Environmental Engineering Reference
In-Depth Information
which can be modified by changing variables from
c
to
c
*
, where
degradation rates shown in Table 5.11 reflect both the
error in assuming that biodegradation is described by a
simple first-order decay model, as well as the variability
in environmental conditions that affect biodegradation,
principally the amount and type of bacteria present in
the subsurface, geologic and hydraulic characteristics,
temperature, and concentration of dissolved oxygen in
the groundwater. The accuracies of first-order decay
rates estimated from field measurements of contami-
nant concentrations at monitoring wells are significantly
influenced by both the heterogeneity of the aquifer and
the methods used to estimate the decay rates, typically
leading to an overestimation of decay rates (Bauer
et al., 2006).
c
=
c e
*
−
λ
t
(5.60)
Substituting Equation (5.60) into Equation (5.59)
and dividing both sides by
e
−
λt
yields
3
3
*
*
2
*
∂
∂
c
t
∂
∂
c
x
∂
∂
c
x
∑
∑
+
V
=
D
(5.61)
i
i
2
i
i
i
=
1
i
=
1
which is exactly the same as the advection-diffusion
equation for a conservative tracer. The practical impli-
cation of this result is that the fate and transport of a
tracer undergoing first-order decay is the same as if the
tracer is initially assumed to be conservative, and the
resulting concentration distribution reduced by a factor
e
−
λt
, where
t
is the time since release of the tracer mass.
The first-order decay coefficient,
λ
, is frequently
expressed in terms of the
half-life
,
T
50
(T), which is the
time required for 50% of the initial mass to decay and
is related to the first-order decay coefficient by
EXAMPLE 5.11
Ten kilograms of a contaminant is spilled into the
groundwater and is well mixed over a 1-m depth. The
mean seepage velocity in the aquifer is 0.5 m/day,
the porosity is 0.2, the longitudinal dispersion coeffi-
cient is 1 m
2
/d, the horizontal-transverse dispersion
coefficient is 0.1 m
2
/d, vertical mixing is negligible, and
the first-order decay constant of the contaminant is
0.01 day
−1
. (a) Determine the maximum concentration
in the groundwater after 1, 10, 100, and 1000 days.
(b) Compare these concentrations to the maximum con-
centration without decay.
=
ln
λ
2
T
50
(5.62)
The half-lives of several organic compounds in soils
are summarized in Table 5.11. The variability of the
TABLE 5.11. First-Order Decay Rates of Selected Organic Compounds in Soil
Half-Life,
T
50
First-Order Decay Rate,
λ
Compound
(d)
(d
−1
)
Acetone
2-14
0.050-0.35
Benzene
10-730
0.00095-0.069
Bis(2-ethylhexyl) phthalate
10-389
0.00178-0.069
Carbon tetrachloride
7-365
0.0019-0.099
Chloroethane
14-56
0.0124-0.0495
Chloroform
56-1800
0.000385-0.0124
1,1-Dichloroethane
64-154
0.00450-0.0108
1,2-Dichloroethane
100-365
0.00190-0.00693
Ethylbenzene
6-228
0.00304-0.116
methyl tertiary-butyl ether (mTBE)
56-365
0.00190-0.0124
methylene chloride
14-56
0.0124-0.0495
naphthalene
1-258
0.00269-0.693
Phenol
0.5-7
0.099-1.39
Toluene
7-28
0.0248-0.099
1,1,1-Trichloroethane
140-546
0.00127-0.00495
Trichloroethene
321-1650
0.000420-0.00216
Vinyl chloride
56-2880
0.000241-0.0124
Xylenes
14-365
0.00190-0.0495
Source of data
: Howard et al. (1991).
Search WWH ::
Custom Search