Modeling CO₂ solubility in deep eutectic solvents using the SAFT-VR Mie and PC-SAFT equations of state

• The solubility predictions with the Hudson-McCoubrey combining rule were comparable to those using the unlike-segment interaction energy parameter optimized to reproduce experimental solubility data. • The Lorentz-Berthelot combining rule leads to inaccurate phase equilibria modeling for hydrophobic DES mixtures. • SAFT-VR Mie and PC-SAFT both provide reliable predictions but their optimal modeling strategies vary based on the hydrophilicity of the DES. • CO₂–DES cross-association has a negligible impact on predictions; however, a detailed hydrogen bonding description generally enhances model accuracy. This study presents the first comparison of SAFT-VR Mie and PC-SAFT in modeling CO₂ solubility in Deep Eutectic Solvents (DESs). Experimental density data was used to adjust pure-component parameters ( m, σ , and ε ) for DESs in the SAFT models, whereas the unlike-segment interaction energy between CO₂ and the DES was either calculated with combining rules or optimized to reproduce experimental solubility data. A simplified Hudson-McCoubrey combining rule (ionization potentials assumed equal), applied for the first time to CO₂–DES systems, was compared with the conventional Lorentz-Berthelot rule. Four hydrophilic and six hydrophobic DESs were modeled as pseudo-pure components, either as non-associating or associating species, following 2B or 4C association schemes in both equations of state. It was found that the Lorentz-Berthelot rule is unsuitable for CO₂–DES phase equilibrium modeling, particularly for hydrophobic DESs, while the Hudson-McCoubrey rule provided excellent agreement with experimental data for both SAFT-VR Mie and PC-SAFT, performing comparably to models with unlike-segment interaction energy obtained empirically. The 2B and 4C association schemes produced accurate solubility predictions and demonstrated slightly superior performance compared to the inert approach, particularly in the case of hydrophobic DESs. Additionally, CO₂ was modeled as either a neutral component or with 2B cross-association with DES, showing no significant difference in results. Finally, Helmholtz energy contributions to the residual pressure of pure hydrophobic DESs were analyzed, revealing that while association effects were minor, they positively influenced CO₂ solubility predictions.