Transport in Porous Media

, Volume 98, Issue 3, pp 699–712 | Cite as

Modeling of Nuclear Species Diffusion Through Cement-Based Materials

  • Thomas Wattez
  • Anne Duhart-Barone
  • Sylvie LorenteEmail author


The use of cement-based materials for radioactive waste confinement and storage must rest on precise measurements of their physical and chemical properties. An important property is the diffusivity of tritium in its liquid form (tritiated water) through a sample considered as representative. Here, we report quantitatively the effect of radioactive decay compared to the effective diffusion coefficient on tritium diffusion. The numerical model was validated by comparing it to experimental data. We found that, in the worst case scenario, the calculated effective diffusion coefficient of tritiated water based on the classical analytical solution to Fick’s law is underestimated by more than 20 %, compared with the results provided by the numerical model, which accounts for the radioactive decay within the material.


Diffusion Tritium Cement-based materials 



The authors would like to acknowledge and thank the National Radioactive Waste Management Agency, Andra, for supporting this study, and contributing to the funding of this research. We would like to address our special thank to A. Le Cocguen from CEA Cadarache for providing the experimental data.


  1. AFPC-AFREM: Méthodes recommandées pour la mesure des grandeurs associées à la durabilité. AFPC-AFREM, Toulouse (1997)Google Scholar
  2. Atabek, R., Bouniol, P., Vitorge, P., Le Bescop, P., Hoorelbeke, J.M.: Cement use for radioactive waste embedding and disposal purposes. Cem. Concr. Res. 22, 419–429 (1992)CrossRefGoogle Scholar
  3. Bégué, P., Lorente, S.: Migration versus diffusion through porous media: time dependent scale-analysis. J. Porous Media 9, 637–650 (2006)Google Scholar
  4. Bejan, A., Dincer, I., Lorente, S., Miguel, A.F., Reis, A.H.: Porous and Complex Flow Structures in Modern Technologies. Springer, Berlin (2004)CrossRefGoogle Scholar
  5. Bejan, A.: Convection Heat Transfer, 3rd edn. Wiley, Hoboken (2004)Google Scholar
  6. Bejaoui, S., Bary, B.: Modeling of the link between microstructure and effective diffusivity of cement pastes using a simplified composite model. Cem. Concr. Res. 37, 469–480 (2007)CrossRefGoogle Scholar
  7. Bejaoui, S., Sercombe, J., Mugler, C., Peycelon, H.: Modelling of radionuclide release from a concrete container. Transp. Porous Media 69, 89–107 (2007)CrossRefGoogle Scholar
  8. Carslaw, H., Jaeger, J.: Operational Methods in Applied Mathematics. Oxford University Press, London (1953)Google Scholar
  9. Cassette, P., Grigorescu, E.L., Razdolescu, A.C.: Obtaining tritiated water standards using triple to double coincidence ratio (TDCR) method. In: IDRANAP Conference, Neptun (2002)Google Scholar
  10. Crank, J.: The Mathematics of Diffusion, 2nd edn. Oxford Science, Oxford (1980)Google Scholar
  11. Delagrave, A., Marchand, J., Pigeon, M.: Influence of microstructure of the tritiated water diffusivity on mortars. Adv. Cem. Based Mater. 7, 60–65 (1998)CrossRefGoogle Scholar
  12. Descostes, M., Pili, E., Felix, O., Frasca, B., Radwan, J., Juery, A.: Diffusive parameters of tritiated water and uranium in chalk. J. Hydrol. 452–453, 40–50 (2012)CrossRefGoogle Scholar
  13. Fick, A.: On liquid diffusion (reprinted from the London Edinburgh, and Dublin Philosophical Magazine and Journal of Science 10 (1855) p. 30). J. Membr. Sci. 100, 33–38 (1995)CrossRefGoogle Scholar
