Performance of Ergun’s Equation in Simulations of Heterogeneous Porous Medium Flow with Smoothed-Particle Hydrodynamics

Abstract

The flow of water through a channel with a heterogeneous porous layer in its central core is simulated using the method of Smoothed-Particle Hydrodynamics (SPH). Three different porous substrates are considered that differ in the geometry of their grain arrays. The heterogeneity is modeled by dividing the porous substrate into four zones that each have a different porosity. The pressure loss and the flow across the channel are simulated at two different scales, the pore scale and the Representative Elementary Volume (REV) scale, based on use of the Ergun equation. Since the computational cost at the REV scale is much lower than at the pore scale, it is therefore important to assess how accurately the REV-scale calculation reproduces the pore-scale results. The REV-scale simulation predicts cross-sectional mainstream velocity profiles and head losses through the channel that differ from the pore-scale results by root-mean-square errors of about 0.01% and 0.3%, respectively.