Numerical simulations of water-gas flow in heterogeneous porous media with discontinuous capillary pressures by the concept of global pressure

• Autores: Brahim Amaziane, Mladen Jurak, Ana Zgaljic Keko
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 236, Nº 17, 2012, págs. 4227-4244
• Idioma: inglés
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• Resumen

  • We present an approach and numerical results for a new formulation modeling immiscible compressible two-phase flow in heterogeneous porous media with discontinuous capillary pressures. The main feature of this model is the introduction of a new global pressure, and it is fully equivalent to the original equations. The resulting equations are written in a fractional flow formulation and lead to a coupled degenerate system which consists of a nonlinear parabolic (the global pressure) equation and a nonlinear diffusion�convection one (the saturation equation) with nonlinear transmission conditions at the interfaces that separate different media. The resulting system is discretized using a vertex-centred finite volume method combined with pressure and flux interface conditions for the treatment of heterogeneities. An implicit Euler approach is used for time discretization. A Godunov-type method is used to treat the convection terms, and the diffusion terms are discretized by piecewise linear conforming finite elements. We present numerical simulations for three one-dimensional benchmark tests to demonstrate the ability of the method to approximate solutions of water�gas equations efficiently and accurately in nuclear underground waste disposal situations.