longitudinal dispersion in nonuniform isotropic porous media

wider. The data are not conclusive in terms of quantitative
predictions of dispersion. The recent review by Greenkorn (1981)
indicates little progress has been made on dispersion in nonuniform
porous media beyond the few studies mentioned here.
43
The first theoretical model which explicitly includes the effects
of nonuniform media on dispersion is that of Haring and Greenkorn
(1970). Their approach is similar to Saffman's (1959), in which the
statistics of a single particle executing a random walk through a three-
dimensional capillary network describe the behavior of a cloud of
particles. In addition to the random orientation of pores, Haring and
Greenkorn (1970) allow for distributions of pore length and radius.
Their model assumes that the pore length distribution and pore radius
distribution can be described by beta distributions. The beta
distributions require specification of a maximum pore length and
maximum pore radius. The seepage velocity is calculated by averaging
the mean longitudinal velocity for each pore over a representative
sample of pores of random radius and orientation. The permeability
determined by combining this expression for the seepage velocity with
Darcy's law. The fact that pores of larger radius will conduct larger
quantities of fluid due to the larger cross-sectional area is
neglected. They find for the permeability
k K(a,S) (2.17)
where a = arithmetic mean pore radius