Two‐phase flow in complex porous media using Lattice‐Boltzmann method

Abstract

Summary We present results on two-phase flow simulation by Lattice-Boltzmann method. In this paper we focus on the steady state simulation that has a fixed saturation of nonwetting and wetting fluids. We used three rock models; Finney’s random dense pack of spheres and two samples of X-ray tomographic Fontainebleau sandstone. These were binary digital models describing the complex pore space. We investigated three aspects of two-phase flow; effect of initial distribution of two fluids on relative permeability, role of wetting fluid at low wetting fluid saturation, and relative permeability under different pressure gradient and surface tension. We found very 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 was almost identical. At high water saturation, even though the nonwetting phase is not connected, they form blobs and move with the wetting phase. Thus the relative permeability of non-wetting phase is still considerable. In the next step, we investigated the role of wetting fluid at low wetting fluid saturation. Many studies and laboratory measurements have shown that small amount of water does not affect relative permeability of non-wetting phase. We observed same results from our simulation. In our digital rock samples, the permeability of non-wetting phase changed very little at a range of less than 10% wetting saturation. However, if we replace the small amount of water trapped in small pores by solid grain, the relative permeability of non-wetting phase decreases dramatically even for very small reduction of porosity. The small amount of wetting phase effectively reduces the viscous effect between grain boundary and nonwetting phase. Lastly, we explored two different regimes of pressure gradient (∆P) and surface tension (σ); when ∆P ≈ σ and when ∆P >σ . We observed the relative permeability of non-wetting phase increases with pressure gradient, while that of wetting phase stays almost the same. The amount of the relative permeability increase strongly depends on the details of pore geometry. In conjunction with lab calibration, this two-phase flow simulation provides a powerful computational tool for efficient estimation of multiphase fluid-flow with different physical parameters, and can complement physical lab measurement.