Brahim Amaziane, Mladen Jurak, Anja Vrbaski
Abstract:
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 CNRS-UMR 5142 Av. de l'Université, 64000 Pau, France email: brahim.amaziane@univ-pau.fr |
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Mladen Jurak Faculty of Science, University of Zagreb Bijenicka 30, 10000 Zagreb, Croatia email: jurak@math.hr |
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Anja Vrbaski Faculty of Science, University of Zagreb Bijenicka 30, 10000 Zagreb, Croatia email: avrbaski@math.hr |
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