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 2D 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 because of the MFE formulation. Several numerical examples in fractured media are presented to demonstrate the superiority of our approach to the classical finite-difference method.
Compositional modeling in fractured media has broad applications in CO2, nitrogen, and hydrocarbon-gas injection, and recycling in gas condensate reservoirs. In addition to species transfer, the compressibility effects should be also considered for such applications. Heterogeneities and fractures add complexity to the fluid-flow modeling. Several conceptually different models have been proposed in the literature for the simulation of flow and transport in fractured porous media.
The single-porosity approach uses an explicit computational representation for fractures (Ghorayeb and Firoozabadi 2000; Rivière et al. 2000). It allows the geological parameters to vary sharply between the matrix and the fractures. However, the high contrast and different length scales in the matrix and fractures make the approach unpractical because of the ill conditionality of the matrix appearing in the numerical computations (Ghorayeb and Firoozabadi 2000).The small control volumes in the fracture grids also add a severe restriction on the timestep size because of the Courant-Freidricks-Levy (CFL) condition if an explicit temporal scheme is used.