Modeling of three-phase displacement in three-dimensional irregular geometries using a lattice Boltzmann method

Three-phase displacement process in a porous media is significantly influenced by wettability of the solid surfaces. It remains a research challenge to model and simulate three-phase flows with moving contact lines, especially on arbitrary complex three-dimensional surfaces. We propose a color-gradient lattice Boltzmann model to simulate immiscible three-phase flows with contact-line dynamics. Unlike the previous models in dealing with wettability through assigning virtual mass fractions to the solid surfaces, the present model realizes the prescribed contact angles by correcting the orientation of the color-gradient parameter at the solid surfaces. We first validate this model against analytical solutions by simulating several typical cases, including a Janus droplet deposited on a flat surface and on a spherical surface, and the spontaneous imbibition of ternary fluids in a cylindrical tube. We then use it to study the displacement of residual oil during tertiary gas injection process. To mimic this process, gas is injected into a simple pore-throat connecting structure after water flooding. Results show that in displacement process, an oil spreading layer forms, which changes the oil flow state from adhering to the bottom wall to spreading over the entire interface between gas and water. Therefore, residual oil can be easily recovered in the form of gas-to-oil-to-water double displacement chain, leading to a high oil recovery regardless of the wetting properties of the solid surface. In the cases without the presence of oil spreading layer, increasing capillary number favors the oil recovery under certain wetting conditions only.