Modeling solubility in supercritical fluids via the virial equation of state

We examine the utility of the virial equation of state (VEOS) for the prediction of the solubility of hexane in supercritical carbon dioxide. We computed virial coefficients up to fourth-order for this mixture at 353.15 K, using Mayer-sampling Monte Carlo applied to established molecular models for carbon dioxide and hexane. At this temperature, neither the third- nor fourth-order VEOS indicate the presence of a critical point for the mixture. However, the VEOS coupled with an ideal-solution treatment for the coexisting subcritical fluid phase (with parameters determined from coexistence data at one pressure) reproduces much of the solubility curve as previously established by Gibbs-ensemble molecular simulation. Comparison of the third- and fourth-order VEOS indicate that the virial treatment is converged at the conditions where it is applied.