Projects per year
Abstract
Flow and transport in fractured porous media are of paramount importance for many applications such as petroleum exploration and production, geological storage of carbon dioxide, hydrogeology, or geothermal energy. We consider here the two-phase discrete fracture model introduced in [3] which represents explicitly the fractures as codimension one surfaces immersed in the surrounding matrix domain. Then, the two-phase Darcy flow in the matrix is coupled with the two-phase Darcy flow in the fractures using transmission conditions accounting for fractures acting either as drains or barriers. The model takes into account complex networks of fractures, discontinuous capillary pressure curves at the matrix fracture interfaces and can be easily extended to account for gravity including in the width of the fractures. It also includes a layer of damaged rock at the matrix fracture interface with its own mobility and capillary pressure functions. In this work, the convergence analysis carried out in [3] in the framework of gradient discretizations [2] is extended to obtain the uniform-in-time convergence of the discrete solutions to a weak solution of the model.
Original language | English |
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Title of host publication | Finite Volumes for Complex Applications VIII—Methods and Theoretical Aspects - FVCA8 2017 |
Editors | Clément Cancès, Pascal Omnes |
Place of Publication | Cham Switzerland |
Publisher | Springer |
Pages | 275-283 |
Number of pages | 9 |
Volume | 199 |
ISBN (Electronic) | 9783319573977 |
ISBN (Print) | 9783319573960 |
DOIs | |
Publication status | Published - 2017 |
Event | Finite Volumes for Complex Applications 2017 - Université Lille 1, Lille, France Duration: 12 Jun 2017 → 16 Jun 2017 Conference number: 8th https://link.springer.com/book/10.1007/978-3-319-57394-6 (Proceedings) |
Publication series
Name | Springer Proceedings in Mathematics & Statistics |
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Publisher | Springer International Publishing |
Volume | 199 |
ISSN (Print) | 2194-1009 |
ISSN (Electronic) | 2194-1017 |
Conference
Conference | Finite Volumes for Complex Applications 2017 |
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Abbreviated title | FVCA 2017 |
Country/Territory | France |
City | Lille |
Period | 12/06/17 → 16/06/17 |
Other | Theme = Hyperbolic, Elliptic and Parabolic Problems |
Internet address |
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Keywords
- Discrete fracture model
- Gradient discretization method
- Two-phase Darcy flow
- Uniform-in-time convergence
Projects
- 1 Finished
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Discrete functional analysis: bridging pure and numerical mathematics
Droniou, J. (Primary Chief Investigator (PCI)), Eymard, R. (Partner Investigator (PI)) & Manzini, G. (Partner Investigator (PI))
Australian Research Council (ARC), Monash University, Université Paris-Est Créteil Val de Marne (Paris-East Créteil University Val de Marne), University of California System
1/01/17 → 31/12/20
Project: Research