Solubility parameters may be useful to simplify very difficult phase equilibria. If you have two chiral salts, two chiral acids, an organic solvent, and CO2, you vary the pressure and temperature as well as composition ...this is a pretty difficult phase equilibrium. But we need to describe it somehow because the practice shows that it gives excellent purities if all parameters are correctly set.
The paper shows how to reduce the number of experiments needed to find an "optimal" parameter set by using precisely calculated Hansen solubility parameters for CO2-cosolvent mixtures under pressure.