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.
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Farid Smaï 1
@article{CRMATH_2009__347_9-10_527_0, author = {Farid Sma{\"\i}}, title = {A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository}, journal = {Comptes Rendus. Math\'ematique}, pages = {527--532}, publisher = {Elsevier}, volume = {347}, number = {9-10}, year = {2009}, doi = {10.1016/j.crma.2009.03.011}, language = {en}, }
TY - JOUR AU - Farid Smaï TI - A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository JO - Comptes Rendus. Mathématique PY - 2009 SP - 527 EP - 532 VL - 347 IS - 9-10 PB - Elsevier DO - 10.1016/j.crma.2009.03.011 LA - en ID - CRMATH_2009__347_9-10_527_0 ER -
%0 Journal Article %A Farid Smaï %T A model of multiphase flow and transport in porous media applied to gas migration in underground nuclear waste repository %J Comptes Rendus. Mathématique %D 2009 %P 527-532 %V 347 %N 9-10 %I Elsevier %R 10.1016/j.crma.2009.03.011 %G en %F CRMATH_2009__347_9-10_527_0
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/
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