The Forchheimer equation in two-dimensional percolation porous media

✍ Scribed by Xiao-Hong Wang; Zhi-Feng Liu

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 195 KB
• Volume: 337
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2004.01.047

✦ Synopsis

Based on solving the Navier-Stokes equations in the two-dimensional percolation porous media for 500 di erent conÿgurations, the scaling relations for the uid permeability k and the inertial parameter ÿ in the Forchheimer equation are studied. In the vicinity of the critical threshold pc, the uid permeability k and the inertial parameter ÿ will crossover from the fractal behaviors: k ∼ L -1 , ÿ ∼ L 2 , where 1 ≈ 1:0, 2 ≈ 2:0 for the small size L, to the constants: k ∼ (p -pc) 1 , ÿ ∼ (p -pc) -2 , where 1 ≈ 4 3 , 2 ≈ 8 3 . Compared to the viscous ow, the resistance to ow will have a larger critical exponent for the ÿnite Reynolds number ows.