposed CP‐PC‐SAFT and sPC‐SAFT of Liang et al. to estimate the thermodynamic properties of aqueous systems in the entirely predictive manner. Similarly to the previously considered systems, CP‐PC‐SAFT remains a realistic estimator of the available data on critical loci, high pressure‐high temperature phase equilibria and volumetric properties also in the cases of non‐polar gases and non‐aromatic hydrocarbons from argon and nitrogen till n‐eicosane and squalene while keeping zero values of binary parameters. Nevertheless, such application of the model poses certain unavoidable compromises on its accuracy. Inter alia, CP‐PC‐SAFT is a particularly inaccurate estimator of the water‐rich liquid phases away from the critical points. sPC‐SAFT predicts these data in a more reliable manner. Moreover, its predictive capability goes beyond the liquid phases and it exhibits a remarkable accuracy in forecasting various phase equilibria below the critical point of water. © 2017 American Institute of Chemical Engineers AIChE J, 2017     

An analytical equation of state for water and alkanols

An analytical equation of state extended from statistical associating fluid theory (SAFT) is modified to describe the thermodynamic properties of fluids with high polarity such as water and alkanols up to the region close to the critical point. Five terms are used in the equation of state: the term for hard convex body, the term for dispersion energy, the term for the chain formation of hard convex body, the term for the change of the dispersion energy because of chain formation, and the term for dipole-dipole interaction. This equation of state is still called SAFT-CP (across critical points). Six fluids water, methanol, ethanol, 1-propanol, 1-butanol and 1-pentanol are used as examples. The new equation of state reproduces saturated pressures and densities in vapor-liquid equilibrium, critical properties (as temperature, pressure and density), and densities in the one-phase region with rational accuracies. The comparison of the calculated critical exponent β with the experimental one for methanol shows the improvement up to the region only with 20 K difference of temperature to the critical point. The result coincides with the estimation of the critical region on the basis of Ginzburg number and also with the available opinion that crossover methods and renormalization theories are necessary in the near-critical region.     

超临界流体p-V-T方程的研究

木文对目前常用的RK、RKS、PR及CS-vdW等状态方程进行了考察,验算了它们对二氧化碳、乙烯、丙烷等十种体系在超临界区、特别在临界点附近区域的适用性.计算结果表明,在上述区域内计算偏差都较大.作者从统计热力学的角度提出了一个“m-RKS”方程:P=RT/(V-b(T))—a(T)/V[V+b(T)],用该方程进行计算,结果与文献报道的实测值之间的偏差大大低于上述常用的诸方程.     

含临界点的统计缔合流体理论研究(Ⅰ)非极性流体

从适合于临界点的计算出发 ,对统计缔合流体理论方程进行改进 :(1)对链状分子的每个链节考虑其非球形度 ;(2 )提出必须考虑链节成链时对色散作用的影响 .建立了扩展的统计缔合流体理论状态方程 ,对于正构烷烃和异构烷烃的计算表明 ,该方程计算温度范围大 ,从低温区到临界区 ,特别是在临界点附近精度有明显提高 ,临界点的计算值和实验值基本符合 .扩展了理论状态方程的适用性 ,可望用于各种含临界区域流体体系的热力学计算     

Modeling the phase behavior in binary mixtures involving blowing agents and thermoplastic resins

The thermophysical properties of mixtures of thermoplastic resins and blowing agents, together with the knowledge of the solubilities of these components, are the basis for the manufacturing of plastic foams. In this work, the solubilities of blowing agents trichlorofluoromethane, dichlorodifluoromethane, chlorodifluoromehane, and 1,2‐dichloro‐1,1,2,2‐tetrafluoroethane in thermoplastic resins poly(styrene), high density poly(ethylene), low density poly(ethylene), poly(propylene), poly(vinyl chloride), poly(carbonate) and poly(propylene oxide) were modeled by using the Perturbed Chain‐Statistical Associating Fluid Theory (PC‐SAFT) and the Sánchez‐Lacombe equations of state (EoS), fitting a single temperature‐dependent binary interaction parameter. PC‐SAFT is a theoretically based equation of state with three pure component parameters that describe efficiently the thermodynamics of complex systems. Earlier works with this EoS have already predicted the phase coexistence properties of various refrigerants and higher order alkane series compounds, along with their mixtures. The pure component parameters for the blowing agents were obtained by regression of vapor pressure and liquid density data, while the pure component parameters for the thermoplastic resins were obtained by regression of pure liquid PVT data. The parameter estimation was performed by using a modified maximum likelihood method. The solubility results obtained with both EoS have been compared; the results from PC‐SAFT showed a higher accuracy in terms of solubility pressure deviations. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

