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. 1996 The American Physical Society.