Numerical Modeling of Momentum Dispersion in Porous Media Based on the Pore Scale Prevalence Hypothesis

Abstract

A macroscopic model that accounts for the effect of momentum dispersion on flows in porous media is proposed. The model is based on the pore scale prevalence hypothesis (PSPH). The effects of macroscopic velocity gradient on momentum transport are approximated using a Laplacian term. A local Reynolds number Red, which characterizes the strength of momentum dispersion, is introduced to calculate the effective viscosity. The characteristic length used in defining Red is the pore size, while the characteristic velocity is the mixing velocity. A Taylor expansion is made for the effective viscosity with respect to Red. The two leading-order terms of the Taylor series are adopted in the present PSPH momentum-dispersion model. The model constants are determined from the direct numerical simulation results of a flow in the same porous medium bounded by two walls. The effective viscosity approaches the molecular viscosity when the porosity is increased to 1. It approaches infinity when the porosity approaches 0. The benchmark studies show that the effects of the macroscopic velocity gradient can be approximated by the Laplacian term. The proposed PSPH momentum-dispersion model is highly accurate in a wide range of Reynolds and Darcy numbers as well as porosities.