*4.1. Effect of Anisotropic Relative Permeability on Pressure Distribution*

In order to observe the effect of anisotropic relative permeability on pressure distribution, we made four cases, which are a homogeneous model with isotropic relative permeability (Case A), a homogeneous model with anisotropic relative permeability (Case

B), a heterogeneous model with isotropic relative permeability (Case C), and a heterogeneous model with anisotropic relative permeability (Case D). The pressure distribution results in these four cases are different, and they are very much affected by the heterogeneity of the relative permeability curves, which is different from Gomez-Hernandez's understanding. He proceeded with a derivation of the algorithm used to condition a realization of relative permeability to pressure and saturation data, and he observed that pressures are not very much affected by the heterogeneity of the relative permeability curves [36].

The results show that the pressure distribution uniformity between the injection well and the production well and the tangent of the pressure isoline along the diagonal is perpendicular to the diagonal line in Case A. In Case B, which considers the anisotropic relative permeability, the pressure propagation mode has changed, and the pressure distribution near the injection well and the production well has shifted in the x direction, and the relative permeability in the x direction is higher than that in the y direction. As far as this model is concerned, it seems that the pressure distribution in case A has been twisted counterclockwise. The pressure propagation of Case C is similar to that of Case B, but there is still a difference. The pressure propagation of Case D is also similar to that of Case B and Case C. However, the torsion of pressure distribution is more severe in Case D (Figure 4).

**Figure 4.** The pressure distribution of the four cases at the 50th time step.

The effective permeability, that is, the product of absolute permeability and relative permeability, determines the flow capacity of one phase in two-phase flow. It is found that both anisotropic absolute permeability and anisotropic relative permeability have an important influence on pressure distribution, and they are not equivalent and cannot be replaced each other, especially since the relative permeability is affected by fluid saturation and at the same time the change of relative permeability is not uniform. Obviously, the pressure propagation shifts to the direction of high relative permeability after considering the anisotropic relative permeability.
