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Non-Darcy flow models in porous media via Atangana-Baleanu derivative

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  • Wei, Qing
  • Zhou, Hongwei
  • Yang, Shuai

Abstract

Two fractional Swartzendruber models applying the Atangana-Baleanu (A-B) derivative are proposed to describe non-Darcy flow in porous media. The analytical solutions of models are obtained by using Laplace transform. Fitting curves with the experimental data display the proposed models are suitable to describe non-Darcy flow problems in low and high permeability media. In addition, sensitivity analysis is performed to clarify the influence of relevant parameters on the A-B Swartzendruber models. In the light of the two-scale thermodynamics, the physical explanations of A-B Swartzendruber model I and II are revealed. The proposed A-B Swartzendruber models connect fluid flow of different scales, and provide a unified description of non-Darcy flow in porous media with low and high permeability.

Suggested Citation

  • Wei, Qing & Zhou, Hongwei & Yang, Shuai, 2020. "Non-Darcy flow models in porous media via Atangana-Baleanu derivative," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    • Handle: RePEc:eee:chsofr:v:141:y:2020:i:c:s096007792030730x
    DOI: 10.1016/j.chaos.2020.110335
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    References listed on IDEAS

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    1. Ali, Farhad & Iftikhar, Muhammad & Khan, Ilyas & Sheikh, Nadeem Ahmad, 2019. "Atangana–Baleanu fractional model for electro-osmotic flow of viscoelastic fluids," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 125-133.
    2. Atangana, Abdon & Koca, Ilknur, 2016. "Chaos in a simple nonlinear system with Atangana–Baleanu derivatives with fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 447-454.
    3. Jarad, Fahd & Abdeljawad, Thabet & Hammouch, Zakia, 2018. "On a class of ordinary differential equations in the frame of Atangana–Baleanu fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 16-20.
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    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.
    2. Wei, Q. & Yang, S. & Zhou, H.W. & Zhang, S.Q. & Li, X.N. & Hou, W., 2021. "Fractional diffusion models for radionuclide anomalous transport in geological repository systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Xiangcheng You & Shiyuan Li & Lei Kang & Li Cheng, 2023. "A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method," Energies, MDPI, vol. 16(5), pages 1-13, February.
    4. Oscar Martínez-Fuentes & Fidel Meléndez-Vázquez & Guillermo Fernández-Anaya & José Francisco Gómez-Aguilar, 2021. "Analysis of Fractional-Order Nonlinear Dynamic Systems with General Analytic Kernels: Lyapunov Stability and Inequalities," Mathematics, MDPI, vol. 9(17), pages 1-29, August.

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