Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media

Handle URI:
http://hdl.handle.net/10754/594301
Title:
Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media
Authors:
Saad, Bilal Mohammed ( 0000-0002-9509-7604 ) ; Saad, Mazen
Abstract:
We study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Saad B, Saad M (2014) Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. Springer Proceedings in Mathematics & Statistics: 713–721. Available: http://dx.doi.org/10.1007/978-3-319-05591-6_71.
Publisher:
Springer Science + Business Media
Journal:
Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems
Conference/Event name:
7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7
Issue Date:
2014
DOI:
10.1007/978-3-319-05591-6_71
Type:
Conference Paper
ISSN:
2194-1009; 2194-1017
ISBN:
9783319055909
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorSaad, Bilal Mohammeden
dc.contributor.authorSaad, Mazenen
dc.date.accessioned2016-01-19T14:45:33Zen
dc.date.available2016-01-19T14:45:33Zen
dc.date.issued2014en
dc.identifier.citationSaad B, Saad M (2014) Convergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Media. Springer Proceedings in Mathematics & Statistics: 713–721. Available: http://dx.doi.org/10.1007/978-3-319-05591-6_71.en
dc.identifier.isbn9783319055909en
dc.identifier.issn2194-1009en
dc.identifier.issn2194-1017en
dc.identifier.doi10.1007/978-3-319-05591-6_71en
dc.identifier.urihttp://hdl.handle.net/10754/594301en
dc.description.abstractWe study the convergence of a combined finite volume nonconforming finite element scheme on general meshes for a partially miscible two-phase flow model in anisotropic porous media. This model includes capillary effects and exchange between the phase. The diffusion term,which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. The convergence of the scheme is proved thanks to an estimate on the two pressures which allows to show estimates on the discrete time and compactness results in the case of degenerate relative permeabilities. A key point in the scheme is to use particular averaging formula for the dissolution function arising in the diffusion term. We show also a simulation of CO2 injection in a water saturated reservoir and nuclear waste management. Numerical results are obtained by in-house numerical code. © Springer International Publishing Switzerland 2014.en
dc.publisherSpringer Science + Business Mediaen
dc.titleConvergence Analysis of a FV-FE Scheme for Partially Miscible Two-Phase Flow in Anisotropic Porous Mediaen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journalFinite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problemsen
dc.conference.date15 June 2014 through 20 June 2014en
dc.conference.name7th International Symposium on Finite Volumes for Complex Applications-Problems and Perspectives, FVCA7en
dc.contributor.institutionEcole Centrale de Nantes, 1, rue de la Noé, BP 92101Nantes, Franceen
kaust.authorSaad, Bilal Mohammeden
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.