Frequency-dependent dispersion in porous media

Several studies have shown that the performance of different chemical processes can be improved by means of periodic operation. An accurate modeling and simulation of these processes requires accounting for the dependence of the system parameters with the operating frequency. This work uses the method of volume averaging to study the behavior of dispersion with frequency (i.e., dynamic dispersion) in homogeneous porous media. In the absence of convection, the dynamic dispersion is reduced to the dynamic diffusivity, showing a decreasing behavior with frequency. In contrast, the dynamic dispersion can be either an increasing or decreasing function of frequency, depending on the particle Peclet number values. At sufficiently high frequency values, the dispersion coefficient approaches the molecular diffusivity. Comparisons with direct numerical simulations for idealized porous medium models evidence the extents and limitations of the upscaling approach.