Metallurgical and Materials Transactions A

, Volume 44, Supplement 1, pp 61–69

Comparison of Different Upscaling Methods for Predicting Thermal Conductivity of Complex Heterogeneous Materials System: Application on Nuclear Waste Forms



To develop strategies for determining thermal conductivity based on the prediction of a complex heterogeneous materials system and loaded nuclear waste forms, the computational efficiency and accuracy of different upscaling methods has been evaluated. The effective thermal conductivity, obtained from microstructure information and local thermal conductivity of different components, is critical in predicting the life and performance of waste forms during storage. Several methods, including the Taylor model, Sachs model, self-consistent model, and statistical upscaling method, were developed and implemented. Microstructure-based finite-element method (FEM) prediction results were used to as a benchmark to determine the accuracy of the different upscaling methods. Micrographs from waste forms with varying waste loadings were used in the prediction of thermal conductivity in FEM and homogenization methods. Prediction results demonstrated that in term of efficiency, boundary models (e.g., Taylor model and Sachs model) are stronger than the self-consistent model, statistical upscaling method, and finite-element method. However, when balancing computational efficiency and accuracy, statistical upscaling is a useful method in predicting effective thermal conductivity for nuclear waste forms.


  1. 1.
    M.M. Abu-Khader: Progr. Nucl. Energ., 2009, vol. 51, no. 2, pp. 225–35.CrossRefGoogle Scholar
  2. 2.
    C. Greenhalgh , A. Azapagic: Environ. Sci. Pol., 2009, vol. 12, no. 7, pp. 1052–67.CrossRefGoogle Scholar
  3. 3.
    K.A. Rogers. Progr. Nucl. Energ., 2009, vol. 51(2), pp. 281–89.Google Scholar
  4. 4.
    M.R. Culley, E. Ogley-Oliver, A.D. Carton, J.C. Street: J. Commun. Appl. Soc. Psychol., 2010, vol. 20, no. 6, pp. 497–512.CrossRefGoogle Scholar
  5. 5.
    D. Clery: Science, 2011, vol. 331, no. 6024, p. 1506.CrossRefGoogle Scholar
  6. 6.
    M. Cooper: Bull. At. Sci., 2011, vol. 67, no. 4, p. 8.Google Scholar
  7. 7.
    R.E. Berlin and C.C. Stanton: Radioactive Waste Management, John Wiley and Sons Inc., New York, NY, 1988.Google Scholar
  8. 8.
    W. J. Weber, A. Navrotsky, S. Stefanovsky, E.R. Vance, and E. Vernaz: MRS Bull., 2009, vol. 34, no. 1, pp. 46–53.CrossRefGoogle Scholar
  9. 9.
    T. Allen, H. Burlet, R.K. Nanstad, M. Samaras, and S. Ukai: MRS Bull., 2009, vol. 34, no. 1, pp. 20–27.CrossRefGoogle Scholar
  10. 10.
    H. Van Eekelen: J. Catal., 1973, vol. 29, no. 1, pp. 75–82.CrossRefGoogle Scholar
  11. 11.
    Z. Hashin and S. Shtrikman: J. Appl. Phys., 1962, vol. 33, no. 10, pp. 3125–31.CrossRefGoogle Scholar
  12. 12.
    A. Decarlis, M. Jaeger, and R. Martin: J. Heat Trans., 2000, vol. 122, p. 171.CrossRefGoogle Scholar
  13. 13.
    Y.M. Lee, R.B. Yang, and S.S. Gau: Int. Commun. Heat Mass Trans., 2006, vol. 33, no. 2, pp. 142–50.CrossRefGoogle Scholar
  14. 14.
    J. Essam: J. Phys. C: Solid State Phys., 1974, vol. 7, p. L258.CrossRefGoogle Scholar
  15. 15.
    S. Kumar, N. Pimparkar, J. Murthy, and M. Alam: J. Appl. Phys., 2011, vol. 109, p. 014315.CrossRefGoogle Scholar
  16. 16.
    S. Torquato and H. Haslach Jr.: Appl. Mech. Rev., 2002, vol. 55, p. B62.CrossRefGoogle Scholar
  17. 17.
    A. Donev, S. Torquato, and F.H. Stillinger: Phys. Rev. E, 2005, vol. 71, no. 1, p. 011105.CrossRefGoogle Scholar
  18. 18.
    D.S. Li, M. Khaleel, X. Sun, and H. Garmestani: Computat. Mater. Sci., 2010, vol. 48, no. 1, pp. 133–39.Google Scholar
  19. 19.
    D. Li, G. Saheli, M. Khaleel, and H. Garmestani: Computat. Mater. Sci., 2006, vol. 38, no. 1, pp. 45–50.Google Scholar
  20. 20.
    D. Li, H. Garmestani, and J. Schwartz: J. Nucl. Mater., 2009, vol. 392(1), pp. 22–27.Google Scholar
  21. 21.
    W. Lutze and R.C. Ewing: Radioactive Waste Forms for the Future, Elsevier Science Publishers Inc., New York, NY, 1988.Google Scholar

Copyright information

© The Minerals, Metals & Materials Society and ASM International 2012

Authors and Affiliations

  1. 1.Fundamental and Computational Science DirectoratePacific Northwest National LaboratoryRichlandUSA

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