Geoscience Reference
In-Depth Information
water infiltration processes, other quantification methods (e.g., using network
models) can be applied. Similar alternative approaches are also appropriate for
modeling displacement of immiscible contaminant phases (NAPLs) in water. We
deal with these problems in
Sect. 11.4
.
The vast majority of literature on quantifying transport processes has been con-
sidered in the framework of laboratory experiments. Field experiments, which often
display fundamental differences in transport behavior relative to laboratory experi-
ments, are inevitably subject to serious uncertainties, relating to initial and boundary
conditions, medium heterogeneity, and experimental control. A major aspect—and
difficulty—lies in integrating laboratory and field measurements and upscaling
small-scale laboratory measurements to treatment of field-scale phenomena.
Throughout the following sections, we consider mechanisms relevant to both the
(partially saturated) vadose and capillary fringe zones as well as to saturated zones.
10.1 Advection, Dispersion, and Molecular Diffusion
At the scale of soil and rock pores, the two principal transport mechanisms are
molecular diffusion and advection. At larger scales, transport is usually quantified
in terms of an additional parameter, referred to as mechanical dispersion.
Molecular diffusion is a process in which chemical species move from regions of
high concentration to regions of low concentration by Brownian motion. The rate of
movement is directly proportional to the concentration gradient, normal to the
direction of movement. Distribution of chemicals in the near surface and subsurface
is not uniform, so that molecular diffusion is an ever-present mechanism.
In bulk water (free solution), the diffusive flux, J
d
, given in units of mass per
area per time, is related to the concentration by Fick's first law,
J
d
¼
D
dc
ð
10
:
1
Þ
dx
;
where D is the diffusion coefficient in free solution, c denotes chemical concen-
tration in the water, and dc/dx is the concentration gradient. In a porous medium,
the diffusion coefficient is modified and called the apparent diffusion coefficient.
The apparent diffusion coefficient, D*, is smaller because the solid matrix forces
ions to follow longer paths of diffusion. Usually, we write D* = xD, where x \ 1
is
an
empirical
coefficient.
Laboratory
studies
typically
indicate
that
0.01 \ x \ 0.5 for nonsorbing ions in soils and rock materials.
In partially saturated media, the diffusion coefficient also is a function of the
volumetric water content, h. Calvet (
1984
) showed that the variation in soil water
content influences the apparent diffusion coefficient for organic contaminants in
two ways: by changing the ratio of gas diffusion of volatilizable pollutants to liquid
diffusion, because the air-filled porosity is affected, and by modifying pollutant
adsorption at low water contents, because of competition between organic and
water molecules.
