Using the Volume Averaging Technique to Perform the First Change of Scale for Natural Random Porous Media

  • D. Bernard
Part of the International Centre for Mechanical Sciences book series (CISM, volume 364)


The volume averaging technique is one of the various theoretical methods providing a rigorous description of the change of scale procedure. Applying this method to pore scale flow through natural porous media gives rise to several theoretical and practical problems. This paper is a progress report of an ongoing effort to solve most of them in order to build physically and structurally realistic models of flow through natural porous media. We present here some recent results concerning the characterisation of the random geometry of those media, the definition of a Representative Elementary Volume (REV) appropriate for the considered change of scale, and the relevance of periodic boundary conditions to solve the closure problem originated in this process.


Porous Medium Representative Elementary Volume Percolation Threshold Permeability Tensor Permeability Evolution 
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  1. 1.
    Whitaker, S.: Flow in porous media I: A theoretical derivation of DARCY’s law, Transport in porous media, 1 (1986), 3–25CrossRefGoogle Scholar
  2. 2.
    Quintard, M. and Whitaker, S.: Transport processes in ordered and disordered porous media, in: Heat and Mass Transfer in Porous Media, QUINTARD, TODOROVIC Eds., Elsevier Sci. Pub., Amsterdam. 1992, 99–110Google Scholar
  3. 3.
    Barrere, J., Gipouloux, O. and Whitaker, S.: On the closure problem for DARCY’s law, Transp. in Porous Media, 7 (1992), 209–222CrossRefGoogle Scholar
  4. 4.
    Dybbs, R.G. and Edwards, R.V.: A new look at porous media fluid mechanics-Darcy to turbulent, in Fundamentals of transport phenomena in porous media, Bear,J., Corapcioglu,Y. Eds, NATO ASI Series E, N° 82, Martinus Nijhoff Pub., Dordrecht, 1984, 199–256Google Scholar
  5. 5.
    Whitaker, S.: Flow in porous media III: Deformable media, Transport in porous media, 1 (1986), 127–154CrossRefGoogle Scholar
  6. 6.
    Anguy, Y., Bernard, D. and Ehrlich, R.: The local change of scale method for modelling flow in natural porous media (I): Numerical tools, Adv. Water Res., 1994, in pressGoogle Scholar
  7. 7.
    Peyret, R. and Taylor, T.D.: Computational methods for fluid flow, Springer-Verlag, Berlin, 1983CrossRefzbMATHGoogle Scholar
  8. 8.
    Patankar, S.V.: Numerical heat transfer and fluid flow, Computational methods in mechanics and thermal sciences, Hemisphere Pub. Co., New York, 1980Google Scholar
  9. 9.
    Quiblier, J.A.: A new three-dimensional modeling technique for studying porous media, J. Coll. Interf. Sci., 98 (1984), 84–102Google Scholar
  10. 10.
    Kirpatrick, S.: Percolation and conduction, Rev. Modern Phys., 45 (1973), 574–590CrossRefGoogle Scholar
  11. 11.
    Ehrlich, R., Crabtree, S.J., Horkowitz, K.O. and Horkowitz, J.P.: Petrography and reservoir physics I: objective classification of reservoir porosity, A.A.P.G. Bulletin, 75 (1991), 1547–1562.Google Scholar
  12. 12.
    McCreesh, C.A., Ehrlich, R. and Crabtree, S.J.: Petrography and reservoir physics II: relating thin section porosity to capillary pressure, the association between pore types and throat sizes, A.A.P.G. Bulletin, 75 (1991), 1563–1578.Google Scholar
  13. 13.
    Ehrlich, R., Etris, E.L., Brumfield, D., Yan, L.P. and Crabtree, Si.: Petrography and reservoir physics III: physical models for permeability and formation factor, A.A.P.G. Bulletin, 75 (1991), 1579–1592.Google Scholar
  14. 14.
    Anguy, Y., Ehrlich, R., Prince, C.M., Riggert, V. and Bernard, D.: The sample support problem for permeability assessment in reservoir sandstones, in A.A.P.G. Spec. Pubi.: Stochastic Modeling and Geostatistics, Practical Applications and Case Histories, Eds. Yarns J. M. and Chambers R. L., 1994, in press.Google Scholar
  15. 15.
    Prince, C.M., Ehrlich, R. and Anguy, Y.: Analysis of spatial order in sandstones II: grain clusters, packing flaws, and the small-scale structure of sandstones, Jour. of Sed. Pet.,1995, in pressGoogle Scholar
  16. 16.
    Anguy, Y.: Application de la prise de moyenne volumique à l’étude de la relation entre le tenseur de perméabilité et la micro-géométrie des milieux poreux naturels, thèse de doctorat, mécanique, Univ. Bordeaux I, 1993, 170 p.Google Scholar
  17. 17.
    Graton, L.C. and Fraser, H.J.: Systematic packing of spheres with particular relation to porosity and permeability, Jour. Geology, 43 (1935), 785–909CrossRefGoogle Scholar
  18. 18.
    Bernard, D., Bodin, F., Goasguen, A. and Fechant, J.C.: Implementing a two-dimensional pore-scale flow model on different parallel machines, in A. Peters et al. (eds.), Computational methods in water resources X, Kluwer Acad. Pub., Dordrecht, 1992, 1507–1514Google Scholar

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© Springer-Verlag Wien 1995

Authors and Affiliations

  • D. Bernard
    • 1
  1. 1.C.N.R.S. URAL.E.P.T.-ENSAMTalenceFrance

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