Ability of a pore network model to predict fluid flow and drag in saturated granular materials

TL;DR

This study evaluates the effectiveness of pore network models in predicting fluid flow and drag in saturated granular materials by comparing them with detailed immersed boundary simulations, demonstrating good accuracy especially in pressure fields and flow channels.

Contribution

The paper introduces a pore network modeling approach using Delaunay tessellations that accurately predicts local pressure, flow paths, and drag forces, validated against detailed IBM simulations.

Findings

PNM accurately captures local pressure fields.

PNM shows good correlation with IBM for flow channels.

Linear graded samples predict drag forces reasonably well.

Abstract

The local flow field and seepage induced drag obtained from Pore Network Models (PNM) is compared to Immersed Boundary Method (IBM) simulations, for a range of linear graded and bimodal samples. PNM were generated using a weighted Delaunay Tessellation (DT), along with the Modified Delaunay Tessellation (MDT) which considers the merging of tetrahedral Delaunay cells. The local pressure field was very accurately captured in all linear graded and bimodal samples. Local flux (flow rate) exhibited more scatter, but the PNM based on the MDT clearly provided a better correlation with the IBM. There was close similarity in the network shortest paths obtained from PNM and IBM, indicating that the PNM captures dominant flow channels. Further, by overlaying the PNM on a streamline profile, it was demonstrated that local pressure drops coincided with the pore constrictions. A rigorous validation was undertaken for the drag force calculated from the PNM by comparing with analytical solutions for ordered array of spheres. This method was subsequently applied to all linear graded and bimodal samples, and the calculated force was compared with the IBM data. Linear graded samples were able to calculate the force with reasonable accuracy, while the bimodal sample exhibited slightly more scatter.