Numerical Comparison of Two and Three Dimensional Flow Regimes in Porous Media

Abstract:

The purpose of this work is to study the fluid flow regimes in a porous media with high enough velocities (in the range of laminar flow). In our study, the results obtained from expanding Darcy’s equation to Forchheimer’s equation with volume averaging method have been used for studdying the fluid flow behavior in 2D and 3D models. Results of numerical simulations show that in all cases, there are weak inertial regime, strong inertial regime and transition zone. In all the cases, the domain of weak inertial regime is relatively narrow, and this problem is intensified in the 3D numerical simulations. This could be the reason of missing the weak inertial regime in experimental studies on inertial fluid flow in porous media. The domain of strong inertial regime in 3D models is so wide that after Darcy’s regime, the governed regime is the strong inertial regime. To obtain more accurate and analytical results, more studies should be done on the 2D and the 3D flow regimes.

• Periodical: Defect and Diffusion Forum (Volumes 312-315)
• Pages: 427-432
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.312-315.427
• Online since: April 2011
• Authors: Ali Akbar Abbasian Arani, Majid Dehghani
• Keywords: Forchhimer Equation, Porous Medium, Strong Inertial Flow, Three-Dimensional Flow, Two Dimensional Flow, Weak Inertial Flow

References

[1] H. Darcy: Les fontaines publiques de la ville de dijon (Librairie des corps impériaux des ponts et chaussées et des Moines, Paris, 1856).

DOI: 10.1016/s0152-9668(02)80022-5

[2] S. Whitaker: Transp. Porous Med. Vol. 1 (1986), p.3.

[3] I.F. MacDonald, M.S. El-Sayed, K. Mow, F.A.L. Dullien: Ind. Eng. Chem. Fundm. Vol. 18 (1979), p.199.

[4] Z., Chen, G. Q., Lyons: Transport in Porous Media 44(2), (2001), p.325.

[5] M. Fourar, G. Radilla, R. Lenormand and C. Moyne: Adv. Water Res. Vol. 27 (2004), p.669.

[6] J. Barrere: PhD thesis (Thèse de l'Université Bordeaux I, 1990).

[7] E. Skjetne and J.L. Auriault: Transp. Porous Med. Vol. 36 (1999), p.131.

[8] M. Firdaouss, J.L. Guermond and P. Le Quéré: J. Fluid Mech. Vol. 343 (1997), p.331.

[9] S. Whitaker: Transp. Porous Med. Vol. 25 (1996), p.27.

[10] J. B. Koch and A.J.C. Ladd: J. fluid Mech. Vol. 349 (1997), p.31.

[11] T. Hayase, J.A.C. Humphrey and R. Greif: J. Comp. Phys. Vol. 98 (1992), p.108.