Agriculture Reference
In-Depth Information
where ω is similar to that developed in the previous model (ω
=
K
e
+
K
k
) and
represents average concentration in solution
,
(Θ
=
Θ
m
C
m
+
Θ
im
C
im
). The total
amount
S
can thus be expressed by the following simplified (Langmuir) form:
__
S
ωΘ
C
=
(8.68)
__
S
1
+ωΘ
C
max
Therefore, the modified mobile-immobile model approaches a one-site
Langmuir isotherm. Moreover, the parameter
f
is absent in Equations 8.41 to
8.52 and, at equilibrium, the amounts sorbed in each fraction depend solely on
K
e
, K
k
,
and
Θ
m
.
Therefore, the partitioning coefficient
f
of the two-region con-
cept, which is a difficult-to-measure parameter, need not be specified and the
amount retained by each soil region is solely a function of the rates of reactions.
Selim and Ma (1995) applied their modified model on miscible displacement
results for atrazine. They showed that their modified approach provided good
BTC predictions for a wide range of aggregate sizes and flow velocities for a
Sharkey clay soil. They also concluded that the modified approach, which
requires fewer parameters, is superior to the original model of Selim and
Amacher (1988). Measured and predicted atrazine BTCs from a soil column
with 4 to 6 mm aggregated Sharkey soil are given Figure 8.18. Predictions
shown are based on the second-order mobile-immobile approach with differ-
ent values of the fraction of mobile water
f.
In Figure 8.19, measured and pre-
dicted BTCs for two columns of Sharkey clay soil having two aggregate sizes;
2 to 4 mm and 4 to 6 mm in diameter. In this example, the second-order model
(SOM) is compared with the coupled second-order model and the immobile-
immobile approach (SOM-MIM). The predictions are based on two estimates
1.0
f values
MS
f
= 1
0.1706
0.0959
0.1343
0.0643
0.8
f
= 0
f
=
F
no
f
0.6
0.4
0.2
0
0
5
10
15
20
25
Pore Volume (V/V
o
)
FIGURE 8.18
Measured and predicted atrazine BTC for 4- to 6-mm aggregated Sharkey. Continuous and
dashed curves are simulations using the second-order mobile-immobile approach with differ-
ent values of the fraction of mobile water
f.
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