To illustrate the lubrication effect, we provide a 2D image showing the distribution of nonwetting fluid, wetting fluid, and solid rock at the final state of the simulation with S nw =50%,M = 5, and log Ca of −0.25 (Fig. 3). Because the wetting fluid layer is always present between the nonwetting fluid and the rock, the wetting fluid moves along the rock surface and the nonwetting phase is confined to the central part of the pore. Thus, the velocity of the nonwetting fluid is affected only by the momentum transfer across fluid–fluid interfaces and not by contact with the pore wall.
At sufficiently high values of M , the wetting fluid acts as a lubricant that enhances the movement of the nonwetting fluid, making its permeability higher than in the single-phase condition such thatk nw is greater than 1 (Fig. 2a). This lubrication effect most strongly affects k nw in the intermediate S nw range, when the wetting fluid forms thick films that provide the nonwetting fluid with a moving boundary (Vafai, 2000). At low S nw, the nonwetting phase tends to form droplets with low connectivity; thus, the lubrication effect is less pronounced. At highS nw, k nw also decreases toward unity because less wetting fluid is present in the rock and the nonwetting phase comes into contact with the rock, degrading the lubrication effect and reducing k nw near to the single-phase condition. Because the lubrication effect occurs at highM values, it is commonly observed in mixtures of heavy oil and water in EOR systems and has been confirmed by experimental results (Goel et al., 2016; Shad et al., 2008).
Our results demonstrate that k w decreases asM increases (Fig. 2b). This phenomenon can be attributed to the increase of shear drag force from the nonwetting phase. As Mincreases, the viscosity of the nonwetting fluid increases, which inhibits the flow of the wetting fluid such that it has a lowerk w.