AN IMPROVED HARD SPHERE EXPANSION CONFORMAL SOLUTION THEORY TO PREDICT VAPOR LIQUID EQUILIBRIA

The HSE (Hard Sphere Expansion) theory calculates the thermodynamic properties of a mixture by separating its properties into contributions from molecular repulsion, which are calculated directly from a hard sphere mixture equation of state, and other contributions from various types of intermolecular attraction, which are obtained by corresponding states from known values of similar contributions in a pure reference fluid. Shape factors are used to establish conformality between individual constituents and the reference fluid. This theoretically based approach represents composition dependence better than the empirical mixing rules used in the traditional mixture equations of state. By applying the first and second order variational principles, a procedure is developed to determine the optimal repulsion contribution and rigid core dimensions. The procedure requires an equation of state capable of predicting accurate second derivatives for the reference fluid. A 32 constant modified Benedict-Webb-Rubin (MBWR) equation with exceptional accuracy is used for this purpose. Engineering equations of state are permissible for constituents other than the reference. The new development allows an accurate analytical approach to be applicable to the differentiation of the mixture Helmholtz free energy property with respect to component moles involved in the phase equilibrium calculations. The importance of the reference fluid selected for phase equilibrium calculations is discussed. The reference fluids used are the three hydrocarbons: methane, ethane, and propane. For mixtures containing polar fluids, such as carbon dioxide or hydrogen sulfide, the total attraction contribution may be evaluated entirely from the attraction in a pure nonpolar reference fluid by means of shape factors. An alternate method is to evaluate separate symmetrical and asymmetrical attraction terms, in which the multipole expansion is used to account for the polar contributions. Both approaches are discussed and compared. The HSE theory are applied to gaseous and liquid phases of binary hydrocarbon mixtures containing high concentrations of hydrogen sulfide or carbon dioxide. Calculations of densities and the vapor-liquid composition ratios (K-values) are presented. Good agreement with experimental data is achieved over a wide range of pressure and temperature. The computational procedure is detailed in this work