longitudinal dispersion in nonuniform isotropic porous media

where
a m
£ m
total porosity
151
= porosity of micropore regions
length scale for the microporous regions
= overall coefficient of molecular diffusion
in the micropore regions
DL = longitudinal dispersion coefficient Ln the porous
medium without microporous regions
KL = longitudinal dispersion coefficient for
macropore/micropore system
The dispersion coefficient is the sum of direct molecular diffusion,
hydrodynamic effects, and the diffusional exchange between flowing and
stagnant regions in the bidisperse pore system. If the time of motion
is not sufficient, the mass transfer process is not described by
advection-diffusion theory. The required time is estimated by
(Passioura, 1971)
t > > 0.1
a £2
T m
-a
D
m m
Systems which display the tailing phenomenon are also known to
show an early initial breakthrough, in which the 50% relative
concentration point penetrates the column with a speed greater than the
seepage velocity. Early breakthrough is a result of the advecting pore
regions Ln the column being displaced from the column before the
diffusion dominated regions have enough time to undergo any significant
mass transfer. This may be detected through the difference in the
total and effective porosities. Early breakthrough will give a lower