Pore-network modelling of transverse dispersion in porous media under non-Darcy flow conditions

Abstract

This work is concerned, for the first time, with estimating the transverse dispersion coefficient under non-Darcy laminar flow conditions in porous media using pore-network modeling. The pore-network modelling approach and the mixed cell method are adopted to simulate both the steady laminar flow and the transient transport of solute for Berea and Bentheimer sandstone samples. For non-Darcy flow, the inertial effect is attributed to the quadratic increase of the pore throat mean velocity, which is embedded in the pressure head losses at either expansion or contraction located at the two ends of any pore throat. A time dependent function, based on both Péclet number and average residence time within the pore throat, is used to incorporate the effect of nonuniform pore throat velocity in the dispersion coefficient. A restrictive upper limit of the time step interval is introduced to prevent numerical overshoots of the concentrations calculated over time. For the same pressure gradient through the sample, the results show a decrease in both Péclet number and the coefficient of transverse dispersion in case of adopting the non-Darcy flow condition instead of the Darcy flow one. The percentage of decrease is up to 20 % for the maximum applied pressure gradient through the sample.