Skip to main content
SpringerLink
Log in

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

  • Published:
Computing and Visualization in Science

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26

Similar content being viewed by others

Notes

  1. \(x^+ =\max (x,0),\, x^- = \min (x,0)\).

  2. Originally, horizontal and vertical permeability \(K_h,\,K_v\) were given, which is not consistent with supposed radial symmetry of the problem. As a consequence we use an isotropic permeability \(K\), given by \(K=\root 3 \of {K_h^2 K_v}\).

References

  1. ANDRA: Dossier 2005 Argile, les recherches de l’Andra sur le stockage géologique des déchets radioactifs à haute activité à vie longue, Collection les Rapports, Andra, Châtenay-Malabry (2005)

  2. Angelini, O., Chavant, C., Chénier, E., Eymard, R., Granet, S.: Finite volume approximation of a diffusion-dissolution model and application to nuclear waste storage. Math. Comput. Simul. 81(10), 2001–2017 (2011)

    Article  MATH  Google Scholar 

  3. Bastian, P.: Numerical computation of multiphase flows in porous media. Habilitationsschrift (1999)

  4. Bear, J., Bachmat, Y.: Introduction to Modeling of Transport Phenomena in Porous Media. Kluwe, London (1991)

    Book  MATH  Google Scholar 

  5. Balay, S., Brown, J., Buschelman, K., Gropp, W.D., Kaushik, D., Knepley, M.G., McInnes, L.C., Smith, B.F., Zhang, H.: PETSc Web page. http://www.mcs.anl.gov/petsc (2011)

  6. Bourgeat, A., Jurak, M.: A two level scaling-up method for multiphase flow in porous media; numerical validation and comparison with other methods. Comput. Geosci. 14(1), 1–14 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. Bourgeat, A., Jurak, M., Smaï, F.: Two-phase, partially miscible flow and transport modeling in porous media; application to gas migration in a nuclear waste repository. Comput. Geosci. 13(1), 29–42 (2009)

    Article  MATH  Google Scholar 

  8. Cancès, C.: Finite volume scheme for two-phase flows in heterogeneous porous media involving capillary pressure discontinuities, M2AN Math. Model. Numer. Anal. 43(5), 973–1001 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Chavent, G., Jaffré, J.: Mathematical Models and Finite Elements for Reservoir Simulation. North-Holland, Amsterdam (1986)

    MATH  Google Scholar 

  10. Chen, Z., Huan, G., Ma, Y.: Computational Methods for Multiphase Flows in Porous Media. SIAM, Philadelphia (2006)

    Book  MATH  Google Scholar 

  11. Croisé, J., Mayer, G., Talandier, J., Wendling, J.: Impact of water consumption and saturation-dependent corrosion rate on hydrogen generation and migration from an intermediate-level radioactive waste repository. Transp. Porous Media 90, 59–75 (2011)

    Article  Google Scholar 

  12. Enchery, G., Eymard, R., Michel, A.: Numerical approximation of a two-phase flow problem in a porous medium with discontinuous capillary forces. SIAM J. Numer. Anal. 43(6), 2402–2422 (2006)

    Google Scholar 

  13. Fučík, R., Mikyška, J., Beneš, M., Illangasekare, T.H.: Semianalytical solution for two-phase flow in porous media with a discontinuity. Vadose Zone J. 7, 1001–1007 (2008)

    Article  Google Scholar 

  14. FORGE. http://www.bgs.ac.uk/forge/home.html

  15. Helmig, R.: Multiphase Flow and Transport Processes in the Subsurface. Springer, Berlin (1997)

    Book  Google Scholar 

  16. Hoteit, H., Firoozabadi, A.: Numerical modeling of two-phase flow in heterogeneous permeable media with different capillarity pressures. Adv. Water Resour. 31, 56–73 (2008)

    Article  Google Scholar 

  17. Huber, R., Helmig, R.: Node-centered finite volume discretizations for the numerical simulation of multiphase flow in heterogeneous porous media. Comput. Geosci. 4(2), 141–164 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  18. McWhorter, D.B., Sunada, D.K.: Exact integral solutions for two-phase flow. Water Resour. Res. 26, 339–413 (1990)

    Article  Google Scholar 

  19. MOMAS. http://www.gdrmomas.org/

  20. Niessner, J., Helmig, R., Jacobs, H., Roberts, J.E.: Interface condition and linearization schemes in the Newton iterations for two-phase flow in heterogeneous porous media. Adv. Water Resour. 28, 671–678 (2005)

    Google Scholar 

  21. Norris, S.: Summary of gas Generation and migration current state-of-the-art, FORGE D1.2-R (2009). Available online at http://www.bgs.ac.uk/forge/reports.html

  22. OECD/NEA: Safety of Geological Disposal of High-level and Long-lived Radioactive Waste in France, An International Peer Review of the “Dossier 2005 Argile” Concerning Disposal in the Callovo-Oxfordian Formation, OECD Publishing (2006)., Available online at http://www.nea.fr/html/rwm/reports/2006/nea6178-argile.pdf

  23. Papafotiou, A., Sheta, H., Helmig, R.: Numerical modeling of two-phase hysteresis combined with an interface condition for heterogeneous porous media. Comput. Geosci. 14(2), 273–287 (2010)

    Article  MATH  Google Scholar 

  24. Senger, R., Ewing, J., Zhang, K., Avis, J., Marschall, P., Gauss, I.: Modeling approaches for investigating gas migration from a deep low/intermediate level waste repository (Switzerland). Transp. Porous Media 90, 113–133 (2011)

    Article  Google Scholar 

  25. van Duijn, C.J., de Neef, M.J.: Similarity solution for capillary redistribution of two phases in a porous medium with a single discontinuity. Adv. Water Resour. 21, 451–461 (1998)

    Article  Google Scholar 

  26. van Duijn, C.J., Molenaar, J., Neef, M.J.: The effect of capillary forces on immiscible two-phase flow in heterogeneous porous media. Transp. Porous Media 21(1), 71–93 (1995)

    Google Scholar 

  27. Zhang, K., Croisé, J., Mayer, G.: Computation of the Couplex-Gaz exercise with TOUGH2-MP: hydrogen flow and transport in the pore water of a low-permeability clay rock hosting a nuclear waste repository. Nucl. Technol. 174, 364–374 (2011)

    Google Scholar 

Download references

Acknowledgments

The research leading to these results has received funding from the European Atomic Energy Community’s Seventh Framework Programme (FP7/2009-2013) under Grant Agreement no230357, the FORGE project. This work was partially supported by the GnR MoMaS (PACEN/CNRS, ANDRA, BRGM,CEA, EDF, IRSN) France, their supports are gratefully acknowledged.

Author information

Authors and Affiliations

  1. UNIV PAU & PAYS ADOUR, IPRA–LMA, CNRS-UMR 5142, Av. de l’université, 64000 , Pau, France

    Brahim Amaziane & Mladen Jurak

  2. Université Moulay Ismaïl, ENSAM, Marjane II, B.P. 4024, Meknes, 50000, Morocco

    Mustapha El Ossmani

Authors
  1. Brahim Amaziane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Mustapha El Ossmani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mladen Jurak
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Brahim Amaziane.

Additional information

Communicated by: Gabriel Wittum.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Amaziane, B., El Ossmani, M. & Jurak, M. Numerical simulation of gas migration through engineered and geological barriers for a deep repository for radioactive waste. Comput. Visual Sci. 15, 3–20 (2012). https://doi.org/10.1007/s00791-013-0196-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00791-013-0196-1

Keywords

Mathematics Subject Classification

Search

Navigation