Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste

Brahim Amaziane (1) , Mustapha El Ossmani (1) , M. Jurak (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 UPPA - Université de Pau et des Pays de l'Adour

In this paper a finite volume method approach is used to model the 2D compressible and immiscible two-phase flow of water and gas in heterogeneous porous media. We consider a model describing water-gas flow through engineered and geological barriers for a deep repository of radioactive waste. We consider a domain made up of several zones with different characteristics: porosity, absolute permeability, relative permeabilities and capillary pressure curves. This process can be formulated as a coupled system of partial differential equations which includes a nonlinear parabolic gas-pressure equation and a nonlinear degenerated parabolic water-saturation equation. Both equations are of diffusion-convection type. An implicit vertex-centred finite volume method is adopted to discretize the coupled system. A Godunov-type method is used to treat the convection terms and a conforming finite element method with piecewise linear elements is used for the discretization of the diffusion terms. An averaging technique is developed to obtain an effective capillary pressure curve at the interface of two media. Our numerical model is verified with 1D semi-analytical solutions in heterogeneous media. We also present 2D numerical results to demonstrate the significance of capillary heterogeneity in flow and to illustrate the performance of the method for the FORGE cell scale benchmark. © 2013 Springer-Verlag Berlin Heidelberg.

Mots clés: Capillary pressure curves; Conforming finite element method; Heterogeneous porous media; Hydrogen migration; Immiscible compressible; Immiscible two-phase flows; Semi-analytical solution; Vertex-centred; Benchmarking; Capillarity; Capillary tubes; Computer simulation; Finite volume method; Nonlinear equations; Numerical models; Partial differential equations; Piecewise linear techniques; Porous materials; Two phase flow; Radioactive wastes

Domaines: Analyse numérique [math.NA]

Brahim Amaziane, Mustapha El Ossmani, M. Jurak. Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Computing and Visualization in Science, 2012, 15 (1), pp.3-20. ⟨10.1007/s00791-013-0196-1⟩. ⟨hal-00861262⟩