Page 225 - Soil and water contamination, 2nd edition

212 Soil and Water Contamination
500 -1
4795
.
C ( 0 . 35 , 0 . 5 ) 0 0 120 mg l
2
This example shows that in practical situations it is indeed safe to ignore the second term
in Equation (11.32).
The longitudinal dispersion coefficient D can thus be estimated by fitting a Gaussian
x
curve from tracer experiments in rivers, groundwater column experiments, and soil. From
the graph of concentration versus time or distance it is possible to estimate the variance σ
and to compute the longitudinal dispersion coefficient using Equation (11.27) (see also
Figure 11.7). The longitudinal dispersion coefficient in natural streams can also be estimated
empirically from river characteristics. Fischer et al. (1979) suggested the following empirical
equation:
u 2 x B 2
D . 0 011 (11.33)
x
H u *
2
-1
2
-1
where D = the longitudinal dispersion coefficient in m s [L T ] B = the width of the river
x
-1
channel [L], H = the depth of the river channel [L], and u = the shear velocity [L T ] given
*
by
g
u gHS u (11.34)
* x
C
-2
-2
where g = the gravitational acceleration constant (= 9.8 m s ) [L T ], S = the river slope [-],
-1
0.5
and C = Chezy’s coefficient [L T ] (see Equation 11.IVc). The shear velocity u can be

*
approximated by:
u * . 0 10 u x (11.35)
Equation (11.35) is only an approximation and does not explicitly account for ‘dead zones’
in the river.
The dispersion coefficient in groundwater is the sum of the diffusion coefficient and the
mechanical dispersion coefficient and is generally linearly related to the linear groundwater
flow velocity if mixing is dominated by mechanical dispersion:
D u (11.36)
-1
2
where D = the dispersion coefficient [L T ], α = the dispersivity of the aquifer [L], and u
-1
is the groundwater flow velocity [L T ]. However, at very low groundwater flow velocities,
molecular diffusion may contribute significantly to mixing. The relative importance of mass
transport by advection compared to dispersion over a certain stretch can be estimated using
the Peclet number :
u x x
Pe (11.37)
D x
where Pe = Peclet number [-] and Δx = some characteristic segment length [L]. The Peclet

number expresses the ratio of transport by bulk fluid motion or advection to the mass
transport by dispersion . If the Peclet number is much larger than 1, advection dominates the
mass transfer, and if it is much smaller than 1, dispersion predominates.
Longitudinal mechanical dispersion also occurs in soil, primarily as a consequence
of bioturbation. Due to the reworking of the soil particles by burrowing earthworms,
arthropoda, or macrofauna (e.g. moles, voles) contaminated soil is displaced and diluted
with deeper uncontaminated soil. If an uncontaminated soil is contaminated by deposition

10/1/2013 6:44:58 PM
Soil and Water.indd 224 10/1/2013 6:44:58 PM
Soil and Water.indd 224