Representing dyestuff solubility in supercritical carbon dioxide with several density-based correlations

For the proper design of supercritical fluid dyeing process, it is essential to have a sound knowledge of the solubilities of dyes and the accurate solubility representation. In this work, we employed four semiempirical density-based models (the Chrastil model, the Bartle model, the K-J model and the M-T model) to correlate solubilities of 32 dyestuffs in supercritical carbon dioxide. The results show that these models perform very well with three temperature-independent parameters and could be applied for satisfactory solubility predictions. A comparison among the four models reveals that the ln y2 versus ln ρ Chrastil model gives much better correlations to the solubility data with an overall average absolute relative deviation (AARD) of 20.6% than the other three models. From the correlation results, the heat of dye-CO2 solvation and that of solute dye vaporization can be separately approximated in the range of 13.0-21.0 and 29.2-101.6 kJ/mol, respectively. Besides, the solubility discrepancies observed for certain dyestuffs have been discussed by using these density-based models.