Environmental Engineering Reference
In-Depth Information
fugacity of the compound is given by
j
M
j
j
V
j
Z
j
f
=
.
(3.20)
This fugacity is common to all phases at equilibrium. Hence, the concentration in
each compartment is given by the following equation:
C
j
=
f
·
Z
j
.
(3.21)
More sophisticated calculations suitable for realistic situations involving time-
dependent inflow and outflow of chemicals into various compartments have been
proposed and discussed in detail by Mackay (1991). The student is referred to this
excellent reference source for more details. The purpose of this section has been to
impress upon the student how the concept of fugacity can be applied to environmental
modeling. The following example should illustrate the concept.
E
XAMPLE
3.5 F
UGACITY
M
ODEL
(L
EVEL
I)
FOR
E
NVIRONMENTAL
P
ARTITIONING
Problem statement
: Consider an evaluative environment consisting of air, water, soil,
and sediment. The volumes of the phases are as follows: air
=
6
×
10
9
m
3
, water
=
7
×
10
6
m
3
, soil
=
4.5
×
10
4
m
3
, and sediment
=
2.1
×
10
4
m
3
. Determine the equi-
librium distribution of a hydrophobic pollutant such as pyrene in this four-compartment
model. The properties for pyrene are as follows: Henry's constant
=
0.9 Pa m
3
/mol;
K
d
(
soil
)
=
1.23
×
10
3
L/kg;
ρ
s
(for sediment and soil
)
=
1.5
×
10
−
2
kg/L; and
K
d
(
sed
)
=
2.05
×
10
3
L/kg. Let the temperature be 300 K and the total inventory of
pyrene be 1000 mol.
Solution
: The first step is to calculate the fugacity capacity
Z
as follows:
1
RT
=
1
(
8.314
×
300
)
=
4
×
10
−
4
.
Air:
Z
1
=
1
H
=
1
0.89
=
Water:
Z
2
=
1.1.
1.23
×
10
3
1.5
×
10
−
2
0.89
K
d
ρ
s
H
=
Soil:
Z
3
=
=
20.7.
2.05
×
10
3
1.5
×
10
−
2
0.89
Sediment:
Z
4
=
=
34.5.
The second step is to calculate the fugacity
f
:
1000
1.2
×
10
7
=
8.5
×
10
−
5
Pa.
f
=
continued
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