A Physically Based Numerical Approach for Modeling Fracture-Matrix Interaction in Fractured Reservoirs

Abstract

Modeling fracture-matrix interaction within a multiple-phase flow system is a key issue for fractured reservoir simulation. Commonly used mathematical models for dealing with such interactions employ dual- or multiple-continuum concepts, in which fractures and matrix are represented as overlapping, different, but interconnected continua, described by parallel sets of conservation equations. The conventional single-point upstream weighting scheme is most commonly used to estimate flow mobility for fracture-matrix flow. However, such a scheme may have serious limitations or flaws, which lead to unphysical solutions or significant numerical errors. To overcome the limitations of the conventional upstream weighting scheme, this paper presents a physically based modeling approach for estimating physically correct relative permeability in calculating multiphase flow between fractures and the matrix, using continuity of capillary pressure at the fracture-matrix interface. The proposed approach has been implemented into two multiphase reservoir simulators and verified using analytical solutions and laboratory experimental data. The new method is demonstrated to be accurate, numerically efficient, and easy to implement in dual- or multiple-continuum reservoir simulators.