Introduction

The lattice Boltzmann (LB) method has evolved into a powerful computational method for the modeling of fluid flow in complex geometries like porous media. It naturally accommodates a variety of boundary conditions such as the pressure drop across the interface between two fluids and wetting effects at a fluid-solid interface. Since the LB method can be derived from the Boltzmann equation, its physical underpinnings can be understood from a fundamental point of view. In addition, the LB method generally needs nearest neighbor information at most so that it is ideally suited for parallel computers. While LB methods are developing rapidly in response to recent theoretical advances and the availability of resources for large scale computation, there is still a lack of critical comparisons between experimental results and simulation. Such comparisons are crucial, not only to validate LB methods, but to further their development. In this paper we examine the utility of the Shan and Chen[1] model of multicomponent fluids for describing large scale flow in complex geometries. This model has been adapted to three dimensions and extended to include fluid-solid interactions and applied forces [2]. After a brief review of the theory of the LB method, results are presented to validate predictions of fluid flow through a few simple pore geometries. Large scale simulations of fluid flow through a Fontainebleau sandstone microstructure, which was generated by X-ray microtomography, will then be presented. Single phase flow calculations were carried out on 510³ systems. We also calculate relative permeability curves as a function of fluid saturation and driving force. The Onsager relation, which equates off-diagonal components of the permeability tensor for two phase flow, is found not to hold for intermediate to low nonwetting saturation as the flow response to an applied body force was nonlinear. Values of relative permeability from three phase flows were compared to corresponding two phase values. Finally, a comparison of the performance of such codes on different computing platforms is given.