Pore-Scale Modeling of Spontaneous Imbibition in Porous Media Using the Lattice Boltzmann Method

A new color-gradient lattice Boltzmann model is developed to simulate spontaneous imbibition in a porous media micromodel, which needs only two-dimensional computational cost but considers essential three-dimensional effects. A modified periodic boundary condition is introduced to deal with inlet and outlet boundaries with great ease and effectiveness. This model is first validated against analytical solutions and micromodel experiment. It is then used to study the spontaneous imbibition process in a homogeneous micromodel for varying viscosity ratios and contact angles. Depending on the viscosity ratio (λ) of wetting to nonwetting fluids, three different imbibition patterns are observed, namely unstable displacement (UD), stable displacement (SD), and crossover from UD to SD, which occur at (Formula presented.), (Formula presented.), and (Formula presented.), respectively. When the crossover occurs, the wetting fluid saturation at breakthrough increases between two plateaus corresponding to UD and SD, respectively. Consistent with theoretical predictions from a single capillary, the wetting fluid saturation versus time follows the relation of (Formula presented.) for (Formula presented.), and (Formula presented.) for (Formula presented.). Due to the increased capillary valve resistance, increasing wetting phase contact angle is found to promote the flow instability, resulting in the development of preferential flow paths and thus some nonwetting fluid trapped in the flow direction. In addition, it is theoretically and numerically demonstrated that the effect of contact angle cannot be properly described by the theoretical equations derived from a single capillary because of the presence of capillary valve effect, which can be suppressed by decreasing contact angle or micromodel depth.