(427d) Modeling the Solubilities of Binary Mixed Solids in Supercritical Carbon Dioxide

The aim of this work is to present a formal modeling approach for estimating the solubilities of various binary mixed solids in supercritical carbon dioxide (SCO₂) via the use of the classical solubility equation which is given in terms of the fugacity coefficient of the solids in the gas mixture, the solid vapor pressures and the solid molar volumes. The fugacity coefficients of each species in the gas were obtained from the Peng-Robinson cubic equation of state (PR CEoS) coupled with the Wong-Sandler mixing rules which in turn employ an expression for the excess Gibbs free energy suitable for highly asymmetric mixtures (Flory-Huggins solution model). The sublimation pressure of the solids were either determined using well-established correlations of the Antoine type or directly regressed from the experimental solubility data of the solid of interest in SCO₂. Lastly, the solid molar volume was estimated from the PR CEoS as closed-packed (approximately equal to the van der Waals co-volume).

The following binary mixtures of solids along with their experimental solubilities in SCO₂ [1,2] were considered here for modeling purposes: naphthalene + phenantrene, palmitic acid + capsaicin, palmitic acid + β-carotene, palmitic acid + tocopherol, capcaicin + β-carotene, capsaicin + tocopherol, and β-carotene + tocopherol. The performance of the present modeling approach was assessed during the prediction of the solubilities of the aforementioned solid mixtures in SCO₂ using only binary energy interaction parameters (k_i,j for the PR CEoS and χ_i,j for the Flory-Huggins model) previously regressed from experimental solubilities of each solid in SCO₂ at 35 and 55 °C, and at pressures from 101 up to 363 bar. The correlating results obtained here were highly satisfactory for the majority of the binary mixtures (solid + CO₂) considered in this study. The extrapolative abilities of the proposed approach were also verified in the direct prediction of observed solubility data of each of the seven binary mixtures of solids in SCO₂ under study merely using the binary interaction parameters previously obtained during the correlation process.

[1] Arenas-Quevedo et al., J. Chem. Eng. Data, 62, 3861 (2017)

[2] Arenas-Quevedo, M.G.; “Estudio de la solubilidad de compuestos sólidos de valor agregado en productos naturales utilizando fluídos supercríticos”, D. Sc. Thesis, ESIQIE-IPN, Mexico City (2018).