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

A theoretical method based on combining the virial expansion and fluctuatio n theory for calculating the chemical potential of a solute in a supercriti cal fluid is presented. The method is compared to literature results from M onte Carlo simulations based the Widom method for evaluating the chemical p otential. For one-center and two-center Lennard Jones (2CLJ) potential mode ls, the average difference from simulated results for the chemical potentia l is about 5% at densities up to twice the critical density. The method req uires virial coefficients up to C(T) (the third) to achieve this level of a ccuracy. Correlations based on corresponding states principles for the pred iction 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 typica l supercritical extraction conditions. These correlations are then used to determine virial coefficients and chemical potentials for naphthalene, benz oic acid and phenanthrene in carbon dioxide at several different state cond itions for which solubility data exist. The theoretical results are compare d to chemical potentials obtained from experimental solubility data. The me thod is found to be accurate, tractable and systematically improvable throu gh the inclusion of higher order terms in the virial expansion. (C) 2001 El sevier Science B.V. All rights reserved.