| Several models have been proposed to describe SFE from solid material. Nevertheless, the model has the advantage of providing a reasonably simple analytical solution to the mass balance equation and a good physical description of the process. As discussed previously, these authors proposed a similar physical representation of the seed particles as being composed of cell broken up during grinding and of cells which are still intact. They hypothesized the existence of two mass transfer resistances during SFE. The first is located in the supercritical mixture and controls the extraction process until all the essential oil in the broken cells is exhausted. The second is in the walls of the undestroyed cells and controls the remaining part of the process. These hypotheses were transferred to the mathematic model by introducing two mass balances for a bed element:
Solid phase :  (3)
Liquid phase :  (4)
The X and Y are the solute mass ratio in the solid and fluid phases respectively, t is time, U is the superficial velocity, p s and p F are the solid and fluid phase densities respectively, ε is the total porosity (bed and particles), h is the axial direction, and J(X,Y) is the interfacial mass transfer rate. The boundary conditions are
X(h, t = 0) = X 0, and
Y(h=0, t) = 0 (5)
The easily accessible solute which surmounts only the diffusion resistance in the solvent is extracted first. When the solid-phase concentration decreases to X k, mass transfer is retarded by the diffusion in the solid phase:
J(X > X k, Y) > J(X ≤ X k, Y) (6) |