Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice Boltzmann method

We describe an implementation of the recently proposed lattice Boltzmann based model of Shan and Chen [Phys. Rev. E 47, 1815 (1993); 49, 2941 (1994)] to simulate multicomponent flow in complex three-dimensional geometries such as porous media. The above method allows for the direct incorporation of fluid-fluid and fluid-solid interactions as well as an applied external force. As a test of this method, we obtained Poiseuille flow for the case of a single fluid driven by a constant body force and obtained results consistent with Laplace's law for the case of two immiscible fluids. The displacement of one fluid by another in a porous medium was then modeled. The relative permeability for different wetting fluid saturations of a microtomography-generated image of sandstone was calculated and compared favorably with experiment. In addition, we show that a first-order phase transition, in three dimensions, may be obtained by this lattice Boltzman method, demonstrating the potential for modeling phase transitions and multiphase flow in porous media.