Capturing Local Fluid Field Characteristics in Porous Media using Pore Network Models

Abstract

Pore Network Models (PNMs) provides a computationally efficient approach to model porous media. A PNM employs a network representation of the pore space, where individual pores are taken as nodes of the network and are connected by constrictions which are edges of the network. In assemblies of spheres, this network representation is often achieved using Delaunaybased tessellation methods. Fluid flow is simulated in the network model using a Stokes flow algorithm which solves for continuity at each node in the network using a local conductivity model. The seepage induced drag forces can be obtained from the resulting flow field and geometric properties of the pores and constrictions. While PNMs are computationally efficient, there is a simplification of the pore space geometry and governing fluid equations. To better understand these assumptions, the local flow field and seepage induced drag obtained from a PNM is compared to fully-resolved Immersed Boundary Method (IBM) simulations. The local pressure field was very accurately captured, while the local flow rate exhibited slightly more scatter and sensitivity to the tessellation method. There was a close similarity in the network shortest paths, indicating that PNM captures dominant flow channels. Comparison of streamline profiles demonstrated that local pressure drops coincided with pore constrictions. In addition, the fluid-particle interaction force was determined reasonably accurately using PNMs. This suggests that a PNM is a viable option to investigate the local behaviour in porous media.