Modeling the solubility of Alkyl Ketene Dimer in supercritical carbon dioxide: Peng-Robinson, group contribution methods, and effect of critical density on solubility predictions

Alkyl Ketene Dimer (AKD) is a sizing agent commonly introduced into cellulose substrates during papermaking to improve its hydrophobicity. High-pressure impregnation of this solute with supercritical carbon dioxide (scCO2) into cellulose and other substrates can achieve excellent hydrophobicity of the substrate, and may be used as an alternative technique to traditional coating (sizing) methods. In this study, the solubility of AKD in scCO2 was modelled using Peng-Robinson equation of state (PR-EOS) with van der Waals mixing rules, and volume-translated PR-EOS (VTPR). Given the unavailability of AKD's experimental critical properties and vapor pressure data, group contribution estimation methods (GCEM) were used to determine these physical constants. Available experimental data from another research group, collected using cloud-point and extraction methods, was used to regress binary interaction parameters and compare the resulting model's capability in predicting solubility. The models for each experimental method predicted crossover pressures within a small range, but fitted the cloud-point experimental data much better than the extraction data, showing good agreement at pressures beyond 15 MPa and all temperatures investigated. The VTPR model showed the least agreement with experimental data. A relative standard deviation of 0.26 was obtained between modelled and experimental data for the cloud-point method, and 0.42 for the extraction method data. The models were confirmed with the Chrastil equation, and strongly demonstrated the linear relationships predicted by this expression. The models additionally predicted a change in temperature dependence around the critical density, with a common linear relationship independent of temperature being observed at densities below the critical value. This newly observed behavior, not predicted by the Chrastil equation, sets the groundwork for further fundamental investigations, while the developed models will assist the design of alternative sizing processes involving AKD and scCO2.