Two-Dimensional Numerical Analysis of Non-Darcy Flow Using the Lattice Boltzmann Method: Pore-Scale Heterogeneous Effects

Abstract

This study simulates pore-scale two-dimensional flows through porous media composed of circular grains with varied pore-scale heterogeneity to analyze non-Darcy flow effects on different types of porous media using the lattice Boltzmann method. The magnitude of non-Darcy coefficients and the critical Reynolds number of non-Darcy flow were computed from the simulation results using the Forchheimer equation. Although the simulated porous materials have similar porosity and representative grain diameters, larger non-Darcy coefficients and an earlier onset of non-Darcy flow were observed for more heterogeneous porous media. The simulation results were compared with existing correlations to predict non-Darcy coefficients, and the large sensitivity of non-Darcy coefficients to pore-scale heterogeneity was identified. The pore-scale heterogeneity and resulting flow fields were evaluated using the participation number. From the computed participation numbers and visualized flow fields, a significant channeling effect for heterogeneous media in the Darcy flow regime was confirmed compared with that for homogeneous media. However, when non-Darcy flow occurs, this channeling effect was alleviated. This study characterizes non-Darcy effect with alleviation of the channeling effect quantified with an increase in participation number. Our findings indicate a strong sensitivity of magnitude and onset of non-Darcy effect to pore-scale heterogeneity and imply the possibility of evaluating non-Darcy effect through numerical analysis of the channeling effect.