Prediction of Solubility of Cholesterol in Supercritical Solvents

In this study the solubility of cholesterol was calculated in two supercritical pure solvents (carbon dioxide and ethane) as binary systems, and four supercritical solvent/co-solvent systems as ternary systems (cholesterol/carbon dioxide/methanol, cholesterol/ethane/acetone, cholesterol/ethane/hexane, cholesterol/ethane/propane) in various temperatures by SRK, PR, and SAFT equations of state. Pure molecular parameters of SAFT equation of state were obtained by fitting vapor pressure and liquid density data. Also the molecular parameters of cholesterol were obtained by fitting the solubility data of binary systems in one temperature, then they were used for the same system in other temperatures and for ternary systems with the same solvent. Results show that the SAFT equation of state can predict the trend and amount solubility of cholesterol in supercritical solvents much better than the other equations of state.     

用微扰理论、平均球近似结合统计缔合流体理论建立纯流体的状态方程

分别采用微扰理论和平均球近似（MSA）处理实际流体偶极──偶极间的相互作用,结合统计缔合流体理论（SAFT）处理氢键缔合相互作用,建立了一个纯缔合流体的状态方程．用分子链节微观参数分别关联了37种纯缔合流体（水、醇、酸和胺）的饱和液相密度和饱和蒸汽压．结果表明：采用微扰理论处理偶极──偶极相互作用的关联结果明显优于平均球近似,与分子模拟数据比较,结论一致．     

Teaching advanced equations of state in applied thermodynamics courses using open source programs

Many advanced equations of state have been developed in the last decades which fulfill important needs of the industry. However, these equations frequently are not taught in applied thermodynamic courses, in part due to the lack of educational resources for including application exercises. This article presents a set of computer programs for the calculation of phase equilibrium and other thermodynamic properties using different equations of state (classical cubic equations, cubic equations with excess Gibbs energy mixing rules, group contribution equations and SAFT equations). All the programs are open-source and allow for different learning approaches, from application exercises with these equations, to correlation of equation parameters or implementation of modified equations and calculation algorithms for more advanced courses. The programs run in the commercial computing software MATLAB as well as in the free, open-source program Octave. The programs have been designed to be easily reusable using an object-oriented programming methodology, and they may have some applications in research. Authors also present their experiences in the application of the programs in applied thermodynamic courses at a Master‘s level.     

Application of the functional renormalization group method to classical free energy models

A simple functional renormalization group method is presented to correct the behavior of classical free energy models near the critical point. This approach is applied to the Soave–Redlich–Kwong equation of state to illustrate its ability to better reproduce the phase behavior of simple fluids and to understand the influence of its parameters on the shape of the vapor‐liquid phase diagram. The method is then extended to account for the correlations induced by intramolecular bonds. It is then applied to a first‐order thermodynamic perturbation theory for chain fluids to examine fluids composed of linearly bonded Lennard‐Jones atoms. Unlike previous approaches for applying renormalization group corrections to chain fluids, this is able to accurately reproduce the critical point without predicting an overly flat liquid‐vapor coexistence region. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2985–2992, 2015     

A crossover‐UNIQUAC model for critical and noncritical LLE calculations

A new model, named the crossover‐UNIQUAC model, has been proposed based on the crossover procedure for predicting constant‐pressure liquid–liquid equilibria (LLE). In this manner, critical fluctuations were incorporated into the classical UNIQUAC equation. Coexistence curves were estimated for systems having a diverse range of asymmetries. These systems included the LLE of five different mixtures, composed of nitrobenzene with one of the members of the alkane homologous family (either pentane, octane, decane, dodecane, or tetradecane), as well as an extra system having a different chemical nature, namely the mixture of n‐perfluorohexane and hexane, to further check the validity of the proposed approach. Using these nonideal mixtures, the validity of the new model was investigated within wide ranges, covering near‐critical to regions falling far away from the critical point. The graphical trends, as well as the quantitative comparison with experimental data indicated the good agreement of the proposed model results with the experimental data. A maximum AARD% value of 3.97% was obtained in calculating molar compositions by the proposed model for such challenging systems covering noncritical, as well as critical regions. In addition, to show the strength of the proposed crossover approach to describe properties other than LLE, molar heat capacities were investigated for the system of nitrobenzene + dodecane. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3094–3103, 2015     

