Pore-Scale Modeling of Three-Phase Flow and the Effects of Wettability

We analyze fluid configurations in a single pore for three-phase flow in mixed-wet systems. After primary drainage solid surfaces in contact with oil may alter their wettability. We consider waterflooding followed by gas injection for any possible combination of oil/water, gas/water and gas/oil contact angles. We compute capillary pressures for the different displacement processes, find the range of capillary pressures for which the various fluid configurations are stable, and obtain expressions for the fluid saturations and conductances. We compute three-phase relative permeabilites for a bundle of tubes of different size with constant triangular cross sections. We model gas injection starting from different initial oil saturations, Soi. We show that the oil remains connected in wetting layers down to low oil saturation with a characteristic layer drainage regime. The only exceptions are non-spreading oils in water-wet media and large gas/oil contact angles. The relative permeability of the phase of intermediate wettability depends on both its own saturation and Soi, while the other relative permeabilities are functions of their own saturation only. In water-wet media, oil is the intermediate-wet phase. In weakly oil-wet media, water is intermediate-wet. In most strongly oil-wet media, gas is intermediate-wet. This contradicts the assumptions made in many empirical models that gas is always the most non-wetting phase and that its relative permeability depends only on the gas saturation. For media that contain regions of different wettabilitites, all three relative permeabilities may depend on both their own saturation and Soi. This work indicates appropriate functional dependencies for three-phase relative permeabilities, as well as being a necessary first step towards the development of a realistic three-dimensional, three-phase predictive pore-scale model that accounts for the effects of wettability.