In this paper, we develop a multiscale model reduction technique thatdescribes shale gas transport in fractured media. Due to the pore-scaleheterogeneities and processes, we use upscaled models to describe the matrix.We follow our previous work \cite{aes14}, where we derived an upscaled model inthe form of generalized nonlinear diffusion model to describe the effects ofkerogen. To model the interaction between the matrix and the fractures, we useGeneralized Multiscale Finite Element Method. In this approach, the matrix andthe fracture interaction is modeled via local multiscale basis functions. Wedeveloped the GMsFEM and applied for linear flows with horizontal or verticalfracture orientations on a Cartesian fine grid. In this paper, we considerarbitrary fracture orientations and use triangular fine grid and developedGMsFEM for nonlinear flows. Moreover, we develop online basis functionstrategies to adaptively improve the convergence. The number of multiscalebasis functions in each coarse region represents the degrees of freedom neededto achieve a certain error threshold. Our approach is adaptive in a sense thatthe multiscale basis functions can be added in the regions of interest.Numerical results for two-dimensional problem are presented to demonstrate theefficiency of proposed approach.
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