Mimetic finite difference simulation of multiphase flow in carbonate fractured media in presence of capillary pressure

Modelling fluid flows in fractured reservoirs is crucial to many recent engineering and applied science research. Various numerical methods have been applied, including finite element methods, finite volume methods. These approaches have inherent limitations in accuracy and application. Considering these limitations, in this paper, we present a novel mimetic finite difference (MFD) framework to simulate two phase flow accurately in fracture reservoirs. A novel MFD method is proposed for simulating multiphase flow through fractured reservoirs by taking advantage of unstructured mesh. Our approach combines MFD and finite volume (FV) methods. Darcy's equation is discreted by MFD method, while the FV method is used to approximate the saturation equation. The resulting system of equations is then imposed with suitable physical coupling conditions along the matrix/ fracture interfaces. This coupling conditions at the interfaces between matrix and fracture flow involve only the centroid pressure of fractures, which brings some simplification in analysis. The proposed approach is applicable for three dimensional systems. Moreover, it is applicable in arbitrary unstructured gridcells with full-tensor permeabilities. Some examples are implemented to show the performance of MFD method. The results showed a big potential of our method to simulate the flow problems with high accuracy and application.