Accurate multiscale finite element method for numerical simulation of two-phase flow in fractured media using discrete-fracture model

Abstract

Numerical simulation in naturally fractured media is challenging because of the coexistence of porous media and fractures on multiple scales that need to be coupled. We present a new approach to reservoir simulation that gives accurate resolution of both large-scale and fine-scale flow patterns. Multiscale methods are suitable for this type of modeling, because it enables capturing the large scale behavior of the solution without solving all the small features. Dual-porosity models in view of their strength and simplicity can be mainly used for sugar-cube representation of fractured media. In such a representation, the transfer function between the fracture and the matrix block can be readily calculated for water-wet media. For a mixed-wet system, the evaluation of the transfer function becomes complicated due to the effect of gravity.In this work, we use a multiscale finite element method (MsFEM) for two-phase flow in fractured media using the discrete-fracture model. By combining MsFEM with the discrete-fracture model, we aim towards a numerical scheme that facilitates fractured reservoir simulation without upscaling. MsFEM uses a standard Darcy model to approximate the pressure and saturation on a coarse grid, whereas fine scale effects are captured through basis functions constructed by solving local flow problems using the discrete-fracture model. The accuracy and the robustness of MsFEM are shown through several examples. In the first example, we consider several small fractures in a matrix and then compare the results solved by the finite element method. Then, we use the MsFEM in more complex models. The results indicate that the MsFEM is a promising path toward direct simulation of highly resolution geomodels.