The Application of Lattice Gas Automata to Study Fluid Flow in Porous Media

Abstract

Abstract This research reports on the development of a two dimensional lattice gas automata (LGA) model to simulate fluid flow in porous media. In lattice gas automata simple rules of particle interactions at a lattice are used to simulate complex flow phenomena. Since the numerical operations involved are largerly bit manipulations, lattice gas automata can be potentially more efficient in memory usage than conventional methods, such as finite difference or finite element methods. There are basically two motivations for the utilisation of lattice-gas automata methods for studying fluid flow in porous media. First, the no-slip boundary condition of hydrodynamics is easily implemented as a simple bounce-back reflection at solid walls. Second, the discrete nature of the lattice-gas method makes it computationally efficient in terms of the work necessary to update a single site of the lattice. Fluid flow in porous media is generally described by Darcy's law, which linearly relates fluid velocity to pressure gradient. Other research on the use of lattice gas automata to model fluid flow in porous media primarily focuses on Stokes flow at the pore level with the intent of understanding flow at the core scale. This work concentrates on modeling Darcy flow in a heterogeneous field. Permeability variations and anisotropy are modeled by a distribution of scatter. Collision of incoming particles with scatterers is a stochastic process.