Pore-scale modelling of fluid flow in porous media using the projection method for incompressible Navier-Stokes equations in irregular domains

Abstract

This paper presents the results of numerical simulation of incompressible viscous flow in porous media, which comprise periodically arranged cylinders. This simulation is based on the numerical solution of the incompressible Navier-Stokes equations in irregular domains using the projection method on staggered grids, where the irregular boundary is represented by its level-set function at the pore-scale level. The main problem in numerical calculation of fluid flow through porous media occurs when the value of the porosity is close to 1 or is close to the threshold value since it is necessary to take a very fine numerical mesh, which requires additional computing power and increases the calculation time. There are exact analytical solutions for simple types of porous media which consist of periodically arranged cylinders. In this paper, the permeabilities of these porous media were numerically calculated and compared with the previous works based on the numerical solution of the Lattice-Boltzmann equation in irregular domains, when the fluid flow obeys Darcy’s law. The comparison of numerical and theoretical values of porosity shows that this method is sufficiently accurate for porosity values φ=0.2–0.8.