A simple mathematical model for determining the equivalent permeability of fractured porous media

Jianjun Liu, Yoshihiko Sano, Akira Nakayama

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

A simple mathematical model has been proposed so as to determine the equivalent permeability of fractured porous media. The model consists of square blocks placed in an array with vertical and horizontal fractures between the blocks. An analytical expression valid for all macroscopic flow directions has been derived for the equivalent permeability of the fractured porous media, assuming a horizontal flow through the blocks placed in a porous medium. The analytical expression agrees well with the existing equations and also with the microscopic numerical results carried out using a unit structure with periodic boundary conditions. The foregoing two-dimensional model has been extended to a three dimensional case in which the cubic rocks are arranged in a cubic array. The resulting three-dimensional analytical expression for the equivalent permeability is found to agree very well with both existing formula and microscopic numerical simulation.

Original languageEnglish
Pages (from-to)220-224
Number of pages5
JournalInternational Communications in Heat and Mass Transfer
Volume36
Issue number3
DOIs
Publication statusPublished - Mar 2009
Externally publishedYes

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Porous materials
mathematical models
permeability
Mathematical models
two dimensional models
Rocks
Boundary conditions
rocks
boundary conditions
Computer simulation
simulation
Direction compound

Keywords

  • Darcy's law
  • Equivalent permeability
  • Fractured porous media
  • Numerical experiment

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics

Cite this

A simple mathematical model for determining the equivalent permeability of fractured porous media. / Liu, Jianjun; Sano, Yoshihiko; Nakayama, Akira.

In: International Communications in Heat and Mass Transfer, Vol. 36, No. 3, 03.2009, p. 220-224.

Research output: Contribution to journalArticle

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