longitudinal dispersion in nonuniform isotropic porous media

108
space in the medium, while the grain S1ze distribution is a measure of
the lengths scaling the solid space in the medium.
The capillary drainage curve for most porous media display a
residual saturation which cannot be removed by increasing the tension
head (Bear, 1972). This residual saturation is apparently due to water
trapped in pendular rings, nonconducting pores, and other situations
which isolate water from conducting pathways. Interpretation of this
problem for pore size distributions is difficult and for this study the
residual saturation will be ignored for the purposes of determining the
pore size distributions. The residual saturation will be taken into
account, however, for the determination of total porosity.
The results of the pore S1ze distribution measurements are shown
1n Figure 4.11. As discussed in Chapter 3, the pore size distribution
corresponds to (equation (3.48»
a
P a (a) "" f n 2 g (n)dn
o
where g(n) is the frequency riistribution (by number) for the occurrence
of pores of a given size a. While the pore sizes for a uniform medium
change rapidly near the extremes of the distribution, the distribution
is relatively flat between the 5 and 95 percentile. The nonuniform
medium pore size distribution has a 50 percentile size close to that of
the uniform medium, but shows a less peaked, more log-normal
distribution of pore sizes. The 5 to 95 percentile range in pore sizes
1S 5.6 times greater than the corresponding range of pore sizes in the
uniform medium. Nominal values for the geometric mean and standard