Tortuosity induced by defects in porous media

F. Graja, A. Duclos, Z. E. A. Fellah, A. Trik, M. Gargouri, C. Depollier

Abstract


In this paper we investigate the effects of defects on the tortuosity of an homogeneous fluid saturated porous medium. These defects are modeled by porous inclusions which alter the steady motion of the viscous fluid flowing in the medium. In this model the fluid velocity is solution of equations deduced from the Darcy’s law in the host medium and in the inclusions, subject to boundary conditions at the interface between the inclusions and the medium. The shape of the perturbed fluid streamlines allows the determination of the tortuosity induced by the defects and its consequences on the acoustic wave propagation in this medium. 


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References


B. Ghanbarian, A. G. Hunt, R.E. Ewing, and M. Sahimi ” Tortuosity in Porous Media : A Critical Review” Soil Science Society of America Journal 77: 1461-1477, (2013).

P.C. Carman ” Fluid flow through granular beds” Trans. Inst. Chem. Eng. 15:150-166 (1937).

NattavadeeSrisutthiyakorn,GeraldM.Mavko”WhatistheroleoftortuosityintheKozeny-Carman equation?”. American Association of Petroleum Geologists and Society of Exploration Geophysi- cists Print ISSN 2324-8858 Online ISSN 2324-8866

Darcy, H. P. G. ”Les fontaines publiques de la ville de Dijon”. Dalmont, Paris (1856).

H. Saomotoa, J. Katagiri ”Direct comparison of hydraulic tortuosity and electric tortuosity based

on finite element analysis” Theoretical and Applied Mechanics Letters5: 177–180 (2015).

D. L. Johnson, Frontiers in Physical Acoustics, Proceedings of the Enrico Fermi Summer School

(1984), Course XCII (Elsevier, New York)

D. Lafarge, J. F. Allard, B. Brouard, C. Verhaegen, and W. Lauriks, ”Characteristic dimensions and prediction at high frequencies of the surface impedance of porous layers” J. Acoust. Soc. Am. 93, 2474-2478 (1993).

Schlumberger ”http://www.glossary.oilfield.slb.com” .

Schiffer, M. and G. Szego ̈ ”Virtual mass and polarization” J. Trans Amer. Math Soc. 67: p 130-205 (1949).

Stoner,E. C. ,“The demagnetizing factors for ellipsoids ,” Philosophical Magazine, Vol. 36 ,Ser. 7 ,No. 263 ,803–821 (1945).

Osborn ,J. A. ,“Demagnetizing factors of the general ellipsoid ,” The Physical Review, Vol. 67 ,No. 11–12 ,351–357 (1945).

Landau, L. and E. Lifchitz ”Electodynamique des milieux continus” MIR Moscou (1969).

Prakash, J. and G.P. Raja Sekhar ”Arbitrary oscillatory Stokes flow past a porous sphere using

Brinkman model” Meccanica 47 p1079-1095 (2012).

P. R. King ”The use oof field theoretic methods for the study of flow in a heterogeneous porous

medium” J. Phys. A: Math. Gen. 20 p 3935-3947 (1987).

King, P.R. ”The use of renormalization for calculating effective permeability” Transpot in porous

media 4 p 37-58 (1989).

Drummond,I.T. and R. R. Horgan ”The effective permeability of a random medium” J. Phys. A:

Math. Gen. 20 p 4661-4672 (1987).

Dzhabrailov, V.V. and R.P. Meilanov ”Filtration in a porous medium with a fluctuating permeabil-

ity” Journal of Engineering Physics and Thermophysics 69 p 188-192 (1996).

Teodorovich,E.V.”Calculationoftheeffectivepermeabilityofarandomlyinhomogeneousporous medium” JETP 85 p 173-178 (1997).

Teodorovich, E. V. ”The effective ”Conductivity of a randomly inhomogeneous Medium” J Appl. Maths Mechs 64p 951-957 (2000).

Stepanyants, Y. A. and E.V. Teodorovich ”Effective hydraulic conductivity of a randomly hetero- geneous porous medium” Water Resources Research 39 p SHB 12-1, SHB 12-9 (2003).

D. T. Hristopulos and G. Christakos ” Variational calculation of the effective fluid permeability of hererogeneous media” Phys. Rev. E 55 p 7288-7298, (1997).

Matyka, Maciej and Khalili, Arzhang and Koza, Zbigniew, ”Tortuosity-porosity relation in porous media flow”, Phys. Rev. E 78-2, p.8 (2008).

Civan Faruk, ”Effective Correlation of Apparent Gas Permeability in Tight Porous Media”, Trans- port in Porous Media 82-2, p.375-384 (2010).

R.W. Vervoort and S.R. Cattle, ”Linking hydraulic conductivity and tortuosity parameters to pore space geometry and pore-size distribution”, Journal of Hydrology 272-1, p.36-49 (2003).

Peng Xu, Boming Yu, Yongjin Feng and Mingqing Zou ”Permeability of the fractal disk-shaped brached network with tortuosity effect” Physics of fluid 18 p 078103 (2006).

Yun Mei-Juan, Boming Yu, Zhang Bin and Huang Ming-Tao ”A geometry model for tortuosity of sreamtubes in porous media with spherical particles” Chin.Phys.Lett 22 p.1464 (2005).

Boming Yu, and Li Jian-Hua ”A geometry model for tortuosity flow path in porous media” Chin.Phys.Lett 21 p.1569 (2004).

S.W. Coleman and J.C. Vassilicos ”Tortuosity of unsaturated porous fractal materials” Phys Rev E. 78, 016308 (2008).


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