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Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling

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submitted on 2024-09-10, 07:05 and posted on 2024-09-10, 07:06 authored by Ahmad Abushaikha, Dominique Guérillot, Mostafa Kadiri, Saber Trabelsi

This paper is dedicated to the modeling, analysis, and numerical simulation of a two-phase non-Darcian flow through a porous medium with phase-coupling. Specifically, we introduce an extended Forchheimer–Darcy model where the interaction between phases is taken into consideration. From the modeling point of view, the extension consists of the addition to each phase equation of a term depending on the gradient of the pressure of the other phase, leading to a coupled system of differential equations. The obtained system is much more involved than the classical Darcy system since it involves the Forchheimer equation in addition to the Darcy one. This model is more appropriate when there is a substantial difference between the phases’ velocities, for instance in the case of gas/water phases, and applications in oil recovery using gas flooding. Based on the Buckley–Leverett theory, including capillary pressure, we derive an explicit expression of the phases’ velocities and fractional water flows in terms of the gradient of the capillary pressure, and the total constant velocity. Various scenarios are considered, and the respective numerical simulations are presented. In particular, comparisons with the classical models (without phase coupling) are provided in terms of breakthrough time among others. Eventually, we provide a post-processing method for the derivation of the solution of the new coupled system using the classical non-coupled system. This method is of interest for industry since it allows for including the phase coupling approach in existing numerical codes and software (designed for solving classical models) without major technical changes.

Other Information

Published in: Mathematical and Computational Applications
License: https://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.3390/mca26030060

Funding

Open Access funding provided by the Qatar National Library.

History

Language

  • English

Publisher

MDPI

Publication Year

  • 2021

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License.

Institution affiliated with

  • Hamad Bin Khalifa University
  • College of Science and Engineering - HBKU
  • Texas A&M University at Qatar

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