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

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. Two local conductivity models are compared in simulating fluid flow in the PNM. The local pressure field was very accurately captured, while the local flux (flow rate) exhibited more scatter and sensitivity to the choice of the local conductance model. PNM based on the MDT clearly provided a better correlation with the IBM. There was close similarity in the network shortest paths, indicating that the PNM captures dominant flow channels. Comparison of streamline profiles 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 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 samples exhibited slightly more scatter.

Physical observations of the transient evolution of the porosity distribution during internal erosion using spatial time domain reflectometry

“…These observations on the transient evolution of the porosity distribution demonstrates the capability of spatial TDR to make physical observations of the mixing process in filtration experiments from onset to progression. Ongoing research aims to employ these physical observations for calibration of numerical particle-scale simulations of the filtration process using coupled computational fluid mechanics and discrete element method (Smith et al, 2020;Che et al, 2021) and pore network models (van der Linden et al, 2018;Sufian et al, 2019). These physical observations can also be applied to large deformation models employing smooth particle hydrodynamic or the material point method.…”

A Perspective on Darcy’s Law across the Scales: From Physical Foundations to Particulate Mechanics

“…Taylor et al (2017)) or the conductance that governs flow in an individual pore throat (e.g. Sufian et al (2019)). As discussed below, homogenization approaches can be applied.…”

“…Partitioning is non-trivial as the void space is continuous and no partitioning algorithm can be wholly objective. For example, Sufian et al (2019) compare PNMs obtained using slightly different approaches to partitioning.…”

Towards replacing physical testing of granular materials with a Topology-based Model

“…In contrast to solving the elliptic Navier-Stokes equations on the void space using FEM, immersed boundary methods, or lattice-Boltzmann methods, solving the PNM can be done with simple Gauss-Seidel over relaxation [16] and conservation of mass, or a solution to a system of linear equations with nodal analysis. Sufian et al [41] showed that the PNMs accurately predict the drops in pressure between pores when compared to numerical solutions of the Navier-Stokes equations. Gackiewicz et al [15] also showed that PNMs computed with the maximum-ball and Delaunay method agreed with FEM solutions to the Navier-Stokes equations for sphere packed materials.…”