A multiscale mixed finite element method with oversampling for modeling flow in fractured reservoirs using discrete fracture model

Abstract

Fractures play a significant effect on the macro-scale flow, thus should be described exactly. 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, considering the computational efficiency and accuracy, traditional numerical methods are not suitable for DFM. In this study, a multiscale mixed finite element method (MsMFEM) is proposed for detailed modeling of two-phase oil–water flow in fractured reservoirs. In MsMFEM, the velocity and pressure are first obtained on coarse grid. The interaction between the fractures and the matrix is captured through multiscale basis functions calculated numerically by solving DFM on the local fine grid. Through multiscale basis functions, this method can not only reach a high efficiency as upscaling technology, but also finally generate a more accurate and conservative velocity field on the full fine-scale grid. In our approach, oversampling technique is applied to get more accurate small-scale details. Triangular fine-scale grid is applied, making it possible to consider fractures in arbitrary directions. The validity of MsMFEM is proved through comparing experimental and numerical results. Comparisons of the multiscale solutions with the full fine-scale solutions indicate that the later one can be totally replaced by the former one. The results demonstrate that the multiscale technology is a promising method for multiscale flows in high-resolution fractured media.