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The Forchheimer equation in two-dimensional percolation porous media

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  • Wang, Xiao-Hong
  • Liu, Zhi-Feng

Abstract

Based on solving the Navier–Stokes equations in the two-dimensional percolation porous media for 500 different configurations, the scaling relations for the fluid permeability k and the inertial parameter β in the Forchheimer equation are studied. In the vicinity of the critical threshold pc, the fluid permeability k and the inertial parameter β will crossover from the fractal behaviors: k∼L−μ1, β∼Lμ2, where μ1≈1.0, μ2≈2.0 for the small size L, to the constants: k∼(p−pc)α1, β∼(p−pc)−α2, where α1≈43, α2≈83. Compared to the viscous flow, the resistance to flow will have a larger critical exponent for the finite Reynolds number flows.

Suggested Citation

  • Wang, Xiao-Hong & Liu, Zhi-Feng, 2004. "The Forchheimer equation in two-dimensional percolation porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 337(3), pages 384-388.
  • Handle: RePEc:eee:phsmap:v:337:y:2004:i:3:p:384-388
    DOI: 10.1016/j.physa.2004.01.047
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    Cited by:

    1. Wu, Bin & Liu, Zhi-Feng & Wang, Xiao-Hong, 2013. "Statistical behaviors for renormalization of correlated permeability field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(15), pages 3115-3121.

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