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Dynamic permeability: reformulation of theory and new experimental and numerical data

Published online by Cambridge University Press:  26 April 2006

D. M. J. Smeulders ,
R. L. G. M. Eggels  and
M. E. H. Van Dongen
D. M. J. Smeulders
Affiliation:
Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven. The Netherlands
R. L. G. M. Eggels
Affiliation:
Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven. The Netherlands
M. E. H. Van Dongen
Affiliation:
Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven. The Netherlands
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Abstract

The dynamic interaction between a rigid porous structure (porosity ϕ) and its saturating fluid is studied. From the microscopic conservation laws and constitutive relations, macroscopic equations are derived. An averaging technique proposed and discussed by for example Lévy, Auriault and Burridge & Keller is used, from which we reformulate the theory by Johnson, Koplik & Dashen. The macroscopic equations then serve to describe the high-frequency behaviour of an oscillating fluid within a porous sample. This behaviour may be characterized by the length parameter Λ and by the tortuosity parameter α∞. It is shown that Λ and α∞, which describe an oscillatory flow behaviour, may be evaluated on the basis of steady potential flow theory. Numerical results are then presented for several pore geometries, and for these geometries, the steady-state permeability k0 is computed numerically also. The parameter 8α∞k0/ϕΛ2, first introduced by Johnson et al., is then evaluated and appears to be weakly dependent on pore geometry. This implies that for many porous media the dynamic interaction is described by an approximate scaling function. New experimental data, concerning oscillating flows through several porous media, are presented. Within limits of accuracy, these data are in agreement with the approximate scaling function.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 245 , December 1992 , pp. 211 - 227
Copyright
© 1992 Cambridge University Press

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References

Auriault J. L. 1980 Dynamic behaviour of a porous medium saturated by a Newtonian fluid. Intl J. Engng Sci. 18, 775–785.Google Scholar
Auriault J. L., Borne, L. & Chambon R. 1985 Dynamics of porous saturated media, checking of the generalized law of Darcy. J. Acoust. Soc. Am. 77, 1641–1650.Google Scholar
Bear, J. & Bachmat Y. 1990 Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer.
Beasley, J. D. & Torquato S. 1988 New bounds on the permeability of a random array of spheres Phys. Fluids A 1, 199–207.Google Scholar
Biot M. A. 1961 Generalized theory of acoustic propagation in porous dissipative media. J. Acoust. Soc. Am. 34, 1254–1264.Google Scholar
Brown R. J. S. 1980 Connection between formation factor for electrical resistivity and fluid–solid coupling factor in Biot's equation for acoustic waves in fluid-filled porous media. Geophys. 45, 1269–1275.Google Scholar
Burridge, R. & Keller J. B. 1981 Poroelasticity equations derived from microstructure. J. Acoust. Soc. Am. 70, 1140–1146.Google Scholar
Charlaix E., Kushnick, A. P. & Stokes J. P. 1988 Experimental study of dynamic permeability in porous media. Phys. Rev. Lett. 61, 1595–1598.Google Scholar
Cuvelier C., Steenhoven, A. A. van & Segal G. 1986 Finite Element Methods and Navier–Stokes Equations. Reidel.
Johnson D. L. 1989 Scaling function for dynamic permeability in porous media. Phys. Rev. Lett. 63, 580.Google Scholar
Johnson D. L., Koplik, J. & Dashen R. 1987 Theory of dynamic permeability and tortuosity in fluid-saturated porous media. J. Fluid Mech. 176, 379–402.Google Scholar
Johnson D. L., Plona T. J., Scala C., Pasierb, F. & Kojima H. 1982 Tortuosity and acoustic slow waves Phys. Rev. Lett. 49, 1840–1844.Google Scholar
Johnson, D. L. & Sen P. N. 1981 Multiple scattering of acoustic waves with application to the index of refraction of fourth sound Phys. Rev. B 24, 2486–2496.Google Scholar
Landau, L. D. & Lifshitz E. M. 1959 Fluid Mechanics. Pergamon.
Larson, R. E. & Higdon J. J. L. 1989 A periodic grain consolidation model of porous media Phys. Fluids A 1, 38–46.Google Scholar
Lévy T. 1979 Propagation of waves in a fluid-saturated porous elastic solid. Intl J. Engng Sci. 17, 1005–1014.Google Scholar
Mei, C. C. & Auriault J. L. 1991 The effect of weak inertia on flow through a porous medium. J. Fluid Mech. 222, 647–663.Google Scholar
Rubenstein, J. & Torquato S. 1989 Flow in random porous media: mathematical formulation, variational principles and rigorous bounds. J. Fluid Mech. 206, 25–46.Google Scholar
Sheng, P. & Zhou M.-Y. 1988 Dynamic permeability in porous media. Phys. Rev. Lett. 61, 1591–1594.Google Scholar
Sheng P., Zhou M. Y., Charlaix E., Kushnick, A. P. & Stokes J. P. 1989 Reply to Johnson, D. L. 1989 Scaling function for dynamic permeability in porous media. Phys. Rev. Lett. 63, 581.Google Scholar
Yavari, B. & Bedford A. 1990 The Biot drag and virtual mass coefficient for face centered cubic granular materials. Intl J. Multiphase Flow 16, 885–897.Google Scholar