longitudinal dispersion in nonuniform isotropic porous media

This expression gives the frequency distribution G(a) in terms of the
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measured cumulative distribution for pore radius by volume, Pa(a). The
distribution G(a) is normalized such that G(oo) = 1. In practice, the
"infinite" radius is the largest radius measured. In this way, we
obtain from measurements the appropriate pore radius distribution for
the theoretical model. The details of implementing this technique for
specific cases is given in Chapter 4.
The pore length distribution is also required for the calculation
of longitudinal dispersion. Very little work has been published
regarding pore length distributions in porous media, and there are no
standard techniques for its measurement. The results for dispersion in
uniform media (Saffman, 1959; 1960) have shown that the pore length is
roughly equal to the grain diameter. To extend this idea for a
nonuniform medium, we will relate the pore length distribution to the
grain size distribution. The grain size distribution for medium and
coarse sand materials is typically measured using mechanical sieving
(to be described in Chapter 4). Sieving gives the cumulative size
distribution of diameters by mass. Assuming that all the grains have the
same density and similar shapes, we can write an expression relating
the frequency distribution for a given grain size, h(d), to the
measured cumulative distribution by mass, Pd(d),
(3.50)