vdW Mixing Rules Research Articles

Equations of state using an extended Twu-Coon mixing rule incorporating UNIFAC for high temperature and high pressure phase equilibrium predictions

A mixing rule recently developed by Twu and Coon [C.H. Twu, J.E. Coon, CEOS/AE mixing rules constrained by the vdw mixing rule and the second virial coefficient, AIChE J. 42 (1996) 3212–3222 is extended to incorporate the UNIFAC group contribution method into an equation of state for the prediction of phase behavior of highly non-ideal systems over wide ranges of temperature and pressure. The mixing rule developed by Twu and Coon reduces to the van der Waals mixing rule. The Helmholtz excess free energy function with respect to a van der Waals fluid at infinite pressure has been related rigorously to the Helmholtz excess free energy at zero pressure. This extension of the Twu-Coon Mixing Rule goes gracefully from the classical van der Waals one-fluid mixing rule for non-polar fluids needed in the refining and gas processing industries to a mixing rule combining excess free energy models at low pressure with equations of state for the strongly polar systems found in the chemical industries. When the UNIFAC group contribution method is incorporated, the mixing rule becomes totally predictive. The completely predictive equation of state is shown to give accurate results for systems for which the UNIFAC model is in agreement with the experimental activity coefficients at low pressure. The UNIFAC-incorporated mixing rule provides a simple way to extend the UNIFAC group contribution method to high temperatures and pressures.

CEOS/AE mixing rules constrained by vdW mixing rule and second virial coefficient

AbstractA new class of mixing rules, with van der Waals one‐fluid mixing rule and second virial coefficient constraints, was developed for cubic equations of state (EOS) for application to various asymmetric, highly nonideal chemical systems. This approach evolved from previous research in the EOS field. The resulting mixing rule is practical in application, yet more flexible than Huron–Vidal or Wong–Sandler mixing rules and depends only on composition and temperature. It also avoids the problems associated with the Wong–Sandler mixing rules. A cubic EOS with the new mixing rules was applied successfully to complex mixtures. The new rules reduce to van der Waals mixing rules when the parameters in the nonrandom excess Helmholtz free energy are set to zero. Since many times the classic mixing rules worked very well for nonpolar systems, it is extremely desirable that the composition‐dependent mixing rules reduce to the classic mixing rules. Preserving this capability also ensures that the binary interaction parameters for the classic quadratic mixing rules in the DECHEMA Chemistry Data Series for mixtures of low boiling substances and other existing databases for systems involving hydrocarbons and gases can be used directly in the new EOS mixing rules, in addition to liquid‐activity coefficient model parameters currently reported in the Series.

On the VDW1 mixing rules applied to conformal binary mixtures at infinite dilution

Henry's constant (HC) for a binary mixture, infinitely dilute in one of the components, is modelled according to the one-fluid conformal solution theory. This theory expresses linearly in closed form the HC in terms of certain thermodynamic properties of the pure solvent component, with coefficients that require knowledge of appropriate mixing rules for their evaluation. The VDW1 mixing rules produce good agreement with simulation data for many mixtures as characterized by size and well-depth ratios of the components; however, the agreement is poor for small values of these ratios. In this paper, a self-consistent approach to improving the performance of the VDW1 rules is presented and illustrated. Comparison with simulation data shows some improvement over the VDW1 rules in the exceptional regions, but some deterioration for large size ratios. One interesting by-product of this exercise is the discovery of an expression for the crosssection virial coefficient in terms of the corresponding pure component ...

On the vdW1 mixing rules: Simple modifications leading to more exact forms

On the vdW1 mixing rules: Simple modifications leading to more exact forms

High pressure phase behavior in systems containing CO 2 and heavier compounds with similar vapor pressures

The separation of the para and ortho isomers of xylene as well as the azeotropic mixture of butyl ether/o-xylene using carbon dioxide at high pressure was investigated. The phase behavior of carbon dioxide and each of these compounds along with the ternary systems; CO 2/p-xylene/o-xylene and CO 2/butyl ether/o-xylene were experimentally determined. The relative volatilities of p-xylene to o-xylene in the CO 2/p-xylene/o-xylene system compared favorably with those obtained in distillation. The results also indicated a substantial shift in the butyl ether/o-xylene azeotrope to higher butyl ether concentrations in the presence of carbon dioxide thus indicating a potential for the separation of these mixtures using carbon dioxide at low temperatures. Thermodynamic models using the Peng—Robinson equation of state were developed and better predictions of the bubble point pressures were obtained when the interaction parameter, δ ij , was allowed to vary with phase density. This approach results in an analytically solvable quartic equation in volume and gives different δ ij 's for the vapor and liquid phases. In this model, the temperature dependence of the binary interaction parameter is contained within its density dependence and, δ ij 's obtained from fitting VLE data at a single temperature could be used for accurate prediction of equilibrium data at other temperatures. The results of such predictions were better than predictions obtained by fitting the actual data using the conventional VDW-1 mixing rules.

Simultaneous calculations of VLE and saturated liquid and vapor volumes by means of a 3P1T cubic EOS

The three-parameter cubic equation of state with one parameter temperature-dependent (3P1T), P = RT/(V − b) − a(T)/[V(V + c) + b(3V + c)], recently developed for asymmetric mixture density calculations for nonpolar substances (Yu and Lu, 1987), has been applied to VLE calculations. The binary interaction parameter k 12 obtained from the conventional random VDW mixing rule for the mixture parameter a has been used for the prediction of volumes of saturated liquid (V ℓ) and saturated vapor (V ν) at the conditions of the VLE data. The 3P1T equation is as capable for VLE calculations as the Soave-Redlich-Kwong, the Peng-Robinson, the Schmidt-Wenzel and the translated Peng-Robinson equations, but it yields lower V ℓ deviations than these equations. The improvement is more evident for highly asymmetric mixtures. The suitability of the form of the equation for representing V ℓ of nonpolar compounds over a wide range of molecular weight is further demonstrated.