Comprehensive evaluation of semi-empirical models, correction of fitting anomalies, and development of a novel seven-parameter model for silymarin solubility in pure/cosolvent-added supercritical carbon dioxide

This work identifies and corrects model fitting errors in the reported solubility data of silymarin (SM) in pure and cosolvent-modified supercritical carbon dioxide (SCCO 2 ) by Yang et al. (2017). The Chrastil, Bartle, and Mendez-Santiago and Teja (MST) models were refitted to provide accurate parameters for future reference. Twenty existing semi-empirical models classified into three categories (f( ρ,P,T ), f( ρ,T ), f( P,T )) were evaluated, and a novel seven-parameter semi-empirical model was developed. The new model avoids overfitting and shows superior fitting accuracy for SM solubility. To validate its generalizability, the model was tested against published solubility data of 17 pharmaceutical compounds covering multiple drug classes in SCCO 2 , and it outperformed the representative top models from the three semi-empirical model categories (Jouyban et al., Belghait et al., Reddy-Garlapati) with an overall AARD % of 8.7551% and all R ² adj above 0.9096. Results confirm that the model is widely applicable to diverse solid solutes beyond silymarin. This study provides reliable corrected parameters, a high-precision predictive tool, and technical support for the design and optimization of SCCO 2 -based extraction and particle production processes in the pharmaceutical and chemical industries.