Semi-Empirical Models and Cubic Equations of State for Correlation of Solids Solubility in scCO2: From Simple to Complex Substances

Jose A.P. Coelho1, 2, *, Rui M. Filipe1, 3, António F. Palavra2, Greta P. Naydenova4, Dragomir S. Yankov4, Roumiana P. Stateva4
1 ISEL - Instituto Superior de Engenharia de Lisboa, Instituto Politécnico de Lisboa, 1959-007 Lisboa, Portugal
2 Centro de Química Estrutural, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
3 CERENA, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisboa, Portugal
4 Institute of Chemical Engineering, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria

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© Coelho et al. Licensee Bentham Open.

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (, which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at ISEL - Instituto Superior de Engenharia de Lisboa, Rua Conselheiro Emidio Navarro, 1, 1959-007 Lisboa, Portugal; Tel: +351-919187951; Email:


The present paper examines the performance of cubic equations of state (CEoSs) and semi-empirical density-based models in correlating the solubility in supercritical carbon dioxide (scCO2) of several solid compounds of interest to the food industry, namely 2-propenamide, bixin, β-carotene and C-tetramethylcalix[4]resorcinarene. The four target solutes are with increasing structural complexity and, are typically pure solids, at ambient or slightly elevated temperatures.

The Soave-Kwong-Redlich (SRK) CEoS with the one-fluid van der Waals mixing rule was chosen as representative of the class of CEoSs, while the group of the density-based models includes Chrastil model, Kumar and Johnston model, Bartle et al. model, Méndez–Santiago and Teja model, Garlapati and Madras model, Nejad et al. model and Khansary et al. model.

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 than the other models with overall average absolute deviations, AARD %, of 6.3, 7.8 and 7.2 %, respectively. The 9.1% overall AARD for the SRK CEoS was considered satisfactory since it can be used as a reliable thermodynamic model to predict the solubility of any compound for which there are no sufficient experimental data available.

Keywords: Cubic equations of state, Semi-empirical models, Solid solubility correlation, Supercritical fluids.