Conformal solution methods based on the hard convex body expansion theory

Abstract

Naumann, K.-H. and Leland, T.W., 1984. Conformal solution methods based on the hard convex body expansion theory. Fluid Phase Equilibria, 18: 1–45. This paper develops an improvement in the hard convex body equation of state of Boublik by introducing a new parameter which forces the equation to predict the computer calculated virial coefficients for hard sphero-cylinders. The technique is analogous to that used in developing the Carnahan-Starling equation for hard spheres. The new hard convex body equation is applicable to both pure components and mixtures. It agrees with computer simulation data for sphero-cylinders which have a length-width ratio as large as three. As the constituents of a mixture approach spherical shape, the new hard convex body equation approaches the hard sphere mixture equation of Mansoori, Carnahan, Starling and Leland. Analytical relationships have been derived between the dimensionless size parameters in the new equation and the Pitzer acentric factor. The convex body surface, mean radius, and volume parameters required in this equation for each component of the hard convex body mixture can then be determined from the acentric factor and an equation of state for the pure component. New pseudo-parameters have been derived which predict the molecular attraction contribution to properties of a mixture of convex molecules from this attraction contribution in a zero acentric factor reference fluid and in a second reference with a larger acentric factor. A theoretical basis is derived for combining the molecular attraction portion of these two references in the Lee-Kesler form to predict attraction properties in a mixture of convex molecules. A new average acentric factor is derived for this purpose. It is shown that molecular repulsion effects in either pure convex molecule components or in mixtures containing them cannot be predicted by the Lee-Kesler technique.