longitudinal dispersion in nonuniform isotropic porous media

iv
ABSTRACT
A theoretical and experimental investigation has been made of the
longitudinal dispersion of chemically and dynamically passive solutes
during flow through nonuniform, isotropic porous media. Both
theoretical and experimental results are limited to the high Pee let
number, low Reynolds number flow regime. The goal of the theoretical
investigation is to provide a quantitative method for calculating the
coefficient of longitudinal dispersion using only measurable structural
features of the porous medium and the characteristics of the carrying
fluid and solute. A nonuniform porous medium contains variations Ln
grain scale pore structure, but is homogeneous at the macroscopic level
for quantities such as the permeability or porosity.
A random capillary tube network model of nonuniform porous media
is developed which uses a pore radius distribution and pore length
distribution to characterize the grain scale structure of porous media.
The analysis gives the asymptotic longitudinal dispersion coefficient
in terms of integrals of kinematic properties of solute particles
flowing through individual, random capillary tubes. However, shear
dispersion within individual capillary tubes is found to have
negligible impact on the overall longitudinal dispersion in porous
media. The dispersion integrals are evaluated using a Monte Carlo
integration technique. An analysis of the permeability in nonuniform
porous media is used to establish a proper flow field for the analysis
of longitudinal dispersion.