Geoscience Reference
In-Depth Information
Fig. 10.1 Effect of different
mechanisms on behavior of
contaminants advancing
through a column of porous
material; the relative
concentration is given by
c/c
o
: a temporal breakthrough
curves at the column outlet,
showing effects of diffusion
and dispersion; b spatial
concentration profiles along
the column, at different times;
c spatial concentration
profiles illustrating effects of
retardation caused by
contaminant absorption
where D
h
is now the hydrodynamic dispersion, and
D
h
a
L
v
þ
D
;
ð
10
:
6
Þ
with a
L
being the longitudinal dispersivity coefficient. This formulation relies on
the fundamental assumption that mechanical dispersion is a Fickian process, which
can be described similarly to molecular diffusion (i.e., using Eq.
10.1
).
Note that Eq. (
10.5
) is written to allow the velocity to vary as a function of
location; typical application of the advection-dispersion equation assumes the
velocity and the hydrodynamic coefficients to be constant. Moreover, the time
dependence of these parameters arises when flow (infiltration) is unsteady or tran-
sient; in these cases, the contact time between contaminants and the solid matrix
(and any immobile water within it) is too short to allow an equilibrium to be reached.
Figure
10.1
shows the behavior of contaminant breakthrough curves (concen-
tration as a function of time, at the column outlet) as well as spatial concentration
profiles, in a water-saturated column initially at concentration c = 0, with a
(constant) inlet concentration c
o
. Piston flow, shown in Fig.
10.1
a, refers to the
hypothetical situation of purely advective transport of a contaminant, given by the
fluid velocity v, in the absence of diffusion, dispersion, and any reactive mecha-
nisms. In reality, diffusion and dispersion (and often reactive mechanisms) are
always present, so that breakthrough curves generally take on an ''S'' shape with
varying degrees of elongation of the early arrival times and late time tails
