Calculation of Solubilities for Systems Containing Multiple Non-Volatile Solutes and Supercritical Carbon Dioxide

Most of the investigations on thermodynamic modeling of solid solubility in supercritical fluids are limited to pure nonvolatile solutes. Even with a presence of solid mixtures, it is considered that the different solids in the mixture behave as if they were alone, that is, they do not interact. Results in the literature show that this is true if the molecules of the solutes have symmetry, both in size or polarity. The aim of this work is to present solubility experimental data of a solid mixture (beta-carotene/bixin) and supercritical carbon dioxide and to propose a thermodynamic model in order to describe this very asymmetric system. The proposed model is based on the Peng-Robinson equation of state and depends on the critical properties and the binary interaction parameters. The binary interaction parameters between carbon dioxide and beta-carotene and between carbon dioxide and bixin were obtained from binary experimental data. For the solid mixture and carbon dioxide the model considers interactions between the solids in the solid phase and relaxes the constraint of equal interaction parameters between the solutes. A new set of experimental data on the solubility in supercritical CO2 of a mixture of bixin and beta-carotene (1: 1, wt) measured at 40 and 60 degrees C and pressures up to 350 bar is presented, and its behavior is well described by the proposed model, with a deviation of 18.2% and 44.6% for beta-carotene and bixin, respectively, opposed to the model without any solid interaction, which poorly. describes the available experimental data (approximately 70% average deviation). This model may be used for solid mixtures even when the solids melt.