Two-parameter model for mass transfer processes between solid matrixes and supercritical fluids: Analytical solution

A simple two-parameter mathematical model with analytical solution applicable for mass transfer processes between solid matrixes and supercritical fluids has been developed. Experimental curves for supercritical extraction of wheat germ (extractors of 10 mL and 100 mL) and supercritical wood impregnation processes (adsorber of 1 L) have been fitted using this model. Moreover, the model has been applied to scale up a supercritical adsorption process onto activate carbon from a laboratory unit (adsorber 10 mL) to pilot plant scale (adsorber of 1 L). The proposed model takes into account the equilibrium step (h) and mass transfer from the bulk of the fluid phase to the surface of the solid (kfa). The adjusted results have demonstrated that the model is able to fit all available experimental results with reasonable accuracy. Thus, the fitting average error was 1–6% for extraction process, 3–7% for wood impregnation and 7–10% for adsorption scale-up. The proposed model is versatile and suitable to adjust with only two parameters different supercritical mass transfer processes. The analytical solution based on modified Bessel functions is useful and easily implemented using common computer mathematical programs. Furthermore, a friendly Excel user-interface for the simulation of adsorption/desorption processes is provided within the supporting information; the program runs using MATLAB 7.0 as simulation engine.