Generalized multiscale finite element methods for the reduced model of darcy flow in fractured porous media

Abstract

In this work, we combine the generalized multiscale finite element method (GMsFEM) with a reduced model based on the discrete fracture model (DFM) to resolve the difficulties of simulating flow in fractured porous media while efficiently and accurately reducing the computational complexity resulting from resolving the fine scale effects of the fractures. The geometrical structure of the fractures is discretely resolved within the model using the DFM. The advantage of using GMsFEM is to represent the fracture effects on a coarse grid via multiscale basis functions constructed using local spectral problems. Solving local problems leads to consideration and usage of small scale information in each coarse grid. Besides, the multiscale basis functions, generated following GMsFEM framework, are parameter independent and constructed once in what we call offline stage. These basis functions can be re-used for solving the problem for any input parameter when it is needed. Combining GMsFEM and DFM has been introduced in other works assuming continuous pressure across the fractures interface. This continuity is obtained when the fractures are much more permeable than that in the matrix domain. In this work, we consider a general case for the permeability in both fracture and matrix domain using the reduced model presented in Martin et al. (2005). The proposed reduction technique has significant impact on enabling engineers and scientist to efficiently, accurately and inexpensively solve the large and complex system resulted from modeling flow in fractured porous media