LBM mesoscale modelling of porous media

Abstract

Permeability is one of the most important bulk properties for the characterization of fluid flow in porous media. However, despite all the considerable body of research work over the past years using experimental, analytical, and numerical approaches, its determination is still a challenge. The methodologies, which have been used to measure, calculate and predict the permeability of different types of porous media, in general, tend to suffer from various levels of limitations in their applicability and, moreover, no general correlation for the permeability is available. Among the different predictive methods for the permeability, numerical pore level fluid flow analyses have been receiving increasing attention in the recent years, due to its robustness and flexibility. In this approach, the viscous fluid flow is directly simulated in the pores of the porous medium with no further modelling required. A simple representation of the pore structure can be in the form of the ordered and random packings of spheres, cylinders or square obstacles. In the present paper, the main objective is to introduce the lattice Boltzmann method (LBM) as a powerful tool for the mesoscopic pore level fluid flow simulation in porous media; two and three-dimensional case studies are presented to demonstrate the capabilities of the mesoscale modelling for porous media fluid flow problems using LBM. To demonstrate an approximation to a reconstructed medium, the fluid flow simulation in a 2D random arrangement of square obstacles with different aspect ratios is presented. Results of the three-dimensional simulations of the fluid flow in ordered packings of spheres are also reported; the results are in excellent agreement with the available analytical correlation for this configuration.