Double porousity theory in geomechanics and multiscale homogenization analysis

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Abstract

The double porosity theory was first given by Bareblatt, Zheltov and Kochina, which considers the effect of fissures and matrix porosity in the rock-mass seepage problem, and they introduced an assumption that the mass flow between the two porosity systems is determined by the pressure gap of the two systems. It was extended to deformable porous media (i.e., consolidation theory). These conventional double porosity theory is based on a local-averaged mixture theory. The modern homogenization theory was developed for the materials with periodic micro-structures. Starting with Navier-Stokes and mass-conservation equations and applying the homogenization procedure to a porous media flow yield Darcy's law and the seepage equation. It is important that the flow field in porous media is determined on a balance of the pressure field and the velocity field, and that we can identify the local pressure/velocity field by the homogenization theory. We here present a new double porosity theory applying on a multiscale homogenization analysis method for porous materials with two-scale porosity systems.

Original languageEnglish
Pages (from-to)130-134
Number of pages5
JournalZairyo/Journal of the Society of Materials Science, Japan
Volume51
Issue number2
Publication statusPublished - Feb 2002
Externally publishedYes

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Geomechanics
homogenizing
Porosity
porosity
Porous materials
seepage
Seepage
velocity distribution
conservation equations
mass flow
consolidation
porous materials
pressure distribution
Consolidation
Conservation
Flow fields
flow distribution
Rocks
rocks
microstructure

Keywords

  • Double porosity
  • Fissured rock
  • Geomechanics
  • Homogenization
  • Multiscale analysis

ASJC Scopus subject areas

  • Chemical Engineering (miscellaneous)
  • Metals and Alloys
  • Polymers and Plastics

Cite this

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abstract = "The double porosity theory was first given by Bareblatt, Zheltov and Kochina, which considers the effect of fissures and matrix porosity in the rock-mass seepage problem, and they introduced an assumption that the mass flow between the two porosity systems is determined by the pressure gap of the two systems. It was extended to deformable porous media (i.e., consolidation theory). These conventional double porosity theory is based on a local-averaged mixture theory. The modern homogenization theory was developed for the materials with periodic micro-structures. Starting with Navier-Stokes and mass-conservation equations and applying the homogenization procedure to a porous media flow yield Darcy's law and the seepage equation. It is important that the flow field in porous media is determined on a balance of the pressure field and the velocity field, and that we can identify the local pressure/velocity field by the homogenization theory. We here present a new double porosity theory applying on a multiscale homogenization analysis method for porous materials with two-scale porosity systems.",
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