The Forchheimer equation in two-dimensional percolation porous media

Xiao-Hong Wang and Zhi-Feng Liu

Physica A: Statistical Mechanics and its Applications, 2004, vol. 337, issue 3, 384-388

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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:337:y:2004:i:3:p:384-388

DOI: 10.1016/j.physa.2004.01.047

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