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

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 (PDEs) which includes a nonlinear parabolic gas-pressure equation and a nonlinear degenerated parabolic water-saturation equation. Both equations are of diffusion-convection types. 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 upscaling technique is developed to obtain an effective capillary pressure curve at the interface of two media. Our numerical model is verified with 1D semianalytical solutions in heterogeneous media. We also present 2D numerical results to demonstrate the signifB. Amaziane UNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR 5142, Av. de l’université, 64000 Pau, France. E-mail: [email protected] M. El Ossmani Université Moulay Ismäıl, LM2I-ENSAM, Marjane II, B.P. 4024, Meknès, 50000, Maroc. E-mail: [email protected] M. Jurak UNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR 5142, Av. de l’université, 64000 Pau, France. E-mail: [email protected] icance of capillary heterogeneity in flow and to illustrate the performance of the method for the FORGE cell scale benchmark.