Unified permeability modeling for transitional Darcy/non-Darcy flow based on 3D pore-level numerical flow tests

Abstract

This study presents a unified representation of the seepage characteristics of virtual soil, including the transition zone from Darcy to non-Darcy flow, by conducting 3D pore-level fluid simulations. According to the concept of mathematical homogenization, the process of defining a virtual test region as a representative volume element (RVE) and then assessing the apparent permeability from virtual 3D pore flow tests in this region is established as “numerical seepage flow testing” (NSFT). Rigid particles of a single size are placed in the virtual test area, with two types of particle configurations: regularly arranged and randomly arranged. Both Darcy and non-Darcy flows are achieved by varying the macroscopic hydraulic gradients and other material or geometrical properties for NSFTs, such as grain diameter or porosity, and the macroscopic seepage flow characteristics are discussed in terms of the relationship between the apparent permeability and Reynolds number. After confirming that the individual relationships depend on the material or geometrical properties, we propose a unified expression of apparent permeability by introducing the “permeability reduction ratio”, and various empirically derived relationships between Darcy and non-Darcy flow speed and hydraulic gradient are used as references for this expression. To validate the proposed unified expression of apparent permeability over a wide range of Reynolds numbers, the NSFT results are illustrated as a relationship between the Reynolds number and permeability reduction ratio when the porosity is fixed. The illustrated relationships confirm that the permeability reduction ratio turns out to be a function of the Reynolds number and porosity only, thus validating the proposed unified expression. Additionally, the influence of the regularity of the particle arrangement and the particle size distribution characteristics of the NSFT specimens is raised as a factor determining the functional form of the permeability reduction ratio.