Darcy and inertial fluid flow simulations in porous media using the non-orthogonal central moments lattice Boltzmann method

Abstract

In this study, two-dimensional (2D) and three-dimensional (3D) lattice Boltzmann method (LBM) has been investigated using the non-orthogonal central moments collision method in order to study the Darcy and inertial (non-Darcy) fluid flow in porous media. A GPU parallel CUDA code has been developed and is employed to study the proposed method. A comparative study has been performed between the non-orthogonal central moments method and the Bhatnagar–Groos–Krook (BGK) method to measure the permeability. The effect of selecting sets of relaxation times and no-slip boundary conditions has been investigated using the 2D hexagonal and 3D body-centered cubic (BCC) structure, and an appropriate model has been presented for flow simulation in porous media. The comparison of the permeability obtained by the proposed numerical method with the analytical solutions shows that the proposed model is highly accurate and eliminates the dependence of permeability on the viscosity, which is one of the problems in the LBM. This model’s capability has been evaluated to simulate Darcy and inertial flows using 2D hexagonal geometry, 2D granular porous media with a random structure, 3D BCC geometry, 3D porous media with a random structure, and real porous media created by using computed tomography (CT) images. In addition, the apparent permeability, the non-Darcy β factor, and the onset of non-Darcy flow have been predicted to demonstrate the capability of the proposed method. The results show the high capability of the proposed model for fluid flow simulation in porous media with complex geometries; so, this model can be used as a powerful and stable tool with the capability of fluid flow simulation in porous media from the Darcy regime to large Reynolds numbers and the inertial regime.