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Theory of dynamic permeability and tortuosity in fluid-saturated porous media

Published online by Cambridge University Press:  21 April 2006

David Linton Johnson ,
Joel Koplik  and
Roger Dashen
David Linton Johnson
Affiliation:
Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108, USA
Joel Koplik
Affiliation:
Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108, USA
Roger Dashen
Affiliation:
Schlumberger-Doll Research, Old Quarry Road, Ridgefield, CT 06877-4108, USA
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Abstract

We consider the response of a Newtonian fluid, saturating the pore space of a rigid isotropic porous medium, subjected to an infinitesimal oscillatory pressure gradient across the sample. We derive the analytic properties of the linear response function as well as the high- and low-frequency limits. In so doing we present a new and well-defined parameter Λ, which enters the high-frequency limit, characteristic of dynamically connected pore sizes. Using these results we construct a simple model for the response in terms of the exact high- and low-frequency parameters; the model is very successful when compared with direct numerical simulations on large lattices with randomly varying tube radii. We demonstrate the relevance of these results to the acoustic properties of non-rigid porous media, and we show how the dynamic permeability/tortuosity can be measured using superfluid 4He as the pore fluid. We derive the expected response in the case that the internal walls of the pore space are fractal in character.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 176 , March 1987 , pp. 379 - 402
Copyright
© 1987 Cambridge University Press

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