Investigation on the influence of capillary number on drainage in porous media using a lattice Boltzmann method

Abstract

This work investigates the effect of the capillary number on the saturation of wetting and nonwetting phases during processes of drainage. A multicomponent Lattice Boltzmann model with a two-relaxation time scheme is used to simulate the flow in 2D and 3D digital models of porous rocks. The capillary number is varied by setting different values of the fluid inlet velocity, while viscosity and interfacial tension are fixed. The results show the invasion of nonwetting phase in the narrow pores of the media, forcing the wetting fluid to leave through the outlet. Different patterns are observed depending on the capillary number and the degree of porosity and heterogeneity of the models. Several pore-scale events are observed and play an important role in the trapping of wetting fluid. The nonwetting phase saturation is measured at breakthrough and quasi-steady states. In 2D models, the effect of the low velocity of the fluid at low Ca provides a better condition for fluid redistribution, causing a higher nonwetting fluid saturation. In 3D models, a lower value of Ca leads to more trapped wetting fluid mainly because of the media geometries. In all cases, the highest Ca range resulted in the highest nonwetting fluid saturation at a quasi-steady state. The saturation and relative permeability curves at the point of irreducible wetting phase saturation show that the degree of heterogeneity in 3D models has an important effect on sweeping effectiveness, which seems to be more significant than porosity or intrinsic permeability of the models.