# Solid-supercritical fluid equilibria: improved solubility predictions through a nonrandomness concept (perturbed hard chain eos, random fluid approximation)

## Description

The purpose of this research project was to improve the accuracy of the predictions for the solubility of hydrocarbon solids in supercritical fluids. The role of size and energy asymmetries of solid-supercritical fluid systems on the attractive and repulsive pressure terms of various equations of state was determined. Modifications to improve the accuracy of the solubility predictions can be made based on the role of these pressure terms in the model The Peng-Robinson equation of state, with different random fluid mixing rules, was used to predict the solubility of a solid in a supercritical solvent. Discrepancies in accurately predicting the solubility appear to be due to the random fluid assumption rather than the form of the particular mixing rule. A modification of the van der Waals one-fluid mixing rule which includes both temperature and density dependence for the attractive parameter of the equation of state was developed based on a probabilistic approach. With the proposed modification, the Peng-Robinson equation of state can provide good solubility predictions Discrepancies in accurately predicting the solubility of solids in supercritical fluids with the more complex Boublik-Alder-Chen-Kreglewski equation of state are again due to the random fluid approximation in the mixing rule. The Perturbed-Hard-Chain equation of state, using rigorously derived mixing rules and eliminating the random fluid assumption (a nonrandomness concept), yields good results for solubility predictions. Importantly, the Perturbed-Hard-Chain approach offers the ability of extrapolative calculations, since the binary interaction coefficient can be obtained from previously compiled data. To give a more theoretical basis for the dependence of the attractive term of the equation of state on density, Local Composition Theory was used with the three equations of state, but its application yielded poor results for solubility predictions To determine the role of the repulsive force contribution to the equation of state, the combinatorial entropy of mixing for the system was calculated using the repulsive term of the three equations of state. Results suggest that the repulsive term of the Perturbed-Hard-Chain equation of state is the most correct form