Estimation of thermodiffusion coefficients in ternary associating mixtures

Following the non‐equilibrium thermodynamics formulation and taking into account the complexities in the structure of aqueous associating mixtures, expressions are proposed to estimate the thermodiffusion coefficients in ternary associating mixtures, such as water and alcohol mixtures. The model expressions are used to estimate the thermodiffusion coefficients in methanol–ethanol–water, dimethyl sulfoxide (DMSO)–ethanol–water and DMSO–t‐butanol–water mixtures at various concentrations. The perturbed‐chain statistical associating fluid theory (PC‐SAFT) equation of state is used to obtain the mixture properties, such as the derivatives of the chemical potentials needed to evaluate the thermodiffusion coefficient expressions. The results show that at certain concentrations of one component, variation of the concentration of the other two components can cause a sign change in the thermodiffusion coefficients. While the model cannot be evaluated due to the lack of any pertinent experimental data, the model predictions may be used to choose suitable mixture compositions in space experiments to be performed onboard the International Space Station (ISS) in near future. © 2011 Canadian Society for Chemical Engineering     

Application of the kirkwoodbuff solution formalism and the hard sphere expansion method with the modified mean density approximation to predict solubility of solutes in supercritical fluids

The Kirkwood-Buff solution theory to give the relations between macroscopic thermodynamic properties and the fluctuation integrals (G_ij) was utilized to predict solubility of solutes in supercritical fluids. The solvent-solute fluctuation integral (G₂₁) in the derivation for solubility of solute is expressed in terms of the solvent-solvent fluctuation integral (G₁₁) using the hard sphere expansion (HSE) conformal solution method with the modified mean density approximation (MMDA) where the scaling factor (R₁₂) represents the ratio of the first peak heights of the radial distribution functions for the mixture and the reference fluid having the mean density determined from the mean density approximation (MDA). The values of R₁₂ were evaluated by considering it as an adjustable parameter and solving the Ornstein-Zernike equation with the hypernetted chain (HNC) closure, and were compared. It is shown that solubility can be evaluated with an equation of state for pure supercritical fluid, three molecular parameters, and the scaling factor (R₁₂) without knowledge of critical properties of solutes, which can not be measured precisely for some organic solids. This model based on the molecular theory leads to better results in solubility calculations than both the Peng-Robinson equation of state with the classical mixing rule and the previous method with the original MDA instead of the MMDA. It might be due to the superiority of the MMDA over the original MDA.     

Solvent effects on esterification equilibria

Solvents are known to have strong impacts on the yields of equilibrium reactions. This work focuses on the thermodynamic investigation of these solvent effects on esterification reactions of acetic acid and propionic acid with ethanol. Esterification of acetic acid was performed in the solvents acetone, acetonitrile (ACN), dimethylformamide (DMF), and tetrahydrofurane as well as in mixtures thereof. ACN promotes the esterification of acetic acid, whereas it is strongly suppressed by DMF. The esterification of propionic acid was investigated with various reactant concentrations in acetone. The experimental equilibrium data in pure solvents and solvent mixtures were modeled using the thermodynamic equilibrium constant K_a and the reactant/product activity coefficients predicted by the perturbed chain‐statistical associating fluid theory (PC‐SAFT). For a given K_a, PC‐SAFT is able to predict the influence of the solvent and even solvent mixtures on the equilibrium concentrations of esterification in almost quantitative agreement with the experimental data. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3000–3011, 2015     

A NEW EQUATION OF STATE (HSFT) BASED ON FRACTAL THEORY

This paper describes the molecular distribution of fluids by some fractal characteristics based on the current understandings of microstructures in fluids. The coordination relation was derived according to this fractal model, and the molecular mean potential function for simple square-well fluids was proposed. By applying this new mean potential function, a new equation of state (EOS) named HSFT was derived from statistical mechanics. Vapor pressures and saturated liquid densities of about 200 pure substances were correlated by the proposed model. Resulting equation parameters were further generalized by acentric factor ω and critical compressibility factor Zc. Saturated properties for 180 substances and enthalpies of vaporization for 115 substances, including compounds with strong polarity, were calculated by the generalized HSFT equation. Compared with several other equations of state, satisfactory results computed by HSFT equation imply that the generalized HSFT equation possesses better adaptability and reliability.