Hard convex body expansion (HCBE) conformal solution method for predicting vapor—liquid equilibria

Abstract

Like the hard-sphere expansion (HSE) theory, the hard convex body expansion (HCBE) theory separates any residual thermodynamic property into a contribution from molecular repulsion, which is calculated directly from a hard convex body (HCB) equation of state, and other contributions from molecular attraction, which are obtained by the corresponding states principle (CSP) using two pure reference fluids. An HCB equation of state developed by Naumann and Leland is applicable to pure components and their mixtures. The HCB equation of state for a pure component is characterized by two dimensionless geometrical parameters, α and τ −1 which are combinations of three molecular dimensions of a convex body—volume ( V), surface area ( S) and mean radius ( R). Two dimensionless geometrical parameters are determined directly from Pitzer's acentric factor. The molecular volume is evaluated by equating the HCB equation of state to the optimal repulsion evaluated by the expansion method. The surface area and the mean radius are obtained from known dimensionless geometrical parameters and the molecular volume. Four kinds of convex bodies are considered in this work. These are prolate spherocylinders, oblate spherocylinders, prolate ellipsoids and oblate ellipsoids.