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, such as the transition zone from low‐velocity Darcy flow to high‐velocity non‐Darcy flow, by conducting 3D pore‐level fluid simulations. 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 low‐velocity Darcy and high‐velocity non‐Darcy flows are achieved by varying the macroscopic hydraulic gradient and other material or geometrical properties of the NSFT, such as the grain diameter or porosity, and the macroscopic seepage flow characteristics are discussed in terms of the relationship between the apparent permeability and the Reynolds number. We confirm that the individual relationships rely on the material or geometrical properties, propose a unified expression for apparent permeability by introducing the “permeability reduction ratio,” and use various empirically derived relationships between Darcy and non‐Darcy flow speeds and hydraulic gradients as references for this expression. The derived relationships confirm that the permeability reduction ratio is a function of the Reynolds number and porosity only, thus validating the proposed unified expression. Additionally, the effect of the regularity of the particle arrangement and the particle size distribution characteristics of the NSFT specimens are a factor that determines the functional form of the permeability reduction ratio.