Existence of solutions for a model of multiphase flow in porous media applied to gas migration in underground nuclear waste repository

Abstract

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 underground nuclear waste repository. This model, modelling fully and partially water saturated situations, consists 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.

Keywords:

• two-phase flow
• porous medium
• underground nuclear waste
• existence of solution

AMS Subject Classifications:

• 76S05
• 76T99
• 35K65

Acknowledgements

This work was partially supported by GNR MoMaS (PACEN/CNRS, ANDRA, BRGM, CEA, EDF, IRSN).