Modelling solubility of solid active principle ingredients in sc-CO2 with and without cosolvents: A comparative assessment of semiempirical models based on Chrastil's equation and its modifications

• Solubility of solids in SCFs with cosolvents has been fitted by classical empirical equations.
• New empirical models based on the q-exponential function were developed.
• The new empirical q-models provided deviations of the same magnitude as the classical ones.
• The q-models are promising because do not present theoretical inconsistencies at high temperatures.

Predicting solubility of solids in supercritical solvents with and without cosolvents is a key step supporting the application of supercritical fluids to processes as the extraction of natural compounds and particle engineering. The aim of this work is modelling the solubility of solid therapeutic compounds in supercritical carbon dioxide with and without cosolvents using semiempirical models. A comparative assessment of eight models is presented based on deviations, number of parameters, range of applicability (concentration of cosolvents and proximity to the mixture critical point) and cosolvent–solute interactions.All equations provide an average deviation on solubility around 10%. The use of the González (with four parameters) and Reddy and Madras equation (with five parameters) is judged the most convenient as they have the smaller number of parameters and are applicable over a suitable range of cosolvent concentrations. In all cases it has been possible to relate the solubility behaviour to the cosolvent–solute interaction and the concentration of cosolvent. However, deviations increase when conditions are slightly close to the mixture critical point.A modification is proposed through the introduction of a “q exponential function”. The modified q-models can be regarded as generalized models based on the Tsallis's statistical non-extensive entropy theory. In fact, the original Chrastil and González equation can be seen as a particular case of the q-Chrastil and q-González models. They have deviations similar to the other model and show potential for further studies.

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