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A Fully Mass Conservative Numerical Method for Multiphase Flow in Fractured Porous Reservoirs

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Abstract

Numerical methods that are mass conservative, computationally stable, and efficient are essential for simulating multiphase flow in fractured porous reservoirs. In this paper, a fully mass conservative numerical method that meets these requirements is proposed and analyzed. Unlike in the implicit pressure and explicit saturation (IMPES) method, in this method, the pressure and saturation equations are solved sequentially in each iteration step. In this framework, the calculation of the saturation-related parameters no longer depends on the initial conditions of the current time step, but on the results of the current and previous iterations. Through this treatment, the discontinuities of the saturation and capillary pressure in the pre- and post-two time steps can be overcome to achieve fully mass conservation. Two numerical examples are designed to verify the robustness and efficiency of the presented method. The numerical results indicate that this new method is fully mass conservative, computationally more stable, and more efficient than the IMPES method. Furthermore, the proposed method is suitable not only for reservoirs with homogeneous permeability distributions but also for reservoirs with heterogeneous permeability distributions, which greatly improves the applicability of the new method.

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Acknowledgements

This work was supported by the National Science and Technology Major Project of China [Grant No. 2017ZX05009005-002] and the Natural Science Foundation of Shanghai, China [No. 19ZR1421400].

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Authors and Affiliations

  1. Department of Modern Mechanics, University of Science and Technology of China, Hefei, 230027, China

    Hailiang Cai, Youzhi Hao, Detang Lu & Yuxi Xian

  2. School of Mechanical and Automotive Engineering, Shanghai University of Engineering Science, Shanghai, 201620, China

    Peichao Li

  3. Well Testing Company, Xibu Drilling Engineering Company Limited, CNPC, Karamay, 834000, China

    Meng Feng

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  1. Hailiang Cai
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  2. Peichao Li
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  3. Meng Feng
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  4. Youzhi Hao
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  5. Detang Lu
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  6. Yuxi Xian
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Correspondence to Detang Lu or Yuxi Xian.

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Cai, H., Li, P., Feng, M. et al. A Fully Mass Conservative Numerical Method for Multiphase Flow in Fractured Porous Reservoirs. Transp Porous Med 139, 171–184 (2021). https://doi.org/10.1007/s11242-021-01636-9

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