Abstract of the paper ``Kozeny-Carman relations and image processing methods for
estimating Darcy's constant'' with Stephen C. Blair
A natural connection is demonstrated
between Kozeny-Carman relations for porous media and the image processing
techniques which have recently been applied to the problem of estimating
the parameters in such relations. We show that the specific surface area term
in the Kozeny-Carman relation is best estimated from a smoothed version of the
actual material surface and then demonstrate that to measure this image
specific surface the magnification of a cross-section
of the porous material should be chosen
so that a typical correlation length for the sample corresponds to a
distance comparable to 100 discrete picture elements. Under these conditions,
the assumptions typically
made in the derivation of a Kozeny-Carman relation are
entirely compatible with the resolution constraints imposed by digitizing
the image. Thus, although the measured image specific surface may be
considerably smaller in magnitude than the true specific surface area of the
material (due
to resolution constraints), this smaller value is nevertheless the required
input to the Kozeny-Carman relation. The argument is based on a known
comparison theorem relating the permeabilities of two porous materials
which differ only by the addition (without rearrangement) of solid to the one
more porous.
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