An Efficient Multiscale Mixed Finite Element Method for Modelling Flow in Discrete Fractured Reservoirs

Abstract

Fractures can significantly impact the flow patterns of carbonate reservoirs and should be accurately accounted for in a geological model. Accurate modeling of flow in fractured media is usually done by discrete fracture model (DFM), as it provides a detailed representation of flow characteristic. However, DFM poses a particular challenge to traditional numerical method with regard to computational efficiency and accuracy. In this study, a multiscale mixed finite element method (MsMFEM) has been proposed for detailed modeling of two-phase oil-water flow in fractured reservoirs. The MsMFEM uses a standard Darcy model to approximate pressure and fluxes on a coarse grid. Fine-scale effects of fractured media are captured through basis functions constructed numerically by solving local DFM on the fine-scale grid. In our approach, we consider arbitrary fracture orientations and use triangular fine grid. Through multiscale basis functions, we can maintain the efficiency of an upscaling technology, while at the same time generate a more accurate and conservative velocity field on the full fine-scale grid. Comparisons of the multiscale solutions to the fine-scale discrete fracture model solutions indicate that the fine-scale flow in fracture networks can be represented within a coarse-scale Darcy flow model. The results demonstrate that the MsMFE technology is a promising method toward fine flow simulation of high-resolution geological models of fractured reservoirs.