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Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository

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  • Shuai Yang

    (School of Energy Engineering, Xi’an University of Science and Technology, Xi’an 710054, China
    State Key Laboratory for GeoMechanics and Deep Underground Engineering, China University of Mining and Technology, Beijing 100083, China)

  • Qing Wei

    (School of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing 100083, China
    Institute of Physics & Astronomy, University of Potsdam, 14476 Potsdam, Germany)

  • Lu An

    (Laboratory 3SR, CNRS UMR 5521, Grenoble Alpes University, 38000 Grenoble, France)

Abstract

Based on the multiple barriers concept of deep geological disposal of high-level waste, fractional advection diffusion equations for radionuclide migration in multiple layers low-permeability porous media are proposed in this work. The presented fractional advection diffusion models in terms of different definitions of fractional derivative are analytically addressed via the Laplace integral transform method. This work provides a theoretical foundation for further simulations of radionuclide migration in the multiple barriers system of the high-level waste repository.

Suggested Citation

  • Shuai Yang & Qing Wei & Lu An, 2022. "Fractional Advection Diffusion Models for Radionuclide Migration in Multiple Barriers System of Deep Geological Repository," Mathematics, MDPI, vol. 10(14), pages 1-7, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2491-:d:865404
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    References listed on IDEAS

    as
    1. 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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    4. Yu, Xiangnan & Zhang, Yong & Sun, HongGuang & Zheng, Chunmiao, 2018. "Time fractional derivative model with Mittag-Leffler function kernel for describing anomalous diffusion: Analytical solution in bounded-domain and model comparison," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 306-312.
    5. Kundu, Snehasis, 2018. "Suspension concentration distribution in turbulent flows: An analytical study using fractional advection–diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 135-155.
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