*4.2. Effect of Anisotropic Relative Permeability on Remaining Oil Saturation*

In this section, we further study the effect of anisotropic relative permeability on the remaining oil saturation. It is indicated that the water flooding is uniform and the remaining oil is symmetrically distributed along the injection-production wells diagonal line in Case A. The remaining oil of Case A is mainly located near the two sides of the production well and is most enriched at both ends of the diagonal line perpendicular to the injection–production line. The water flooding process obviously shifts to the x direction in Case B, with less remaining oil in the x direction and more remaining oil in the y direction, which is consistent with the experimental results. The result of Case C is not similar to that of Case B. Though the permeability in the x direction is large, there is more remaining oil in the x direction. Case D is the superposition of Case B and Case C, and the process of water flooding obviously shifts in the x direction (Figure 5).

**Figure 5.** The remaining oil saturation distribution of the four cases at the 50th time step.

The area swept by injection water obviously shifts to the x direction in Case B because the relative permeability in the x direction is greater than that in the y direction. With regard to the phenomenon of Case C, we need to review the pressure distribution characteristics of Case C. Since the pressure at both the injection well and the production well propagates preferentially in the x direction, the injected water flows in the x direction first, and the production well also gives priority to producing oil in the x direction. Therefore, the process of water flooding does not seem to shift blindly to the x direction, but there is an equilibrium point on the injection–production line.

Before the equilibrium point, there is more remaining oil in the y direction, and after the equilibrium point, there is less remaining oil in the y direction. Here, we notice that case B and Case C have similar pressure propagation patterns, and the reason why there is such a big difference in remaining oil saturation is the relative permeability is affected by saturation. The relative permeability in the x direction is larger in Case B, the injected water is rapidly transferred near the production well, and the rapid increase in water saturation makes the flow capacity of water exceed that of oil. As a result, although the relative permeability in the x direction is larger, the movement ability of water in the y direction is higher than that of the oil in the x direction. Therefore, the remaining oil saturation of Case B occurs. However, the evolution of remaining oil saturation of Case C is different from that of Case B because it uses isotropic relative permeability and the absolute permeability is not affected by saturation. From the above analysis, it is not difficult to infer that the influence and mechanism of anisotropic relative permeability and absolute permeability on oil–water two-phase flow are different.
