Electron. J. Diff. Equ., Vol. 2012 (2012), No. 102, pp. 1-22.

Existence for a global pressure formulation of water-gas flow in porous media

Brahim Amaziane, Mladen Jurak, Anja Vrbaski

We consider a model of water-gas flow in porous media with an incompressible water phase and a compressible gas phase. Such models appear in gas migration through engineered and geological barriers for a deep repository for radioactive waste. The main feature of this model is the introduction of a new global pressure and it is fully equivalent to the original equations. The system is written in a fractional flow formulation as a degenerate parabolic system with the global pressure and the saturation potential as the main unknowns. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. Under some realistic assumptions on the data, including unbounded capillary pressure function and non-homogeneous boundary conditions, we prove the existence of weak solutions of the system. Furthermore, it is shown that the weak solution has certain desired properties, such as positivity of the saturation. The result is proved with the help of an appropriate regularization and a time discretization of the coupled system. We use suitable test functions to obtain a priori estimates and a compactness result in order to pass to the limit in nonlinear terms.

Submitted June 5, 2012. Published June 18, 2012.
Math Subject Classifications: 35K55, 35K65, 76S05.
Key Words: Degenerate system; global pressure; immiscible compressible; nonlinear parabolic system; nuclear waste; porous media; two-phase flow, water-gas.

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Brahim Amaziane
Univ Pau & Pays Adour
Laboratoire de Mathématiques et de leurs Applications
Av. de l'Université, 64000 Pau, France
email: brahim.amaziane@univ-pau.fr
Mladen Jurak
Faculty of Science, University of Zagreb
Bijenicka 30, 10000 Zagreb, Croatia
email: jurak@math.hr
Anja Vrbaski
Faculty of Science, University of Zagreb
Bijenicka 30, 10000 Zagreb, Croatia
email: avrbaski@math.hr

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