Model evaluation for the prediction of solubility of active pharmaceutical ingredients (APIs) to guide solid–liquid separator design

The assumptions and models for solubility modelling or prediction in systems using non-polar solvents, or water and complex triterpene and other active pharmaceutical ingredients as solutes aren't well studied. Furthermore, the assumptions concerning heat capacity effects (negligibility, experimental values or approximations) are explored, using non-polar solvents (benzene), or water as reference solvents, for systems with solute melting points in the range of 306–528 K and molecular weights in the range of 90–442 g/mol. New empirical estimation methods for the ΔfusCpi of APIs are presented which correlate the solute molecular masses and van der Waals surface areas with ΔfusCpi. Separate empirical parameters were required for oxygenated and non-oxygenated solutes. Subsequently, the predictive capabilities of the various approaches to solubility modelling for complex pharmaceuticals, for which data is limited, are analysed. The solute selection is based on a principal component analysis, considering molecular weights, fusion temperatures, and solubilities in a non-polar solvent, alcohol, and water, where data was available. New NRTL-SAC parameters were determined for selected steroids, by regression. The original UNIFAC, modified UNIFAC (Dortmund), COSMO-RS (OL), and COSMO-SAC activity coefficient predictions are then conducted, based on the availability of group constants and sigma profiles. These are undertaken to assess the predictive capabilities of these models when each assumption concerning heat capacity is employed. The predictive qualities of the models are assessed, based on the mean square deviation and provide guidelines for model selection, and assumptions concerning phase equilibrium, when designing solid–liquid separators for the pharmaceutical industry on process simulation software. The most suitable assumption regarding ΔfusCpi was found to be system specific, with modified UNIFAC (Dortmund) performing well in benzene as a solvent system, while original UNIFAC performs better in aqueous systems. Original UNIFAC outperforms other predictive models tested in the triterpene/steroidal systems, with no significant influence from the assumptions regarding ΔfusCpi. Keywords: Solubility, Solid–Liquid Equilibrium, Model prediction, Active pharmaceutical ingredient