Modeling solid solute solubility in supercritical carbon dioxide by machine learning algorithms using molecular sigma profiles

Supercritical carbon dioxide (ScCO₂) is a solvent used in industries due to its non-toxic, non-flammable nature and unique liquid–gas properties. To predict the solubility of different solid solutes in ScCO₂ for extraction or pharmaceutical process design, machine learning (ML) has been widely used to correlate the thermodynamics parameters with solubility. This work presents an investigation of the solubility of 116 drug-like solutes (comprising 2791 data points) in ScCO₂ using machine learning models. Deep neural network (DNN) and random forest (RF) methods were employed with temperature, pressure, CO₂ density, molecular weight, and sigma profile (σ-profile) as input features for predicting solubility. Results indicate strong ML model capabilities with R² and ALD-x values of DNN being 0.9911 and 0.090 and those of RF being 0.9892 and 0.087, though DNN showed slightly higher errors. The effect of reducing input features of σ-profile on prediction accuracy revealed a negligible increase in error but maintained overall performance. This demonstrates that using a reduced number of σ-profile features offers practical estimation with limited computational resources. This work shows the robust potential of machine learning in accurately predicting the solubility of solids in ScCO₂ using σ-profiles.