Environmental Engineering Reference
In-Depth Information
Fig. 19.3
Dispersion in a porous medium, illustrating the influence of pore size, friction in the
pores and tortuosity
At the field scale also macroscopic heterogeneities, particularly of aquifer proper-
ties such as hydraulic conductivity and porosity, have to be considered in addition to
pore-scale heterogeneity. Macroscopic heterogeneities cause the flow to be focused
into zones of higher conductivity, to diverge around less permeable formations and
to be refracted in the presence of conductivity boundaries. Therefore, the moving
contaminant will experience variations from the average linear velocity also at the
macroscale.
Mechanical dispersion can occur both, along the flow direction (longitudinal dis-
persion) and normal to the flow path (transverse dispersion). The dispersive mass
flux is often described by a Fickian type law; the hydromechanical dispersion coef-
ficient is often described as the product of the dispersivity and the average linear
velocity. The overall process of hydrodynamic dispersion, taking into account the
simultaneous occurrence of molecular diffusion and hydromechanical dispersion,
can be described by means of hydrodynamic dispersion coefficients, as follows:
D
L
=
D
p
+
α
L
v
i
(19.10)
D
T
=
D
p
+
α
T
v
i
(19.11)
where
D
L
[L
2
T
−
1
] and
α
L
[L] are the longitudinal dispersion coefficient and dis-
persivity,
D
T
[L
2
T
−
1
] and
α
T
[L] are the transverse dispersion coefficient and
dispersivity and
D
p
is the pore diffusion coefficient (e.g.
D
e
/
n
). Recent research on
transverse dispersion points towards a nonlinear relationship between the hydrome-
chanical dispersion coefficient and the flow velocity (Chiogna et al.
2010
; Klenk
and Grathwohl
2002
; Olsson and Grathwohl
2007
).
The effect of hydrodynamic dispersion on the movement of a contaminant front
in one dimension is depicted in Fig.
19.4
. It can be observed that hydrodynamic
dispersion causes solutes to move both faster and slower than the advective front,
resulting in smooth concentration profiles.
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