Homogenization Analysis and Permeability of Porous Media

  • Yasuaki Ichikawa
  • A. P. S. Selvadurai
Chapter

Abstract

The Navier-Stokes’ (NS) equations can be used to describe problems of fluid flow. Since these equations are scale-independent, flow in the microscale structure of a porous medium can also be described by a NS field. If the velocity on a solid surface is assumed to be null, the velocity field of a porous medium problem with a small pore size rapidly decreases (see Sect.5.3.2). We describe this flow field by omitting the convective term \(\mathbf{v} \cdot \nabla \mathbf{v}\), which gives rise to the classical Stokes’ equation. We recall that Darcy’s theory is usually applied to describe seepage in a porous medium, where the scale of the solid skeleton does not enter the formulation as an explicit parameter. The scale effect of a solid phase is implicitly included in the permeability coefficient, which is specified through experiments. It should be noted that Kozeny-Carman’s formula (5.88) involves a parameter of the solid particle; however, it is not applicable to a geometrical structure at the local pore scale.

Keywords

Porous Medium Characteristic Function Clay Mineral Saturated Density Interlayer Water 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yasuaki Ichikawa
    • 1
  • A. P. S. Selvadurai
    • 2
  1. 1.Okayama UniversityOkayamaJapan
  2. 2.McGill UniversityMontréalCanada

Personalised recommendations