longitudinal dispersion in nonuniform isotropic porous media

2.4 SUmmary
46
Several different classes of permeability and dispersion models
have been reviewed and compared with published experimental data. The
vast majority of experimental and theoretical work pertain to transport
in uniform media. Both experimental and theoretical results for uniform
media indicate that miscible mass transport may be described by the
advection-diffusion equation with an enhanced dispersion coefficient.
Theoretical expressions derived by Saffman (1959) and Carman (1937) are
found to give accurate predictions of permeability for uniform media.
Experimental evidence supports the hypothesis that the two permeability
relations are equivalent. Theoretical results for longitudinal
dispersion (Saffman, 1959, 1960; Bear, 1972) show acceptable agreement
with experimental measurements, while for transverse dispersion,
theoretical calculations (Saffman, 1959, 1960) are found to have the
correct trend but do not have quantitative agreement with the
experimental data. The Saffman (1959, 1960) models are particularly
satisfying since the three dispersion mechanisms (given in Section 1.3)
are explicitly included in the analysis of solute transport through a
random capillary tube network.
Research on dispersion in nonuniform media is quite limited, but
the evidence indicates an increased dispersion due to nonuniformity.
Attempts to use an average grain size in uniform media dispersion
theories to predict dispersion in nonuniform media have not been
successful. Through an extension of the Saffman (1959) model, Haring