Agriculture Reference
In-Depth Information
reaction between Cr(VI) in solution and the soil was ascribed to an irrevers-
ible reaction, which is included in the model (Equation 6.15). It is important
to realize that only the reactions of Cr(VI) with the two types of reaction sites
were assumed to attain equilibrium in 336 h. Overall retention had not reached
equilibrium because of the irreversible reaction. However, if the magnitude of
the irreversible term is small as is the case here, then reliable estimates of
S
max
and
F
can be made, although the actual
S
max
is somewhat smaller. The statistical
results indicated a close approximation of the two-site Langmuir equation to
the experimental sorption isotherms shown in Figure 6.11.
Data sets of time-dependent retention of Cr(VI) by Olivier, Windsor, and
Cecil soils and for several input (initial) concentrations (
C
o
) were used to pro-
vide estimates of the kinetic rate coefficients of the second-order approach.
Both
S
max
and
F
values previously obtained were used as model inputs and
nonlinear parameter optimization was used to estimate
k
1
,
k
2
,
k
3
,
k
4
, and
k
s
.
Two versions of SOM were used: a three-parameter or a one-site version (
k
1
,
k
2
, and
k
s
) in which
S
max
was not differentiated into type 1 and type 2 sites
(
F
= 1) and a five-parameter or a two-site version (
k
1
,
k
2
,
k
3
,
k
4
, and
k
s
) in which
two types of reaction sites were considered. For most values of
C
o
, either the
three- or five-parameter versions described the data adequately, with high
R
2
values and low parameter standard errors. The exception was the descrip-
tion of retention data for Olivier soil at high
C
o
where the retention of Cr(VI)
was not highly kinetic and more scatter in experimental data was observed.
Model calculations and data for the Olivier, Windsor, and Cecil soils are
shown in Figures 6.12, 6.13, and 6.14, respectively.
C
o
= 100
100
5
75
25
10
10
5
2
1
1
Olivier
0.1
0 8 6
144
192
240
288
336
Time, h
FIGURE 6.12
Time-dependent retention of Cr(VI) by Olivier soil. Closed squares are the data points and
solid lines are second-order model predictions for different initial concentration curves (
C
o
= 1,
2, 5, 10, 25, 50, 75, and 100 mg @ L
-1
). (From H. M. Selim and M. C. Amacher. 1997.
Reactivity and
Transport of Heavy Metals in Soils
. Boca Raton, FL: CRC Press. With permission.)
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