Reference:
N.S. Martys and E.J. Garboczi, Physical Review B 46, 6080-6090 (1992).
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Length scales relating the fluid permeability and electrical conductivity in random
two-dimensional model porous media
N.S. Martys and E.J. Garboczi
National Institute of Standards and Technology
226/B350 Building Materials Division
Gaithersburg, Maryland 20899
Abstract
We present results of a study testing proposed length scales
l relating the bulk electrical
conductivity σ of fluid-saturated porous medium to its permeability k, via the relation
k 
l 2
σ/
σo, where σo is the fluid conductivity. For a class of two-dimensional model random porous media, we compute σ, k, and the following three length
scales: h, the ratio of pore volume to pore surface area; Λ, as defined by electrical
conductivity measurements; and dc, as defined by a non-wetting fluid injection experiment. Over
a range of two and half decades in k, we find that both Λ and
dc are reasonably good
predictors of k, whereas h clearly fails. We also examine differences between the electric fields
and the fluid-flow fields for a given pore structure by comparing their respective two-point
correlation functions. The length scale Λ is analytically related to an electric field
correlation length, and is found, to a good approximation, to be proportional to a fluid velocity
correlation length. The results of this paper demonstrate the important effect that spatial
randomness in the pore space has on flow problems. In a random pore structure, with a
distribution of pore sizes, the flow will tend to go more through the largest pore necks, decreasing
the importance of the narrowest necks that tend to dominate the behavior of periodic models.
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