Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part I. Molecular thermodynamic framework

Consistent calculation of fugacities of fluid mixtures remains as one of the most important subjects in contemporary molecular thermodynamics. In practice, equations of state (EOSs) and g^E-models have been used. However, most EOSs are erroneous for condensed phases at high densities and g^E-models are inapplicable for pressuresensitive systems. Recently to remedy the shortcomings in both approaches, there has been a surge of new g^E-EOS mixing rules. By equating any set of EOS and g^E-models, the limitations in both approaches could be resolved significantly. However, the self-consistency in the underlying concept of those mixing rules remains controversial. During the last several years, the present authors proposed a new lattice-fluid EOS and its simplification relevant to phase equilibrium calculations. Without employing any g^E-EOS mixing rule and with only two parameters for a pure component and one adjustable interaction energy parameter for a binary mixture, results obtained to date demonstrated that the EOSs are quantitatively applicable to a great variety of phase equilibrium properties of mixtures, especially, for complex and/or macromolecular systems. In the present article we summarize the EOSs and extended the applications to liquid-liquid Equilibria. In part I, we discussed briefly the molecular thermodynamic aspects of general derivation of the EOS and a brief discussion of applying the EOSs to pure fluids while the illustrative application to various real mixture systems is discussed in part II.     

A multi-fluid nonrandom lattice fluid model: General derivation and application to pure fluids

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems is presented. The multi-fluid nonrandom lattice fluid (MF-NLF) model with the local composition concept was capable of describing properties for complex systems. However, the MF-NLF model has strong temperature dependence of energy parameters and segment numbers of pure systems; thus empirical correlations as functions of temperature were represented for reliable and convenient use in engineering practices. The MF-NLF model without temperature dependence of pure parameters could not predict thermodynamic properties accurately. It was found that the present model with three parameters describes quantitatively the vapor pressure and the saturated density for the pure fluid.     

A modified segment-based nonrandom two-liquid model for the calculation of vapor-liquid equilibrium of aqueous polymer-salt solutions

A new model for representation of the excess Gibbs energy of polymer-electrolyte solutions is proposed. The excess Gibbs energy of a polymer-electrolyte solution is expressed as a sum of contributions of a combinatorial, a long-range and a short-range excess Gibbs energy term. The Flory-Huggins expression and the Pitzer's extension of Debye-Hückel function are used, respectively, as a combinatorial and a long-range contribution to the excess Gibbs energy. A new expression based on the local composition concept, which is the modified nonrandom two-liquid (NRTL) model, is developed to account for the short-range contribution to the excess Gibbs energy. The model provides a versatile and flexible thermodynamic framework for both correlating and predicting the phase equilibrium of electrolyte solutions, polymer solutions and complex systems containing both electrolytes and polymers. The utility of the model is demonstrated with successful representation of vapor-liquid equilibrium of several PEG or PPG-salt-H₂O systems at different polymer molar masses. Results are compared with those obtained from the NRTL model.     

A multi-fluid nonrandom lattice fluid model: Mixtures

A multi-fluid nonrandom lattice fluid model with no temperature dependence of close packed volumes of a mer, segment numbers and energy parameters of pure systems and its consistent method for phase equilibrium calculation were presented in the previous paper. In this work, the model was extended to mixtures by using consistent method for phase equilibrium calculation with fugacity coefficients derived from the present equation of state and it was applied to vapor-liquid equilibrium. We consistently tested the present model on 17 phase equilibrium data sets of vapor-liquid equilibria and compared it with the MF-NLF model and the SAFT model. The present model (3 pure parameters for pure component and one binary interaction parameter) showed better results for most systems than the MF-NLF model (6 adjustable pure parameters and one binary interaction parameter) and the SAFT model (3 pure parameters and one binary interaction parameter).     

Unified equation of state based on the lattice fluid theory for phase equilibria of complex mixtures part II. Application to complex mixtures

In part I of the present article [Yoo et al., 1995], new rigorous and simplified lattice-fluid equations of state (EOS) were derived and their characteristic features of the molecular thermodynamic foundation were discussed by applying to pure fluids. In this part II, both EOSs were extended to various phase equilibrium properties of mixtures. Comparison of the models with experimental mixture data ranges from density, to equilibria of vaporliquid, vapor-solid and liquid-liquid phases for nonpolar/nonpolar, nonpolar/polar, polar/polar mixtures. Both models were also applied to supercritical fluid phase equilibria and activities of solvents in polymer solutions. With two temperature dependent parameters for pure compounds and one temperature-independent binary interaction energy parameter for a binary mixtures, results obtained to date illustrated that both EOSs are quantitatively applicable to versatile phase equilibria of mixtures over a wide range of temperatures, pressures and compositions.     

Nonrandom lattice fluid group contribution parameter for vapor-liquid equilibrium of esters and their mixtures

A group contribution version of the nonrandom lattice fluid equation of state (NLF-GC EOS) has been used to predict the vapor-liquid phase equilibria (VLE) of esters and their mixtures. The investigated esters were divided into groups according to the contribution scheme. Two different types of parameters were regressed from experimental datasets. Size parameters were fitted to pure component properties, and the group-group energy interaction parameters were simultaneously fitted to several binary mixture data sets. For systems containing propylene oxide, missing binary VLE data was predicted by using the COSMO-RS method. Parameters obtained by using the COSMO-RS method were later used to successfully predict experimentally measured binary propylene oxide+esters systems. The overall good prediction capability of the NLF-GC EOS could be proven for the investigated systems. This article is dedicated to Professor Chul Soo Lee in commemoration of his retirement from Department of Chemical and Biological Engineering of Korea University.