Prediction of high pressure solid-liquid equilibria for benzene-cyclohexane system based on the van der Waals types of equation of state

In order to develop a method for calculating high-pressure solid-liquid equilibria (SLE) for simple eutectic organic compound mixtures, we tested the applicability of the method using equations of state for both liquid and solid phases. By applying two van der Waals types of equation of state to liquid phase, the effect of equation of state for liquid phase on the prediction of high-pressure SLE was investigated. The two equations of state used for liquid phase were the Carnahan-Starling-van der Waals equation (CS-vdW equation) with a hard sphere fluid as a reference system and the Boublik-van der Waals equation (B-vdW equation) with a hard convex body fluid as a reference system. For calculation of molar volume of solid phase, a simple linear pressure dependence equation was assumed. High-pressure SLE for the benzene-cyclohexane system was selected as a simple eutectic model system, since the physical significance of the parameters in the equations of state can be well defined for the two constituting compounds, and accurate experimental data for high-pressure SLE were reported. It was found that both the CS-vdW and B-vdW equations can predict SLE with almost the same accuracy in the composition range where benzene crystallizes, while the CS-vdW equation can predict better than the B-vdW equation in the composition range where cyclohexane crystallizes. The accuracy for representation of PVT relationships for liquid phase with equation of state was found to correlate well with the accuracy of high-pressure SLE prediction. It should be noted that for high-pressure SLE prediction, it is inevitable that accurate equation of state be available.