(80e) A New Mixing Rule to Model the Solubility of Solids in Supercritical Fluids

Currently, supercritical-fluid technology in the pharmaceutical and microelectronics industries is increasingly applied to solve difficult processing problems. The solubility of a solute in a supercritical fluid is the most important thermophysical property that needs to be determined and modeled as a first step to develop any supercritical fluids application. This research was undertaken to develop a reliable mathematical model to compute the solubility of solids in supercritical fluids. As a result, a new combination rule is proposed along with a novel approach to obtain general correlations for its parameters. The new combination rule is a modification of the classical van der Waals mixing rules where the binary cohesive parameter a12 is correlated in terms of the reduced pressure. A database containing experimental solubility data for 126 isotherms was used in this study. Half of the isotherms were judiciously selected to develop the correlations in the new combination rule. The rest of the isotherms were then used to validate the results. Detailed error calculations were carried out for different thermodynamic models that included the Peng-Robinson and Patel-Teja equations of state and van der Waals, cubic, and Rao mixing rules. The conclusion, after comparing the calculated errors for various models, was that the best results were obtained for the Patel-Teja EoS and the new mixing rule proposed here. This work is a significant contribution in the field in two ways. First, it provides a specific correlation that gives excellent values of solubility. Second, it proposes a novel approach that can be extended to other mixing rules and may result in a fully predictive method.