A theoretically correct mixing rule for cubic equations of state

Abstract

A new mixing rule developed for cubic equations of state equates the excess Helmholtz free energy at infinite pressure from an equation of state to that from an activity coefficient model. Use of the Helmholtz free energy insures that the second virial coefficient calculated from the equation of state has a quadratic composition dependence, as required by statistical mechanics. Consequently, this mixing rule produces the correct low-and high-density limits without being density-dependent.As a test, the mixing rule is used for ternary mixtures of cyclohexane + benzene + water, ethanol + benzene + water and carbon dioxide + n-propane + water, and all the constituent binaries. The new mixing rule and a simple cubic equation of state can be used for the accurate correlation of vapor-liquid and liquid-liquid equilibria for binary mixtures. Using the parameters obtained from binary systems, the phase behavior of ternary mixtures can be predicted. Also, unlike previous empirical mixing rules, this theoretically based mixing rule is equally applicable and accurate for simple mixtures containing hydrocarbons and inorganic gases and mixtures containing polar, aromatic and associating species over a wide range of pressures. This mixing rule makes it possible to use a single equation of state model with equal accuracy for mixtures usually described by equations of state and for those traditionally described by activity coefficient models. It is the correct bridge between these two classes of models.

Modeling vapor liquid equilibrium of ionic liquids + gas binary systems at high pressure with cubic equations of state

“…This behavior was expected due to the high complexity of the systems reviewed here. A possible solution to this problem would be to use more elaborate mixing rules, such as the Wong-Sandler (WS) type mixing rules (Wong and Sandler, 1992).…”

A Survey of Equations of State for Polymers

“…This is the only difference between this mixing rule and the one proposed by Wong and Sandler [8]. As a result, only one parameter is necessary in the new mixing rule, which is much simpler than the method of Wong and Sandler [8], and is as simple as Kontogeorgis et al method [9]. When using the new mixing rule for ten polymer solutions in a wide temperature range, the results show that it allows cubic equations of state to correlate the vapor-liquid equilibrium of polymer solutions precisely even if just one temperature independent parameter is used.…”

“…Zhong and Masuoka [51], in the proposal of this new mixing rule, considered a null Helmholtz free energy in the limit when pressure tends to infinity. This is the only difference between this mixing rule and the one proposed by Wong and Sandler [8]. As a result, only one parameter is necessary in the new mixing rule, which is much simpler than the method of Wong and Sandler [8], and is as simple as Kontogeorgis et al method [9].…”

“…Attempting to straighten out the theoretical inconsistency of the aforementioned mixing rules, Wong and Sandler [8] proposed a new method in which the rules fulfill the QDSVC with the composition at low pressure condition. The basic idea was to consider the excess Helmholtz free energy as much less dependent on pressure than the excess Gibbs free energy.…”

Prediction of Vapor-Liquid Equilibrium of Polypropylene Oxide Solution Systems by Cubic Equations of State

“…For this work, the Flory-Huggins model has been chosen, which includes two contributions to the thermodynamics of binary polymer solutions, entropy of a thermal mixing due to size difference between the species, and an enthalpy of mixing due to difference of the intermolecular forces, as (33) Here, χ is the Flory interaction parameter, Φ is the volume fraction, and r is the number of solvent size segments that make up the polymer, which is approximated by the hardcore volumes. [29]. Actually, the only difference between this mixing rule and the Wong-Sandler one is the absence of excess Helmholtz energy at infinite pressure, , which was set equal to zero in this case.…”