  14. Frizon, F., Lorente, S., Ollivier, J.P., Thouvenot, P.: Transport model for the nuclear decontamination of cementitious materials. Comput. Mater. Sci. 27, 507–516 (2003)CrossRefGoogle Scholar
  15. Kamali-Bernard, S., Bernard, F., Prince, W.: Computer modelling of tritiated water diffusion test for cement based materials. Comput. Mater. Sci. 45, 528–535 (2009)CrossRefGoogle Scholar
  16. Locoge, P., Massat, M., Ollivier, J.P., Richet, C.: Ion diffusion in microcracked concrete. Cem. Concr. Res. 22, 431–438 (1992)CrossRefGoogle Scholar
  17. Lorente, S., Ollivier, J.P.: Scale analysis of electrodiffusion through porous media. J. Porous Media 9, 307–320 (2006)CrossRefGoogle Scholar
  18. Lorente, S., Voinitchi, D., Bégué-Escaffit, P., Bourbon, X.: The single-valued diffusion coefficient for ionic diffusion through porous media. J. Appl. Phys. 101, 024907 (2007)CrossRefGoogle Scholar
  19. Lorente, S.: Constructal view of electrokinetic transfer through porous media. J. Phys. D Appl. Phys. 40, 2941–2947 (2007)CrossRefGoogle Scholar
  20. Motellier, S., Devol-Brown, I., Savoye, S., Thoby, D., Alberto, J.-C.: Evaluation of tritiated water diffusion through the Toarcian clayey formation of the Tournemire experimental site (France). J. Contam. Hydrol. 94, 99–108 (2007)CrossRefGoogle Scholar
  21. Nield, D.A., Bejan, A.: Convection in Porous Media, 3rd edn. Springer, Berlin (2006)Google Scholar
  22. Norme Française M60–326: Détermination du coefficient de diffusion effectif de l’eau tritiée dans un matériau de confinement. AFNOR, La Plaine Saint-Denis (2006)Google Scholar
  23. Odian, G., Kruse, R.: Diffusional effects of radiation-induced graft in polymerization. J. Polym. Sci. 22, 691–712 (1969)Google Scholar
  24. Richet, C.: Etude de la migration des radioéléments dans les liants hydrauliques—Influence du vieillissement des liants sur les mécanismes et la cinétique des transferts. Thèse de l’Université Paris XI, Orsay (1992)Google Scholar
  25. Savoye, S., Page, J., Puente, C., Imbert, C., Coelho, D.: New experimental approach for studying diffusion through an intact and unsaturated medium: a case study with Callovo-Oxfordian argillite. Environ. Sci. Technol. 44, 3698–3704 (2010)CrossRefGoogle Scholar
  26. Tevissen, E., Soler, J.M., Montarnal, P., Gautschi, A., Van Loon, L.R.: Comparison between in situ and laboratory diffusion studies of HTO and halides in Opalinus clay from the Mont Terri. Radiochim. Acta 92, 781–786 (2004)CrossRefGoogle Scholar
  27. Tits, J., Jakob, A., Wieland, E., Spieler, P.: Diffusion of tritiated water and \(^{22}{\rm Na}^{+}\) through non-degraded hardened cement pastes. J. Contam. Hydrol. 61, 45–62 (2003)CrossRefGoogle Scholar
  28. Vokal, A., Vopalka, D., Vecernik, P.: An approach for acquiring data for description of diffusion in safety assessment of radioactive waste repositories. J. Radioanal. Nucl. Chem. 286, 751–757 (2010)CrossRefGoogle Scholar
  29. Wilson, J.: Diffusion effects of the photochemistry of solid films. J. Chem. Phys. 22, 334–343 (1954)CrossRefGoogle Scholar
  30. Yamaguchi, T., Negishi, K., Hoshino, S., Tanaka, T.: Modeling of diffusive mass transport in micropores in cement based materials. Cem. Concr. Res. 39, 1149–1155 (2009)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Thomas Wattez
    • 1
    • 2
  • Anne Duhart-Barone
    • 2
  • Sylvie Lorente
    • 1
    Email author
  1. 1.Laboratoire Matériaux et Durabilité des Constructions (LMDC)Université de Toulouse, UPS, INSAToulouse Cedex 04France
  2. 2.DEN/DSN/SEEC/LECDSaint Paul Lez DuranceFrance

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