A thermodynamic approach for correlating the solubility of drug compounds in supercritical CO2 based on Peng-Robinson and Soave-Redlich-Kwong equations of state coupled with van der Waals mixing rules

In the present study, the effect of equations of state and mixing rules in a thermodynamic approach has been investigated for the correlation of the solubility of four new solid pharmaceutical compounds, namely, benzamide, cetirizine, metaxalone and niflumic acid in supercritical CO2 at different temperatures and pressures. Two equations of state, the Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK), coupled with mixing rules of one-parameter van der Waals (vdW1) and two-parameter van der Waals (vdW2) were used, where the binary interaction parameters for these sets of equations were evaluated. The approach correlations and the robustness of the numerical technique were validated with the experimental data previously reported for these compounds at different temperatures and pressures. The calculated average absolute relative deviations (AARD) were 7.51 and 5.31 % for PR/vdW1 and PR/ /vdW2 couples, and 11.05 and 10.24 % for SRK/vdW1 and SRK/vdW2 couples, respectively. It was also found that the PR equation of state results in modeling performance better than the SRK equation, and the vdW2 mixing rule better than the vdW1 one. These results obviously demonstrate that the combined approach used in this study is applicable for correlation of solid solubilities of some pharmaceutical compounds in supercritical CO2. Additionally, a semi-empirical correlation is proposed for estimating the solubility of drug solids in supercritical CO2 as a function of pressure and temperature.