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

<p dir="ltr">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 cons...

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Main Author: Ahmad Abushaikha (17148349) (author)
Other Authors: Dominique Guérillot (14150973) (author), Mostafa Kadiri (19569316) (author), Saber Trabelsi (19569319) (author)
Published: 2021
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author Ahmad Abushaikha (17148349)
author2 Dominique Guérillot (14150973)
Mostafa Kadiri (19569316)
Saber Trabelsi (19569319)
author2_role author
author
author
author_facet Ahmad Abushaikha (17148349)
Dominique Guérillot (14150973)
Mostafa Kadiri (19569316)
Saber Trabelsi (19569319)
author_role author
dc.creator.none.fl_str_mv Ahmad Abushaikha (17148349)
Dominique Guérillot (14150973)
Mostafa Kadiri (19569316)
Saber Trabelsi (19569319)
dc.date.none.fl_str_mv 2021-08-25T03:00:00Z
dc.identifier.none.fl_str_mv 10.3390/mca26030060
dc.relation.none.fl_str_mv https://figshare.com/articles/journal_contribution/Buckley_Leverett_Theory_for_a_Forchheimer_Darcy_Multiphase_Flow_Model_with_Phase_Coupling/26975533
dc.rights.none.fl_str_mv CC BY 4.0
info:eu-repo/semantics/openAccess
dc.subject.none.fl_str_mv Engineering
Resources engineering and extractive metallurgy
Forchheimer’s law
Darcy’s law
two-phase flows
phases coupling
fractional flow
Buckley–Leverett theory
capillary pressure
dc.title.none.fl_str_mv Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
dc.type.none.fl_str_mv Text
Journal contribution
info:eu-repo/semantics/publishedVersion
text
contribution to journal
description <p dir="ltr">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.</p><h2>Other Information</h2><p dir="ltr">Published in: Mathematical and Computational Applications<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/mca26030060" target="_blank">https://dx.doi.org/10.3390/mca26030060</a></p>
eu_rights_str_mv openAccess
id Manara2_f3c796fa530fce394eb8ea98893e33ed
identifier_str_mv 10.3390/mca26030060
network_acronym_str Manara2
network_name_str Manara2
oai_identifier_str oai:figshare.com:article/26975533
publishDate 2021
repository.mail.fl_str_mv
repository.name.fl_str_mv
repository_id_str
rights_invalid_str_mv CC BY 4.0
spelling Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase CouplingAhmad Abushaikha (17148349)Dominique Guérillot (14150973)Mostafa Kadiri (19569316)Saber Trabelsi (19569319)EngineeringResources engineering and extractive metallurgyForchheimer’s lawDarcy’s lawtwo-phase flowsphases couplingfractional flowBuckley–Leverett theorycapillary pressure<p dir="ltr">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.</p><h2>Other Information</h2><p dir="ltr">Published in: Mathematical and Computational Applications<br>License: <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank">https://creativecommons.org/licenses/by/4.0/</a><br>See article on publisher's website: <a href="https://dx.doi.org/10.3390/mca26030060" target="_blank">https://dx.doi.org/10.3390/mca26030060</a></p>2021-08-25T03:00:00ZTextJournal contributioninfo:eu-repo/semantics/publishedVersiontextcontribution to journal10.3390/mca26030060https://figshare.com/articles/journal_contribution/Buckley_Leverett_Theory_for_a_Forchheimer_Darcy_Multiphase_Flow_Model_with_Phase_Coupling/26975533CC BY 4.0info:eu-repo/semantics/openAccessoai:figshare.com:article/269755332021-08-25T03:00:00Z
spellingShingle Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
Ahmad Abushaikha (17148349)
Engineering
Resources engineering and extractive metallurgy
Forchheimer’s law
Darcy’s law
two-phase flows
phases coupling
fractional flow
Buckley–Leverett theory
capillary pressure
status_str publishedVersion
title Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
title_full Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
title_fullStr Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
title_full_unstemmed Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
title_short Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
title_sort Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
topic Engineering
Resources engineering and extractive metallurgy
Forchheimer’s law
Darcy’s law
two-phase flows
phases coupling
fractional flow
Buckley–Leverett theory
capillary pressure