Fractals and Porous Media

From Pore to Geological Scales
  • R. Lenormand
Part of the International Centre for Mechanical Sciences book series (CISM, volume 378)


Modeling of fluid flow through porous media presents three main properties: very large range of length scales, strong heterogeneity and, in some cases, flow instability. All these properties can be studied using a fractal approach and statistical physics. The purpose of this course is to illustrate this approach for various kinds of fluid displacements.
  1. 1)

    The internal surface of rocks is very rough due to mineralization and dissolution (diagenesis). This surface can be modeled using fractal geometry and different techniques are used to measure the surface fractal dimension.

  2. 2)

    For heterogeneous media, permeability can be calculated using effective medium theory or renormalization.

  3. 3)

    Displacements in porous media subject to an instability such as viscous fingering and matrix etching can be described by a statistical process called DLA.

  4. 4)

    Immiscible displacements are controlled by capillary effects. The displacement of a wetting fluid by a nonwetting fluid is described by invasion percolation. The reverse process is more complicated and depend upon pore size and topology. One of the mechanism leads to stable displacements related to crystal growth.

  5. 5)

    Spreading of a tracer depends strongly of the scale of observation. At large scale, spreading is controlled by permeability heterogeneities. In some cases, the transport equation may involve fractional derivatives.

  6. 6)

    Multifractal is a useful tool for describing heterogeneity and correlation of the permeability field. A method for constructing a multifractal field is presented and the difference between fractal and multifractal is explained.



Porous Medium Fractal Dimension Capillary Pressure Fractional Derivative Percolation Cluster 


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Copyright information

© Springer-Verlag Wien 1997

Authors and Affiliations

  • R. Lenormand
    • 1
  1. 1.Institut Français du PétroleRueil-MalmaisonFrance

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