Comptes Rendus
Partial Differential Equations
A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository
Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 527-532.

We prove existence of solutions for a new model of two compressible and partially miscible phase flow in porous media, applied to gas migration in an underground nuclear waste repository. This model, modeling fully and partially water saturated situations, consist of a coupled system of quasilinear parabolic partial differential equations. We seek a new set of variables in order to obtain a system which belongs to the class of equations considered by Alt and Luckhaus such that it would be possible to use their existence theorem. A simulation of a numerical test case is performed in order to numerically demonstrate the ability of this model to take in account the appearance of one phase.

On démontre l'existence d'une solution pour un nouveau modèle d'écoulement en milieu poreux de deux phases compressibles et partiellement miscibles en application à la migration de gaz en stockage souterrain de déchets nucléaires. Ce nouveau modèle prend en compte à la fois les régimes saturé et insaturé, il consiste en un système d'équations aux dérivés partielles quasi linéaires parabolique couplé. On cherche un changement de variables qui permet une formulation entrant dans la classe des équations considérées par Alt et Luckhaus ; ce qui permet d'appliquer leur théorème d'existence et ainsi de prouver l'existence d'une solution du modèle. Un test numérique est présenté afin de confirmer la capacité de ce modèle à prendre en compte l'apparition d'une phase.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2009.03.011

Farid Smaï 1

1 Université de Lyon, Université Lyon 1, UMR 5208 institut Camille-Jordan, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
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Farid Smaï. A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository. Comptes Rendus. Mathématique, Volume 347 (2009) no. 9-10, pp. 527-532. doi : 10.1016/j.crma.2009.03.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.03.011/

[1] H.W. Alt; S. Luckhaus Quasilinear elliptic–parabolic differential equations, Math. Z., Volume 183 (1983), pp. 311-341

[2] A. Bourgeat; M. Jurak; F. Smaï Two partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository, Comput. Geosci., Volume 6 (2009) no. 4, pp. 309-325

[3] Y. Wu; P. Forsyth On the selection of primary variables in numerical formulation for modeling multiphase flow in porous media, J. Contam. Hydrol., Volume 48 (2001), pp. 277-304

[4] http://www.andra.fr/interne.php3?id_article=913&id_rubrique=76 (Andra, Couplex-gaz)

[5] http://www-cast3m.cea.fr/cast3m/index.jsp (CEA, Cast3m)

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