The design of novel mathematical models and state-of-the-art simulators for unconventional shale gas reservoirs plays an increasingly important role in the current energy mix of the world’s growing energy demand. In this paper, we present a robust and scalable framework, which is based on the chemical potential-based modeling and the fully implicit method (FIM), to model and simulate this highly nonlinear flow transport problem on a large scale. In the proposed approach, a thermodynamically consistent mathematical model of gas flow in shale formations, which employs the gas density and the chemical potential gradient, is developed to satisfy the second law of thermodynamics and meanwhile guarantee the energy dissipation property. And then the family of fully implicit finite element algorithms is utilized to accurately capture the complicated flow physics behind the transport process in shale media on high resolution grids. In particular, our approach further enhances the numerical formulation by proposing the family of Newton–Krylov methods for efficiently computing, and the parallel implementation of the simulator is achieved by using the domain decomposition technique. Numerical experiments are presented to demonstrate the robustness and parallel scalability of the solution strategies for several interesting shale gas flow problems in two or three dimensions. With the proposed parallel method, large-scale reservoir simulation can be obtained on the Shaheen-II supercomputer with up to 40 960 processors, which enables to achieve a good strong scalability by saving more than 90 percent of computing time, when the problem size is enlarged to hundreds of millions of degrees of freedom.
Bibliographical noteKAUST Repository Item: Exported on 2023-05-09
Acknowledgements: The authors would like to express their appreciation to the anonymous reviewers for the invaluable comments that have greatly improved the quality of the manuscript. This work is supported by National Natural Science Foundation of China (No. 11971006 and No. 12131002), Shenzhen Science and Technology Program (No. JCYJ20210324130801003), Guangdong Basic and Applied Basic Research Foundation (No. 2022A1515010147), and Hunan Province Natural Science Foundation of China (No. 2020JJ2002).