AN EVALUATION OF RELATIVE PERMEABILITY AND THE CAPILLARY PRESSURE-SATURATION RELATIONSHIP IN POROUS MEDIA USING LATTICE-BOLTZMANN METHODS

Classic macro-scale multiphase models rely on the extended version of Darcy’s law taking into account empirical relationships of both relative permeability and capillary pressure versus wetting-phase saturation. These relationships can be captured at the microscopic scale by lattice-Boltzmann methods. Here, we present results from three-dimensional pore-scale simulations of two-phase flow in a body-centered sphere packed bed. The simulations are conducted using an immiscible, two-color, Bhatnagar-Gross-Krook lattice-Boltzmann model. In order to maintain constant phase saturation, fluids are driven by a body force in a domain with fully periodic boundary conditions. The body force is chosen small enough to guarantee that the two-phase flow is controlled by capillary forces. We first test the accuracy of this model by determining the known absolute permeability under single-phase flow. At steady state, the relative permeability is then calculated as the product of two terms, one being the ratio of the total velocity of a particular phase to the single-phase velocity, and the other being the ratio of the driving pressure for a single-phase flow to the two-phase flow. The relationship between capillary pressure and wetting phase saturation is also studied and compared to the empirical relationship.