Modeling the effects of capillary pressure with the presence of full tensor permeability and discrete fracture models using the mimetic finite difference method

Capillary dominated flow or imbibition—whether spontaneous or forced—is an important physical phenomena in understanding the behavior of naturally fractured water-driven reservoirs (NFR’s). When the water flows through the fractures, it imbibes into the matrix and pushes the oil out of the pores due to the difference in the capillary pressure. In this paper, we focus on modeling and quantifying the oil recovered from NFR’s through the imbibition processes using a novel fully implicit mimetic finite difference (MFD) approach coupled with discrete fracture/discrete matrix (DFDM) technique. The investigation is carried out in the light of different wetting states of the porous media (i.e., varying capillary pressure curves) and a full tensor representation of the permeability. The produced results proved the MFD to be robust in preserving the physics of the problem, and accurately mapping the flow path in the investigated domains. The wetting state of the rock affects greatly the oil recovery factors along with the orientation of the fractures and the principal direction of the permeability tensor. We can conclude that our novel MFD method can handle the fluid flow problems in discrete-fractured reservoirs. Future works will be focused on the extension of MFD method to more complex multi-physics simulations.