Beyond one-fluid approximations for the thermodynamics of fluid mixtures

Developing analytic equations of state for fluid mixtures based on perturbation theories requires simplifying approximations, in which mixture properties are determined from effective pure component properties. While these one-fluid approximations reduce model complexity, they also introduce inaccuracies. In this work, a simple algebraic correction factor for perturbation theories applying a one-fluid approximation is proposed. The correction factor is defined as the ratio of the rigorous first-order perturbation term in Helmholtz energy to the respective first-order perturbation term in the one-fluid approximation. An approximate closed-form expression for the correction factor is derived in terms of the fundamental measures of the particles using symbolic regression. The new approach is thoroughly evaluated by applying it to a range of equations of state, including the uv-theory and the PCP-SAFT equation of state, to predict the thermodynamic properties of square-well, Lennard-Jones, and real-substance mixtures. New molecular simulation data for strongly size-asymmetric binary, ternary, and quinary Lennard-Jones mixtures are generated to test the proposed approach. Compared to the predictions obtained from a one-fluid approach, the correction factor significantly improves the accuracy of predicted phase equilibria and thermodynamic properties for model fluids. Its impact on real-fluid predictions with the PCP-SAFT equation of state is rather small, because PCP-SAFT segment size parameters of most substances are rather similar, whereas the correction factor primarily accounts for segment size asymmetry.