Estimation of the Axial Dispersion Effect on Supercritical Fluid Extraction from Bidisperse Packed Beds

The general hydrodynamic equations of a mathematical model for supercritical fluid extraction are derived within the framework of the continuum mechanics approach. The shrinking core concept is used to describe the mass transfer on the solid-liquid interface. The complete system of macroscopic differential mass-balance equations is reduced to a one-dimensional approximation and accounts for the axial dispersion effect. Correlation formulas available in the literature are used to calculate the axial dispersion coefficient for the conditions of supercritical CO₂ filtration. The effect of axial dispersion on the characteristics of the macroscopic process is analyzed for the typical laboratory-scale extraction conditions in the framework of the suggested model. The numerical simulations demonstrate that the difference between the values of the current mass of accumulated extract calculated in terms of the complete approach, which accounts for the axial dispersion, and the one related to the simplified model (in which the axial dispersion is neglected), is less than 10%. The same comparison is made for the outlet concentrations of the target compounds; the difference reaches 200%.