Environmental Engineering Reference
In-Depth Information
in which
a
T
is the transverse dispersion coefficient,
a
L
is the longitudinal dispersion
coefficient and both parameters have the dimension of a length. The transverse
dispersion coefficient is about one order of magnitude lower than the longitudinal
one.
The longitudinal and transverse dispersion coefficients can be determined in the
laboratory or
in situ
by inverse analysis of tracing tests. The values obtained in the
two cases differ; they often have the same magnitude as the tested sample length or
the same magnitude of heterogeneities of the sample. This indicates sensitivity to
the measurement scale that must be taken into account in any pollutant transport
modeling.
At very large scale (more than 100 m during the study of regional aquifers), the
dispersion coefficients are likely to vary. These changes probably result, at least in
part, from the natural heterogeneity of soil and rocks. They may also be an artifact.
Analysis of this heterogeneity and the spatial variability of the material properties is
likely to partially remove this ambiguity [BEA 87, BIV 93]
13.2.4.
Transport laws: diffusion
Even in the absence of any fluid flow, pollutant diffusion occurs from high
concentrations to low ones and tends towards uniform concentrations. This is due to
molecular agitation. The corresponding Fick's diffusion law is isotropic. The
diffusion pollutant flow (average or homogenized REV value) is:
v
=− ∇
d
C
[13.9]
m
diffusion
The concentration appears as a chemical potential here.
d
m
is the molecular
diffusion coefficient, expressed in m
2
/s. In open water, the diffusion coefficient
varies for ions between 5 x 10
-10
and 100 x 10
-10
m
2
/s. In a porous medium, it is
altered on one hand by the presence of the solid phase, which reduces the volume of
fluid allowing diffusion; and on the other hand by the tortuosity of the channels. As
a consequence, diffusion processes are usually extremely slow.
It is impossible to experimentally separate molecular diffusion from mechanical
dispersion. The two are often grouped under so-called
hydrodynamic dispersion
.
13.2.5.
Transport laws: synthesis
The transfer flow of a miscible pollutant (average or homogenized REV value) is
equal to the sum of three components outlined below:
