IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i19p3038-d1488163.html
   My bibliography  Save this article

Two-Phase Incompressible Flow with Dynamic Capillary Pressure in a Heterogeneous Porous Media

Author

Listed:
  • Mohamed Lamine Mostefai

    (Department of Mathematics, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
    Laboratory of Pure and Applied Mathematics, Amar Teleji Laghouat University, Laghouat 03000, Algeria)

  • Abdelbaki Choucha

    (Department of Material Sciences, Faculty of Sciences, Amar Teleji Laghouat University, Laghouat 03000, Algeria
    Laboratory of Mathematics and Applied Sciences, Ghardaia University, Ghardaia 47000, Algeria)

  • Salah Boulaaras

    (Department of Mathematics, College of Sciences, Qassim University, Buraydah 51452, Saudi Arabia)

  • Mufda Alrawashdeh

    (Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia)

Abstract

We prove the existence of weak solutions of a two-incompressible immiscible wetting and non-wetting fluids phase flow model in porous media with dynamic capillary pressure. This model is a coupled system which includes a nonlinear parabolic saturation equation and an elliptic pressure–velocity equation. In the regularized case, the existence and uniqueness of the weak solution are obtained. We let the regularization parameter be η → 0 to prove the existence of weak solutions.

Suggested Citation

  • Mohamed Lamine Mostefai & Abdelbaki Choucha & Salah Boulaaras & Mufda Alrawashdeh, 2024. "Two-Phase Incompressible Flow with Dynamic Capillary Pressure in a Heterogeneous Porous Media," Mathematics, MDPI, vol. 12(19), pages 1-22, September.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3038-:d:1488163
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/19/3038/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/19/3038/
    Download Restriction: no
    ---><---

    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:jmathe:v:12:y:2024:i:19:p:3038-:d:1488163. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.