*4.3. Effect of Anisotropic Relative Permeability on Water Cut*

It is shown that Case A is the first to produce water, followed by Case C, Case B, and Case D, respectively. The reason for the difference can be made clear by comparing the corresponding remaining oil saturation. The flooding process of Case A is uniform, and it is the first to produce water. Most of the remaining oil distributes on both sides of the injection–production line near the production well. The sweep range of Case C is larger than that of Case A, so the time the model begins to produce water is later than in Case A. The flooding degree along the x direction in Case B is higher than Case C, as a result, Case B produces water later than Case C. Case D is affected by both anisotropic relative permeability and absolute permeability, and the degree of water flooding in x direction is the highest so it is the last to see water. However, although the time at which it sees the water is late, once there is a breakthrough, the later the breakthrough, the faster the water cut rises, and the higher the final water cut is (Figure 6).

**Figure 6.** The changing process of water cut of the four cases.

It can be seen from the water cut curves that when the water cut exceed 0.75, the difference between the water cut curves of the four cases is very small, and there is little difference in saturation. However, when the water cut is less than 0.75, there are obvious differences in breakthrough time and the rising speed of water cut. Because of the homogeneity or heterogeneity of the model itself and the relative permeability isotropy or anisotropy, the movement direction and velocity of the displacement fronts of reservoir are sensitive from the beginning of displacement, as described in Section 4.2. Due to the simplicity of the model and well pattern, after breakthrough, the injected water continues to spread to the unused remaining oil area, and the remaining oil is gradually produced. When the water cut reaches a certain value, the difference in saturation and water cut of the four cases gradually decreases.
