A mimetic finite difference simulation method of multiphase flow in fractured reservoir considering capillarity and full tensor permeability

Key words:  spontaneous imbibition  mimetic finite difference  capillarity  full tensor permeability  discrete fractures

Abstract:

The mimetic finite difference method has been applied in the field of fluid mechanics, because it has good local conservation and is suitable for complex grids. In this paper, a two-phase flow model for fractured media based on the mimetic finite difference method was established, and the basic principles of the mimetic finite difference method were described in detail. In the new model, the capillarity was considered, and the corresponding scheme of fractured two-phase flow in fractured reservoirs was deduced. A full implicit scheme was used to solve the two-phase flow problem. The new method can overcome the shortcomings of the traditional method that cannot effectively deal with the full tensor permeability. In order to verify the correctness of the method and the robustness of the program, the accuracy and convergence of the mimetic finite difference method for fractured media under different wetting conditions were analyzed, and the method was also applied in a field case study. The results show that, when capillary pressure is considered, the water displacement front slowly passes through the matrix and fractures before reaching to the producing well, while the capillary pressure is ignored, the flow of water through the matrix is relatively slow, but the fluid flows rapidly through the fracture, reaching to the producing well quickly. The new method can accurately simulate the capillary pressure and gravity under different wetting conditions and at different fracture locations.