Mathematical representation of solute solubility in supercritical carbon dioxide using empirical expressions

Solubility data of drugs in supercritical fluids (SCF) are crucial for designing pharmaceutical processes, such as micronization of drug powders or extraction using SCF. A new empirical equation is proposed to correlate solute solubility in supercritical carbon dioxide (SC CO2) with temperature, pressure and density of pure SC CO2. The proposed equation is ln y2=M0+M1P+M2P2+M3PT+(M4T)/P+M5 ln ρ, where y2 is the mole fraction solubility of the solute in the supercritical phase, M0–M5 are the model constants calculated by least squares method, P (bar) is the applied pressure, T is temperature (K) and ρ is the density of pure SC CO2. The accuracy of the proposed model and four other empirical equations employing P, T and ρ variables, was evaluated using 106 published solubility data sets by calculating the average of absolute relative deviation (AARD). The mean AARD for the proposed model is 21.4 (±15.9)%, which is an acceptable error when compared with the experimental uncertainty. The AARD values for other equations were 33.7 (±24.5), 36.2 (±27.2), 48.3 (±77.2) and 27.1 (±21.2). The mean AARD of the new equation is significantly lower than those obtained from previous empirical models (paired t-test, P<0.0005). The proposed model presented more accurate correlation for solubility data in SC CO2. It can be employed to speed up the process of SCF applications in the pharmaceutical industry.