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Numerical studies of a class of linear solvers for fine-scale petroleum reservoir simulation

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Computing and Visualization in Science

Abstract

Numerical simulation based on fine-scale reservoir models helps petroleum engineers in understanding fluid flow in porous media and achieving higher recovery ratio. Fine-scale models give rise to large-scale linear systems, and thus require effective solvers for solving these linear systems to finish simulation in reasonable turn-around time. In this paper, we study convergence, robustness, and efficiency of a class of multi-stage preconditioners accelerated by Krylov subspace methods for solving Jacobian systems from a fully implicit discretization. We compare components of these preconditioners, including decoupling and sub-problem solvers, for fine-scale reservoir simulation. Several benchmark and real-world problems, including a ten-million-cell reservoir problem, were simulated on a desktop computer. Numerical tests show that the combination of the alternating block factorization method and multi-stage subspace correction preconditioner gives a robust and memory-efficient solver for fine-scale reservoir simulation.

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Acknowledgements

This paper was finished during Li’s visit to the State Key Laboratory of Scientific and Engineering Computing (LSEC), China. Li is thankful for the kind support from LSEC. The authors would like to thank RIPED, PetroChina, for providing numerical test data and support through PetroChina New-generation Reservoir Simulation Software (2011A-1010) and PetroChina Joint Research Funding 12HT1050002654. Feng is partially supported by the NSFC Grant 61603322, Hunan Provincial Natural Science Foundation of China (2016JJ2129) and Open Foundation of Guangdong Provincial Engineering Technology Research Center for Data Science (2016KF03). The authors also appreciate various valuable comments from an anonymous referee on the early version of this paper.

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Authors and Affiliations

  1. Kunming University of Science and Technology, Kunming, 650504, China

    Zheng Li

  2. PetroChina Research Institute of Petroleum Exploration and Development, Beijing, 100083, China

    Shuhong Wu

  3. LSEC and NCMIS, Academy of Mathematics and Systems Science, Beijing, 100085, China

    Chen-Song Zhang

  4. Department of Mathematics, Penn State University, University Park, PA, USA

    Jinchao Xu

  5. School of Mathematics and Computational Science, Xiangtan University, Hunan, 411105, China

    Chunsheng Feng

  6. Guangdong Provincial Engineering Technology Research Center for Data Science, Guangzhou, 510631, Guangdong, China

    Chunsheng Feng

  7. Department of Mathematics, Tufts University, Medford, MA, 02155, USA

    Xiaozhe Hu

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  1. Zheng Li
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  2. Shuhong Wu
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  3. Chen-Song Zhang
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  4. Jinchao Xu
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  6. Xiaozhe Hu
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Correspondence to Zheng Li.

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Communicated by Gabriel Wittum.

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Li, Z., Wu, S., Zhang, CS. et al. Numerical studies of a class of linear solvers for fine-scale petroleum reservoir simulation. Comput. Visual Sci. 18, 93–102 (2017). https://doi.org/10.1007/s00791-016-0273-3

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  • DOI: https://doi.org/10.1007/s00791-016-0273-3

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