longitudinal dispersion in nonuniform isotropic porous media

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CHAPTER 3
A THEORETICAL MODEL FOR PERMEABILITY AND LONGITUDINAL DISPERSION
IN NONUNIFORM POROUS MEDIA
In this chapter, a theoretical method is developed for computing
permeability and longitudinal dispersion in isotropic, nonuniform
porous media based on structural features of the medium. As discussed
in Chapter 2, the spectrum of length scales present in a nonuniform
medium is important in determining the transport behavior of miscible
solutes. Because of additional variables describing the distribution
of length scales, there are more dimensionless groups to correlate
through experimentation. Since the range of parameters is large, it
would be helpful to have reliable models. Of the models presented in
Chapter 2, the network model, statistical capillary tube model, and the
volume-averaging model are capable of being extended to nonuniform
media. The model to be developed here is an extension of the random
capillary tube model proposed by Saffman (1959). No extensions were
attempted with the network model or the volume-averaging model.
As for the original model for uniform media (Saffman, 1959), the
extended model is also limited to high Pec1et number flows. The model
follows the original Saffman (1959) model closely, and is similar in
some respects to the nonuniform media model proposed by Haring and
Greenkorn (1970); however, there are some important differences:
1. Molecular diffusion is included as in the Saffman (1959) model such
that an asymptotic longitudinal dispersion coefficient may be obtained,
in contrast to the Haring and Greenkorn (1970) model.