Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling
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...
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| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/26/3/60 |
| _version_ | 1797518292349353984 |
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| author | Ahmad Abushaikha Dominique Guérillot Mostafa Kadiri Saber Trabelsi |
| author_facet | Ahmad Abushaikha Dominique Guérillot Mostafa Kadiri Saber Trabelsi |
| author_sort | Ahmad Abushaikha |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T07:27:49Z |
| format | Article |
| id | doaj.art-3098cfa258af4b16a1d669b407446158 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T07:27:49Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-3098cfa258af4b16a1d669b4074461582023-11-22T14:07:13ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472021-08-012636010.3390/mca26030060Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase CouplingAhmad Abushaikha0Dominique Guérillot1Mostafa Kadiri2Saber Trabelsi3College of Science and Engineering, Hamad Bin Khalifa University, A0036-I LAS Building, Education City, Doha P.O. Box 34110, QatarTerra 3E SAS, 12 Rue Haute, 92500 Rueil-Malmaison, FranceScience Program, Texas A&M University at Qatar, Doha P.O. Box 23874, QatarScience Program, Texas A&M University at Qatar, Doha P.O. Box 23874, QatarThis 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.https://www.mdpi.com/2297-8747/26/3/60Forchheimer’s lawDarcy’s lawtwo-phase flowsphases couplingfractional flowBuckley–Leverett theory |
| spellingShingle | Ahmad Abushaikha Dominique Guérillot Mostafa Kadiri Saber Trabelsi Buckley–Leverett Theory for a Forchheimer–Darcy Multiphase Flow Model with Phase Coupling Mathematical and Computational Applications Forchheimer’s law Darcy’s law two-phase flows phases coupling fractional flow Buckley–Leverett theory |
| 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 | Forchheimer’s law Darcy’s law two-phase flows phases coupling fractional flow Buckley–Leverett theory |
| url | https://www.mdpi.com/2297-8747/26/3/60 |
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