Environmental Engineering Reference
In-Depth Information
TABLE 4.3. Parameters Used to Estimate Volatization Coefficient,
k
v
Henry's Law constant,
H
a
(Pa·m
3
/mol)
Compound
Φ
Ψ
A
b
B
b
Benzene
0.638
0.590
507
17.06
3194
Chlorobenzene
0.601
0.499
311
15.00
2689
Chloroethane
0.694
0.645
1030
15.80
2580
Trichloromethane (chloroform)
0.645
0.485
310
22.94
5030
1,1-Dichloroethane
0.643
0.529
465
17.01
3137
1,2-Dichloroethane
0.643
0.529
112
10.16
1522
Ethylbenzene
0.569
0.512
559
23.45
4994
Methyl tertiary-butyl ether (MTBE)
0.583
0.558
64.3
c
30.06
d
7721
d
Dichloromethane (methylene chloride)
0.697
0.568
229
20.01
4268
naphthalene
0.560
0.470
56.0
c
-
-
Tetrachloroethene
0.585
0.417
1390
22.18
4,368
Methylbenzene (toluene)
0.599
0.547
529
16.66
3024
1,1,1-Trichloroethane
0.605
0.461
1380
18.88
3399
Trichloroethene (TCE)
0.617
0.464
818
19.38
3702
Chloroethene (vinyl chloride)
0.709
0.510
2200
17.67
2931
1,2-Dimethylbenzene (
o
-xylene)
0.569
0.512
409
17.07
3220
1,4-Dimethylbenzene (
p
-xylene)
0.569
0.512
555
15.00
2689
a
All values are at 20°C, except where indicated.
b
All values are for temperatures in the range 10-30°C and were derived from Ashworth et al., (1988), except where indicated.
c
At 25°C.
d
For temperatures in the range 20-50°C, derived from Robbins et al., (1993).
concentration of the substance in the water (mol/m
3
).
The values of the Henry's law constant,
H
, given in
Table 4.2, are mostly at a temperature of 20°C, and the
variation of
H
(Pa·m
3
/mol) with temperature can be
described by the empirical equation
Solution
(a) First, calculate the volatization coefficient,
k
v
, of
TCE using Equation (4.52), where
−
1
1
1
RT
H k
k
=
+
v
B
T
d
Φ
k d
Ψ
(4.55)
ln
H A
=
−
a
3
From the data given,
d
= 1m
,
T
= 24°C = 297.15 K,
and it is known that
R
= 8.31 J/K·mol. From Table
4.2, Φ = 0.617, Ψ = 0.464,
A
= 19.38, and
B
= 3702.
Using Equation (4.55), the Henry's law constant,
H
,
at 297.15 K, is given by
where
T
is the temperature (K), and values of
A
and
B
for several voCs are listed in Table 4.2. Additional
values of
A
and
B
for many other voCs may be found
in Rathbun (1998). Substances with low volatility are
sometimes characterized by
H
< 1 Pa·m
3
/mol, and
voCs are characterized by
H
> 1 Pa·m
3
/mol.
B
T
3702
297.15
ln
H A
=
−
=
19.38
−
=
6.922
which gives
H
= 1014
P
a·m
3
/mol. From the data
given,
V
= 0.2 m/s, and
d
= 1m
; therefore, both the
o'Connor and Dobbins (1958) and owens et al.
(1964) formulas in Table 4.5 are appropriate for
calculating
k
a
at 20°C. According to the o'Connor
and Dobbins formula,
EXAMPLE 4.9
A stream has a mean velocity of 20 cm/s, an average
width of 10 m, and an average depth of 1 m. The water
and air temperatures are both 24°C, and the average
wind speed is 3 m/s. (a) If the longitudinal dispersion
coefficient in the river is 1.4 m
2
is estimate the maximum
concentration 5 km downstream of a location where
10 kg of trichloroethene (TCE) has been spilled into the
stream. (b) Would your result change significantly if
volatization is neglected?
V
d
0.5
3.93
0.2
1
0.5
k
=
3.93
=
=
1.76
d
−
1
a
1.5
1.5
and according to the owens et al. formula,
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