Environmental Engineering Reference
In-Depth Information
where
k
is the i rst-order abiotic rate constant for methyl chloroform loss,
A
is the Arrhenius con-
stant,
E
a
is the activation energy (in kJ/mol),
R
is the gas constant [8.3145 × 10
−3
kJ/(mol K)], and
T
is the absolute temperature (in K). For the abiotic degradation of methyl chloroform, the rate constant
k
is the lumped sum of the reaction rates for the elimination reaction,
k
e
, and the hydrolysis or sub-
stitution reaction,
k
s
:
k
k
s
. The elapsed time of reaction corresponding to the ratio of the con-
centration of the elimination product, 1,1-dichloroethylene, to that of its parent, methyl chloroform,
can be determined by applying the literature values of the reaction rates, as shown in Equation 9.3
(Gauthier and Murphy, 2003).
=
k
e
+
[
]
Ê
k
1,1-dichloroethylene
ˆ
1
ln 1
t
=
+
.
(9.3)
Á
˜
[
]
k
k
methyl chloroform
Ë
¯
e
A “i eld-estimate” of the abiotic rate constant
k
can be derived by plotting time-series data as the
natural logarithm of the molar concentration ratios from monitoring points. The natural logarithm
of the molar concentration ratio in Equation 9.3 is plotted on the
y
-axis and time on the
x
-axis as
dates or Julian days. A best-i t straight line then has a slope equal to the estimated
k
, and the
x
-intercept provides an estimate of the date at which hydrolysis began, that is, the approximate date
when dissolved methyl chloroform was i rst subjected to abiotic degradation. This date does not
account for the time since the actual spill, disposal, or tank leak, but rel ects the date when methyl
chloroform entered groundwater as a dissolved phase. Pure (nonaqueous phase) methyl chloroform
does not participate in abiotic degradation reactions; however, condensed water vapor in vapor
degreasers is likely to facilitate abiotic reactions that form 1,1-dichloroethylene. The molar ratios
measured in down-gradient monitoring points within the plume can only represent a travel time
from the source zone and not the date when the spill occurred (Gauthier and Murphy, 2003). In
order for
k
to be determined by time-series data from a single well, that well must be at the plume
front. If the methyl chloroform was released in the dissolved phase, for example, from wastewater
discharge out of a vapor degreaser water trap or other wastewater, measurement of the ratio of 1,1-
dichloroethylene to methyl chloroform at any location or time can be used to determine the date
when hydrolysis began (Gauthier and Murphy, 2003).
In performing ratio analysis to discern the timeframe of a release, uncertainty due to variable
rates of migration among the constituents should be considered. The primary transport parameter
that may affect the molar ratio of 1,1-dichloroethylene to methyl chloroform is sorption, which is
governed by the fraction of organic carbon in soil (
f
oc
) and the compound's organic carbon partition
coefi cient,
K
oc
. The
K
oc
for methyl chloroform is more than twice that of 1,1-dichloroethylene (152
and 65 mL/g, respectively; Pankow and Cherry, 1996). The degree to which retardation of methyl
chloroform relative to 1,1-dichloroethylene affects the ratio depends on the
f
oc
and can be signii cant
where
f
oc
is greater than 0.1%, as summarized in
Table 9.8
(Gauthier and Murphy, 2003). At higher
f
oc
values, the migration rate of 1,1-dichloroethylene may substantially exceed that of methyl chlo-
roform and so affect the molar concentration ratios. This possibility is seen by the measured and
predicted range of volume concentration ratios observed with increasing distance from the methyl
chloroform source, as shown in
Figure 9.1
.
Where biologic transformation of methyl chloroform is also evident from detection of 1,1-
dichloroethane and chloroethane, Equation 9.4 can be used:
[
]
[
]
Ê
ˆ
Ê
1,1-dichloroethylene
ˆ
1,1-dichloroethane
1
k
t
=
ln 1
+
+
,
(9.4)
Á
˜
Á
˜
[
]
[
]
k
k
methyl chloroform
methyl chloroform
Ë
¯
Ë
¯
T
e
where the total rate constant
k
T
k
b
, and
k
b
is the biodegradation rate constant for the reductive
dechlorination of methyl chloroform to 1,1-dichloroethane (Gauthier and Murphy, 2003).
=
k
+
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