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

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Amaziane, Brahim¹  Jurak, Mladen²  Keko, Ana Zgaljic³ 

[1] Univ Pau & Pays Adour, Lab Math & Leurs Applicat, CNRS, UMR 5142, F-64000 Pau, France

[2] Univ Zagreb, Dept Math, Zagreb 10000, Croatia

[3] Univ Zagreb, Fac Elect Engn & Comp, Zagreb 10000, Croatia

关键词: Immiscible compressible;    Two-phase flow;    Global pressure;    Heterogeneous porous media;    Finite volume;    Nuclear waste;   

DOI  :  10.1016/j.cam.2012.05.013

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free