Environmental Engineering Reference
In-Depth Information
movement of the total solution is referred to as advection.
Because the flow of groundwater can be described by the
hydraulic conductivity as was discussed in Chap. 4, the
higher the K value the higher the potential transport by
advection of a solute, especially if the solute has a high
solubility in water and low tendency for sorption. Because
advection is related to the rate of movement of groundwater
and therefore the aquifer hydraulic conductivity, K , Darcy's
Law can be used to estimate the general extent of solute
transport by advection for a contaminant that behaves as a
conservative tracer.
The movement of a solute in groundwater does not
behave as a “plug” of solute that moves uniformly through
the subsurface. For example, the direct observation of the
downgradient extent of solute transport often revealed that
the solute was farther down the groundwater-flow path than
predicted solely on advection using Darcy's Law. This can
be explained by the fact that aquifers are not composed of
homogeneous sediments and, therefore, flowpaths are not of
equal length. This variation in K causes a variation in
groundwater velocity. The difference in sediments encoun-
tered by the solute causes some solute particles to be
retarded relative to the bulk movement of groundwater and
some solute particles to move ahead of the bulk movement
of groundwater.
These processes of dispersion are accounted for in the
solute transport equation. Dispersion includes solute move-
ment by mechanical mixing as well as the movement of
solutes along concentration gradients, or diffusion. Disper-
sion, therefore, is mathematically described as
14.2
Framework That Accounts for Solute
Transport and Plant Processes
The contaminant mass-reduction approach introduced above
may be more useful at sites where the groundwater plumes
have a discrete source area located upgradient of a phytore-
mediation application; i.e., the plants are downgradient of
the contaminant source typically to stop the migration of a
dissolved-phase plume to offsite areas. Although this sce-
nario characterizes many sites, other sites may contain mul-
tiple source areas, have DNAPL, or are smaller sites where
planting options are limited to the source area. These
conditions require a different approach in order to evaluate
the effectiveness of phytoremediation on contaminant fate.
Fortunately, past study of natural attenuation processes pro-
duced solute-transport models that describe the chemical,
physical, and biological processes that affect contaminant
fate. These models can be applied for use at phytore-
mediation sites, with slight modification.
The factors that affect the concentration of a solute in
groundwater include physical forces that drive the growth of
plumes and the physical, chemical, and biological forces that
resist plume growth (Chapelle et al. 2001). A meaningful
expression of the interaction of these processes and their
effect on solute transport in groundwater is given by the
solute-transport equation as:
Solute concentration
¼
ð
advection
Þð
dispersion
þ
diffusion
þ
sorption
þ
volatilization
D
¼
D o T
þ a
V
(14.8)
þ
biodegradation
Where D is dispersion, and D o is the diffusion coefficient
(L 2 /T) that is specific for the solute, T is a factor used to
describe the different tortuosity that the solute will encounter
based on the heterogeneity of the sediments,
þ
plant processes
Þ
(14.6)
and can be expressed mathematically as
represents the
dispersivity of the aquifer sediments (L) that is scale depen-
dent ( a increases as the flowpath increases) and sediment
type dependent, and V is the groundwater velocity (L/T).
Dispersivity is often measured at the field scale using
tracer tests with a conservative (nonreactive) solute. Under
conditions of relatively fast groundwater-flow rates, say
greater than 1-ft/day (0.3 m/day), then diffusive movement
of a solute is considered negligible and Eq. 14.8 becomes
a
D d 2 C
d x 2
d C
=
d t
¼
=
v d C
=
d x
P b K d =
n e d C
=
d x
kC
kV
kP
(14.7)
where D is the coefficient of hydrodynamic dispersion
(length squared per time), V is the velocity of groundwater
(length per time), P b is the soil bulk density, K d is the linear
sorption distribution coefficient, n e is effective porosity, k is
the first-order biodegradation coefficient, D is proportional
to V and aquifer dispersivity (ft), kV is the first-order volatil-
ization coefficient, and kP is the loss due to plant processes.
Each of these processes is described below.
D
¼ a
V
(14.9)
14.2.1 Advection and Dispersion
14.2.2 Diffusion
The movement of a solute dissolved in groundwater
that moves through a porous media that is caused by the
Diffusion is the movement of solute in response to a
gradient in concentration of the solute over space. Our first
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