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Fig. 10.4 Measured breakthrough curve of bromide with CTRW and advection-dispersion
equation (ADE) fits. Here, the quantity j represents the normalized, flux-averaged concentration:
(top) complete breakthrough curve (bottom) region identified by the bold-framed rectangle in the
top plot. Note the difference in scale units between the plots. Pressure head h =-10 cm; water
velocity v = 2.82 cm/h. The dashed line is the best advection-dispersion equation solution fit.
The solid line is the best CTRW fit. (Cortis and Berkowitz 2004 )
for these physical transport mechanisms, as well as other factors that influence
transport of reactive contaminants, such as sorption.
Of specific interest here are the analyses by Cortis and Berkowitz ( 2004 )of
transport in partially saturated, laboratory columns. Three typical breakthrough
curves from a series of miscible displacement experiments in partially saturated
soils, presented by Nielsen and Biggar ( 1962 ) and Jardine et al. ( 1993 ), were
reanalyzed using the CTRW approach. Jardine et al. ( 1993 ) measured break-
through curves on undisturbed cylindrical soil columns (8.5 cm diameter, 24 cm
length). The soil columns were saturated with 0.05 M CaCl 2 from the bottom then
allowed to drain. Bromide was used as the nonreactive, passive tracer. Cortis and
Berkowitz ( 2004 ) reexamined three breakthrough curves obtained from three
different degrees of saturation. As shown in Fig. 10.4 , the CTRW solutions were
found to reproduce the breakthrough behavior far more effectively than the
advection-dispersion equation solution. Nielsen and Biggar ( 1962 ) reported sys-
tematic deviations in the calculated parameter values using the advection-dis-
persion
equation
from
the
experimental
data,
which
displayed
non-Fickian
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