Simulation of Flow in Multi-Scale Porous Media Using the Lattice Boltzmann Method on Quadtree Grids (Communications in Computational Physics, 2018)
The unified lattice Boltzmann model is extended to the quadtree grids forsimulation of fluid flow through porous media. The unified lattice Boltzmann modelis capable of simulating flow in porous media at various scales or in systems wheremultiple length scales coexist. The quadtree grid is able to provide a high-resolutionapproximation to complex geometries, with great flexibility to control local grid density.The combination of the unified lattice Boltzmann model and the quadtree grids resultsin an efficient numerical model for calculating permeability of multi-scale porousmedia. The model is used for permeability calculation for three systems, includinga fractured system used in a previous study, a Voronoi tessellation system, and acomputationally-generated pore structure of fractured shale. The results are comparedwith those obtained using the conventional lattice Boltzmann model or the unified latticeBoltzmann model on rectangular or uniform square grid. It is shown that the proposedmodel is an accurate and efficient tool for flow simulation in multi-scale porousmedia. In addition, for the fractured shale, the contribution of flow in matrix and fracturesto the overall permeability of the fractured shale is studied systematically.