Geometry models of porous media based on Voronoi tessellations and their porositypermeability relations
In this paper, we present methods that directly model the random structure of porous media using Voronoi tessellations. Three basic structures were generated and they correspond to porous medium geometries with intersecting fractures (granular), interconnected tubes (tubular), and fibers (fibrous). Fluid flow through these models was solved by a massively parallelized lattice Boltzmann code. We established the porositypermeability relations for these basic geometry models. It is found that, for granular and tubular geometries, the specific surface area is a critical structural parameter that can bring their porositypermeability relations together under a unified KozenyCarman equation. A connected fracture network, superimposed on the basic Voronoi structure, increases the dimensionless permeability relative to the KozenyCarman equation; isolated large pores (vugs), on the other hand, decreases the dimensionless permeability relative to the KozenyCarman equation. The KozenyCarman equation, however, cannot distinguish a heterogeneous structure with an embedded partially penetrating fracture. The porositypermeability relation for fibrous geometries in general agrees with those established for simple-cubic, body-centered cubic, and face-centered cubic models. In the dilute limit, however, the dependence on the solid fraction is weaker in Voronoi geometries, indicating weaker hydrodynamic interactions among randomly interconnected fibers than those in the idealized models.
porous media voronoi tessellation porositypermeability relation heterogeneity lattice boltzmann method parallel computing fibrous media