Predicting solubility in supercritical solvents using estimated virial coefficients and fluctuation theory

A theoretical method based on combining the virial expansion and fluctuation theory for calculating the chemical potential of a solute in a supercritical fluid is presented. The method is compared to literature results from Monte Carlo simulations based the Widom method for evaluating the chemical potential. For one-center and two-center Lennard Jones (2CLJ) potential models, the average difference from simulated results for the chemical potential is about 5% at densities up to twice the critical density. The method requires virial coefficients up to C(T) (the third) to achieve this level of accuracy. Correlations based on corresponding states principles for the prediction of B(T) [AIChE J. 20 (1974) 263; AIChE J. 21 (1975) 827; AIChE J. 24 (1978) 1978] and C(T) [AIChE J. 29 (1983) 107] are used to estimate these virial coefficients. A comparison with experimentally determined values for naphthalene in carbon dioxide shows the estimates to be accurate at typical supercritical extraction conditions. These correlations are then used to determine virial coefficients and chemical potentials for naphthalene, benzoic acid and phenanthrene in carbon dioxide at several different state conditions for which solubility data exist. The theoretical results are compared to chemical potentials obtained from experimental solubility data. The method is found to be accurate, tractable and systematically improvable through the inclusion of higher order terms in the virial expansion.