Influence of fractal surface roughness on multiphase flow behavior: Lattice Boltzmann simulation

Accurate characterization of surface roughness and understanding its influence on multiphase flow behavior are important for industrial and environmental applications such as enhanced oil recovery, CO2 geological sequestration, and remediation of contaminated aquifers. Although some experimental and simulation studies have been conducted for investigating surface roughness in regular geometry structures, a more realistic description of roughness and its quantitative influence on multiphase flow need to be further explored. In this study, an optimized color-gradient lattice Boltzmann model is applied to simulate the steady-state two-phase flow in two-dimensional porous media modeled by a fourth-order Sierpinski carpet. The model is validated by comparing with the analytical solution and literature results, indicating reliability of our method. Then, rough surfaces with different roughness height and surface fractal dimension are characterized by a modified Weierstrass-Mandelbrot function and these effects on two-phase flow are investigated systematically by our model. The results show that the surface roughness has a negative effect on single-phase and two-phase fluid flow, which implies that the absolute and relative permeabilities for both wetting phase and nonwetting phase decreases with the increase of roughness height or surface fractal dimension. In addition, the surface roughness has influence on the two-phase distribution, velocity distribution and fluid-fluid/fluid-solid interface area, especially under the neutral wetting condition. Our study provides a pore-scale insight into the effect of surface roughness on two-phase flow, which is important for a fundamental understanding on macroscopic multiphase flow behaviors.