Compositional Modeling of Fractured Reservoirs Without Transfer Functions by the Discontinuous Galerkin and Mixed Methods

Abstract

Abstract In a recent work, we introduced a numerical approach that combines the mixed finite element (MFE) and the discontinuous Galerkin (DG) methods for compositional modeling in homogeneous and heterogeneous porous media. In this work, we extend our numerical approach to fractured media. We use the discrete fracture model (crossflow equilibrium) to approximate the two-phase flow with mass transfer in fractured media. The discrete fracture model is numerically superior to the single-porosity model and overcomes limitations of the dual-porosity model including the use of a shape factor. The MFE method is used to solve the pressure equation where the concept of total velocity is invoked. The DG method associated with a slope limiter is used to approximate the species balance equations. The cell-based finite volume schemes that are adapted to a discrete fracture model have deficiency in computing the fracture-fracture fluxes across three and higher intersecting fracture branches. In our work, the problem is solved definitively due to the MFE formulation. Several numerical examples in fractured and unfractured media are presented to demonstrate the superiority of our approach to the classical finite difference and finite volume methods.