Multiscale model reduction for shale gas transport in fractured media

TL;DR

This paper introduces a multiscale model reduction technique using GMsFEM for simulating nonlinear shale gas transport in fractured media with arbitrary fracture orientations, improving computational efficiency and adaptability.

Contribution

The paper extends GMsFEM to nonlinear flows with arbitrary fracture orientations and develops online basis functions for adaptive accuracy improvement.

Findings

Efficient simulation of nonlinear shale gas transport in fractured media.

Adaptive multiscale basis functions enhance convergence.

Numerical results demonstrate the method's effectiveness.

Abstract

In this paper, we develop a multiscale model reduction technique that describes shale gas transport in fractured media. Due to the pore-scale heterogeneities and processes, we use upscaled models to describe the matrix. We follow our previous work \cite{aes14}, where we derived an upscaled model in the form of generalized nonlinear diffusion model to describe the effects of kerogen. To model the interaction between the matrix and the fractures, we use Generalized Multiscale Finite Element Method. In this approach, the matrix and the fracture interaction is modeled via local multiscale basis functions. We developed the GMsFEM and applied for linear flows with horizontal or vertical fracture orientations on a Cartesian fine grid. In this paper, we consider arbitrary fracture orientations and use triangular fine grid and developed GMsFEM for nonlinear flows. Moreover, we develop online basis function strategies to adaptively improve the convergence. The number of multiscale basis functions in each coarse region represents the degrees of freedom needed to achieve a certain error threshold. Our approach is adaptive in a sense that the multiscale basis functions can be added in the regions of interest. Numerical results for two-dimensional problem are presented to demonstrate the efficiency of proposed approach.