IDEAS home Printed from https://ideas.repec.org/a/gam/jeners/v16y2023i5p2175-d1078744.html
   My bibliography  Save this article

A Study of the Non-Linear Seepage Problem in Porous Media via the Homotopy Analysis Method

Author

Listed:
  • Xiangcheng You

    (State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China)

  • Shiyuan Li

    (State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China)

  • Lei Kang

    (State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China)

  • Li Cheng

    (State Key Laboratory of Petroleum Resources and Prospecting, College of Petroleum Engineering, China University of Petroleum-Beijing, Beijing 102249, China)

Abstract

A non-Darcy flow with moving boundary conditions in a low-permeability reservoir was solved using the homotopy analysis method (HAM), which was converted into a fixed-boundary mathematical model via similarity transformation. Approximate analytical solutions based on the HAM are guaranteed to be more accurate than exact analytical solutions, with relative errors between 0.0089% and 2.64%. When λ = 0, the pressure drop of the Darcy seepage model could be instantaneously transmitted to infinity. When λ > 0, the pressure drop curve of the non-Darcy seepage model exhibited the characteristics of tight support, which was clearly different from the Darcy seepage model’s formation pressure distribution curve. According to the results of the HAM, a moving boundary is more influenced by threshold pressure gradients with a longer time. When the threshold pressure gradients were smaller, the moving boundaries move more quickly and are more sensitive to external influences. One-dimensional, low-permeability porous media with a non-Darcy flow with moving boundary conditions can be reduced to a Darcy seepage model if the threshold pressure gradient values tend to zero.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jeners:v:16:y:2023:i:5:p:2175-:d:1078744
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/1996-1073/16/5/2175/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/1996-1073/16/5/2175/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Al-Qudah, Alaa & Odibat, Zaid & Shawagfeh, Nabil, 2022. "A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 505-522.
    2. Zhou, Yang & Zhang, Li-ying & Wang, Tao, 2021. "Analytical solution for one-dimensional non-Darcy flow with bilinear relation in porous medium caused by line source," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    3. 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).
    4. Sardanyés, Josep & Rodrigues, Carla & Januário, Cristina & Martins, Nuno & Gil-Gómez, Gabriel & Duarte, Jorge, 2015. "Activation of effector immune cells promotes tumor stochastic extinction: A homotopy analysis approach," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 484-495.
    5. Jun Yao & Wenchao Liu & Zhangxin Chen, 2013. "Numerical Solution of a Moving Boundary Problem of One-Dimensional Flow in Semi-Infinite Long Porous Media with Threshold Pressure Gradient," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Li, Wei & Zhang, Ying & Huang, Dongmei & Rajic, Vesna, 2022. "Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Zhou, Yang & Zhang, Li-ying & Wang, Tao, 2021. "Analytical solution for one-dimensional non-Darcy flow with bilinear relation in porous medium caused by line source," Applied Mathematics and Computation, Elsevier, vol. 392(C).
    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.
    5. 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).
    6. Naik, Parvaiz Ahmad & Zu, Jian & Ghoreishi, Mohammad, 2020. "Estimating the approximate analytical solution of HIV viral dynamic model by using homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    7. Al-Qudah, Alaa & Odibat, Zaid & Shawagfeh, Nabil, 2022. "A linearization-based computational algorithm of homotopy analysis method for nonlinear reaction–diffusion systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 505-522.
    8. Zhang, Qitao & Liu, Wenchao & Dahi Taleghani, Arash, 2022. "Numerical study on non-Newtonian Bingham fluid flow in development of heavy oil reservoirs using radiofrequency heating method," Energy, Elsevier, vol. 239(PE).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jeners:v:16:y:2023:i:5:p:2175-:d:1078744. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.