longitudinal dispersion in nonuniform isotropic porous media

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(3.44» involving the pore size distribution, pore length distribution,
and porosity which characterize the structure of the porous medium.
The utility of the model is dependent on a means of determining these
properties. Measurements of the porosity follow standard methods which
are described in Chapter 4.
The pore radius distribution as determined by capillary drainage
or mercury porosimetry experiments gives the "effective" pore size as a
function of the pore volume of the sample. For a given pore radius, we
can measure what fraction of the pore volume is "controlled" by pores
with effective radii less than or equal to the given pore radius. This
type of pore radius distribution is a volume-weighted distribution,
while the theoretical model requires a pore radius distribution
according to the frequency of occurrence of a given pore radius. The
necessary change is made as follows.
Following Haring and Greenkorn (1970), we can relate the measured
pore radius distribution to the random capillary tube network model.
Let N be the total number of pores contained in the medium. Assuming
the pore length to vary independently of the pore radius, the fraction
of pore volume contained in an infinitesimal range dn of pore radius
n is given by
(3.45 )
where £ 1S the mean pore length. The cumulative volume of pore space
in the medium with pore radius between 0 and a is given by integrating