Semi-empirical models and a cubic equation of state for correlation of solids solubility in scCO(2): dyes and calix[4]arenes as illustrative exemples

Knowledge of a compound's solubility in the supercritical solvent is crucial to the definition of the optimal operating conditions and consequently to the development of supercritical applications. The present paper examines the performance of two of the most widely used groups of models for correlating the solubility of solid solutes in supercritical carbon dioxide – equations of state (EoSs) and semi-empirical density based models. The Soave-Kwong-Redlich (SRK) EoS with the one-fluid van der Waals mixing rule represents cubic EoSs, while the group of the density-based models includes Chrastil, Kumar and Johnston, Bartle et al., Méndez-Santiago and Teja, Garlapati and Madras, Nejad et al. and Khansary et al. models. The seven solutes chosen as illustrative examples are compounds of interest to the dry dyeing processing techniques and biotechnological processes and have diverse structural complexity. The results obtained reveal that the more recently advocated density-based models (Garlapati and Madras, Nejad et al. and Khansary et al. models) perform better with overall average absolute deviations, AARD, of 6.5, 9.0 and 9.3%, respectively. The 6.7% overall AARD for the SRK CEoS is acceptable and it can be used as a reliable thermodynamic model to predict the solubility of any compound for which there is no sufficient experimental data available.