A discrete fracture model for two-phase flow involving the capillary pressure discontinuities in fractured porous media

Abstract

The discrete fracture model (DFM) has been widely used to describe the flow problems in fractured media. In low-permeability media with conductive fractures embedded in, there is large capillary pressure contrast between fracture and matrix. It may cause very sharp changes of physical quantities near the matrix-fracture interface, which makes it difficult to calculate the matrix-fracture transfer flux accurately in the traditional DFM. In this article, mathematical analysis for the flow characteristics near the matrix-fracture interface is present. Three flow patterns can be distinguished for the two-phase steady flow across the matrix-fracture interface under the assumption of negligible capillary pressure in fracture. The analytical solutions for the three different patterns are derived and then employed to construct an alternative numerical scheme of calculating matrix-fracture transfer flow rate. Numerical examples show that the calculated results of the proposed model are in agreement with the reference solution. It indicates that the proposed model can overcome the difficulty of accurately predicting the matrix-fracture transfer flux in the traditional numerical scheme and then dramatically improve the computational accuracy for the two-phase flow in low-permeability reservoirs with conductive fractures.