Numerical simulation of oil-water displacements in naturally fractured reservoirs using a hybrid grid MPFA-streamline (SLS-HyG) formulation

The numerical simulation of fluid displacements in naturally fractured reservoirs is rather expensive in terms of CPU requirements and challenging, due to the random spatial distribution of fractures of different sizes and shapes. In this paper, we present a numerical formulation to simulate the 2-D two-phase flow of oil and water in naturally fractured oil reservoirs using unstructured quadrilateral meshes. In our Hybrid-Grid MPFA-Streamline (SLS-HyG) formulation, the elliptic pressure equation is discretised by a finite volume method with a Multipoint Flux Approximation using a Diamond stencil. This formulation is able to handle a full permeability tensor representation in an arbitrary polygonal grid. For the advective saturation problem, we used the streamline-based method, which decouples the transport equations into several 1-D problems solved along each streamline. These formulations were implemented in the framework of the Hybrid-Grid (HyG) representation of fractures, where the fractures in the physical domain are represented by 1-D objects in 2-D domains and extended to the same dimension of the matrix problem. The coupling between the flow and the transport problem is done by a modified implicit pressure explicit saturation procedure. We have solved some reference problems from the literature, obtaining promising results when compared to other classical formulations.