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Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media

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  • Wenwen Zhong
  • Changpin Li
  • Jisheng Kou

Abstract

Numerical simulation of two-phase flow in fractured porous media is an important topic in the subsurface flow, environmental problems, and petroleum reservoir engineering. The conventional model does not work well in many cases since it lacks the memory property of fracture media. In this paper, we develop a new numerical formulation with fractional time derivative for two-phase flow in fractured porous media. In the proposed formulation, the different fractional time derivatives are applied to fracture and matrix regions since they have different memory properties. We further develop a two-level time discrete method, which uses a large time step for the pressure and a small time step size for the saturation. The pressure equation is solved implicitly in each large time step, while the saturation is updated by an explicit fractional time scheme in each time substep. Finally, the numerical tests are carried out to demonstrate the effectiveness of the proposed numerical model.

Suggested Citation

  • Wenwen Zhong & Changpin Li & Jisheng Kou, 2013. "Numerical Fractional-Calculus Model for Two-Phase Flow in Fractured Media," Advances in Mathematical Physics, Hindawi, vol. 2013, pages 1-7, August.
    • Handle: RePEc:hin:jnlamp:429835
    DOI: 10.1155/2013/429835
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    Cited by:

    1. Abdumauvlen Berdyshev & Dossan Baigereyev & Kulzhamila Boranbek, 2023. "Numerical Method for Fractional-Order Generalization of the Stochastic Stokes–Darcy Model," Mathematics, MDPI, vol. 11(17), pages 1-27, September.
    2. Dossan Baigereyev & Dinara Omariyeva & Nurlan Temirbekov & Yerlan Yergaliyev & Kulzhamila Boranbek, 2022. "Numerical Method for a Filtration Model Involving a Nonlinear Partial Integro-Differential Equation," Mathematics, MDPI, vol. 10(8), pages 1-24, April.
    3. Dossan Baigereyev & Nurlana Alimbekova & Abdumauvlen Berdyshev & Muratkan Madiyarov, 2021. "Convergence Analysis of a Numerical Method for a Fractional Model of Fluid Flow in Fractured Porous Media," Mathematics, MDPI, vol. 9(18), pages 1-25, September.

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