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.