A versatile thermodynamic consistency test for incomplete phase equilibrium data of high-pressure gas–liquid mixtures

A new method to test the thermodynamic consistency of phase equilibrium data in binary mixtures containing a liquid solute and a supercritical fluid is presented. For the systems of interest, mixtures containing a liquid solute and a supercritical fluid, not only the P–T–x–y data are not available for the whole concentration range, but also the solute concentration in the gas phase is low (mole fractions from 10−1 down to 10−4). For these cases, the classical differential or integral methods described in standard books, are not applicable. The proposed method is specially designed for treating incomplete P–T–x–y data. That is, data that do not cover the whole range of concentration of the components in the mixture, as those usually found in supercritical fluid mixtures. The method is based on the Gibbs–Duhem equation, on the fundamental equation of phase equilibrium and on an appropriate combination between equations of state, mixing rules and combining rules. The new method is applied to eleven isothermal sets of data for high-pressure binary mixtures and consistency criteria are defined.