## Advances in mathematical modeling of supercritical extraction processes

##### Apstrakt

A new trend in mathematical modeling of supercritical extraction process from plant material is presented. The most of the previously published models considered properties of the fixed bed of plant material during the extraction to be constant. This assumption might be quite true in the case of plant materials with relatively low quantity of extractables. However, the fixed bed property change may occur in the case of extraction from material with high quantities of extractables. Recently, mathematical model which took into account particle density, bed porosity and particle diameter as variables was derived. In this chapter, the model is further improved by introducing variable solubility of the extract in supercritical fluid. On the basis of new experimental results on the binary equilibrium of the system supercritical fluid - extract present in solid, a relationship between solubility in supercritical fluid and oil content in solid was established. The new model was derived which t...ook into account particle density, bed porosity, particle diameter and solubility in supercritical fluid as variables. The model was verified on results from experiments in which the kinetics of supercritical extraction from rapseed was analyzed. Parameters of the model showed expected behaviour with respect to the change of particle size. Further analysis, shown in this chapter, showed that, if the dependency of solubility from the concentration in the solid phase is not accounted for, the model tends to overestimate the yield of the extraction. The new model is so far, the most realistic model and one of the most demanding models regarding experimental work and mathematical tools for the description of mass transfer in fixed beds.