Monotone Embedded Discrete Fracture Method for the Two-Phase Flow Model

Abstract

We propose an application of the new monotone embedded discrete fracture method (mEDFM) [13] to the two-phase flow model. The new method for modelling of flows in fractured media consists in coupling of the embedded discrete fracture method (EDFM) with the nonlinear monotone finite volume (FV) scheme with two-point flux approximation, which preserves non-negativity of the discrete solution. The resulting method combines effectiveness and simplicity of the standard EDFM approach with accuracy and physical relevance of the nonlinear FV schemes for non-orthogonal grids and anisotropic media. Numerical experiments show that the two-phase flow modelling with the mEDFM provides much more accurate solution compared to the conventional EDFM, and is in a good agreement with the discrete fracture method, which directly applies the nonlinear FV method to a grid with fractures explicitly represented by 3D cells.