Effect of Initial Distribution of Two Fluids on Relative Permeability using Lattice-Boltzmann Method

We present results on two-phase flow simulation by Lattice-Boltzmann method (LBM). The Lattice-Boltzmann method can handle complicated pore geometries, such as porous media. We have shown the single-phase LBM estimates absolute permeability of porous media very accurately and efficiently. We extended the method to two-phase flow and will show some characteristics of the two-phase LBM method. We particularly focus on one aspect of two-phase flow - the effect of initial fluid distribution on relative permeability. We found our code for two-phase LBM honors laws of fluid dynamics and simulates corresponding physical parameters, such as capillary pressure and contact angle of the interface between solid and fluids. The simulated physical parameters showed very good agreement with theoretical predictions. After verifying that the two-phase LBM can simulate two-phase fluid flow through porous media, we applied the method to more complicated digital pore geometries; a Finney's random dense pack of spheres and samples from X-ray tomographic Fontainebleau sandstone. These were binary digital models describing the complex pore space. We used a steady state simulation that mimics a steady state measurement in laboratory. We experimented with four different kinds of the initial distribution of two fluids; (1) uniform distribution (fine mixture), (2) random distribution, (3) coating the grains with the wetting fluid, and (4) patch distribution. We found small differences in relative permeability with various initial distributions of two fluids. Although the final distributions were a little different due to different initial distributions, the relative permeability, which is a macroscopic value, was not much different. The difference at intermediate wetting-phase saturation was greater than one at low or high wetting-phase saturation. The patch type initial saturation showed the biggest difference among the initial distributions of two fluids.