Environmental Engineering Reference
In-Depth Information
For an instantaneous release, the resulting concen-
tration distribution is given by
TABLE 5.10. Values of
K
d
(cm
3
/g) for Selected Elements
Element
Sand
Silt
Clay
Organic
Am
1900
9600
8400
112,000
M
Hnt D D
(
x Vt
D t
−
)
2
y
D t
2
C
5
20
1
70
c x y t
( ,
, )
=
exp
−
−
4
4
4
π
Cd
80
40
560
800
L
T
L
T
Co
60
1300
550
1000
Cr
70
30
1500
270
where
M
= 1 kg,
n
= 0.2,
H
= 1 m,
D
L
= 0.03/
R
d
m
2
/d,
D
T
= 0.003/
R
d
m
2
/d,
V
= 0.1/
R
d
m/d,
x
= 0 m,
and
y
= 0 m. Substituting these values into the
expression above for the concentration distribution
yields
Cs
280
4600
1900
270
I
1
5
1
25
mn
50
750
180
150
mo
10
125
90
25
ni
400
300
650
1100
np
5
25
55
1200
( )
( )( . )
1
R
0 1
4 0 0
(
−
.
/
R t
)
2
Pb
270
16,000
550
22,000
d
d
c
( ,
0 0
, )
t
=
exp
−
Pu
550
1200
5100
1900
( .
3
/
R t
)
4
π
1 0 2
t
( .
0 03 0 003
)( .
)
d
Ra
500
36,000
9100
2400
41 95
.
R
0 083
.
t
Se
150
500
740
1800
d
3
=
exp
−
kg/m
t
R
Sr
15
20
110
150
d
Tc
0.1
0.1
1
1
Th
3200
3300
5800
89,000
In the absence of sorption,
R
d
= 1, for a sorbing
contaminant
R
d
= 29, and the concentrations at
t
= 1
hour, 1 day, and 1 week are as follows:
U
35
15
1,600
410
Zn
200
1300
2400
1600
Source of data
: Thibault et al. (1990).
Without Sorption
(
R
d
= 1)
With Sorption
(
R
d
= 29)
Time
(kg/m
3
)
(kg/m
3
)
state and speciation. As a general rule, clays will have
the largest
K
d
values for specific inorganic solutes,
cations are more strongly adsorbed than anions, and
divalent cations will be adsorbed more readily than
those of monovalent species. Thibault et al. (1990)
estimated
K
d
values for metals in soils based on soil
texture, where soils containing greater than 70% sand-
sized particles were classed as sands, those containing
more than 35% clay-sized particles were classed as
clays, loam soils had an even distribution of sand-, clay-,
and silt-sized particles or consisted of up to 80% silt-
sized particles, and organic soils contained more than
30% organic matter. The geometric mean
K
d
values for
several metals and other elements in various soils are
shown in Table 5.10.
The retardation factor,
R
d
, is most often used as
a reduction factor to be applied to the mean velocity
(as described previously); however, this factor is also
useful as a measure of the fraction of contaminant that
is in the pore water. To see this clearly, the retardation
factor defined by Equation (5.54) can be expressed in
the form
1 hour
199
28,960
1 day
7.7
1215
1 week
0.67
170
(b) Sorption results in higher contaminant concentra-
tions in the groundwater near the spill. This is a
result of the requirement that higher water concen-
trations are necessary to maintain an equilibrium
with the sorbed mass. Unrealistically high concen-
trations calculated at early times are a result of the
model assumption that the spill occurs over an infin-
itesimally small volume. To be realistic, the calcu-
lated concentrations must be less than the solubility
of the contaminant.
The sorption characteristics of metals and radionu-
clides are more difficult to predict than for organic
compounds. metals usually exist as cations in the
aqueous phase, and the degree to which metals partition
onto the solid matrix is determined by the
cation-
exchange capacity
of the solid matrix and the presence
of other cations that compete for exchange sites. The
cation-exchange capacity is greatest in matrices with
high clay content and organic matter. Several metals can
exist in several oxidation states and are often complexed
with
ligands
that are present in the aqueous phase.
The mobility of metals depends on both the oxidation
K
ρ
Vnc K Vnc
Vnc
+
ρ
d
b
d
b
R
= +
1
=
d
n
(5.56)
pollutant mass in soil and water
=
pollutant mass in water alone
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