Environmental Engineering Reference
In-Depth Information
E
XAMPLE
6.8 E
VAPORATION FROM A
W
ELL
-S
TIRRED
S
URFACE
Many compounds of low solubility (such as pesticides, PCBs, and hydrocarbons) evap-
orate from open waters in lakes and oceans. For a 1 m
2
of area with depth
Z
cm, estimate
the half-life for evaporation of the following compounds: benzene, biphenyls, aldrin,
and mercury.
Theevaporationisassumedtooccurfromavolume
Z
cm
×
1cm
2
=
Z
cm
3
ofsurface
water that is well mixed as a result of surface turbulence. A material balance over the
volume
Z
cm
3
gives
input
=
output
+
reaction
+
accumulation.
0
=
K
w
(C
w
−
C
a
K
aw
)
+
0
+
Z
d
C
w
d
t
,
(6.74)
where the rate of loss by reaction is zero on account of the refractory nature of the
chemical. Rearranging and integrating with
C
w
=
C
0
at
t
=
0, we obtain
C
0
−
exp
.
C
a
K
aw
+
C
a
K
aw
−
K
w
t
Z
C
w
=
(6.75)
If background air concentration is negligible,
C
a
=
0.
C
w
=
C
0
exp
−
K
w
t
Z
=
C
0
exp
(
−
k
voln
t)
.
(6.76)
Hence, the half-life is
t
1
/
2
=
0.693
Z/K
w
. Mackay and Leinonen (1975)
give values of
K
w
for several compounds at 298 K:
0.693
/k
voln
=
P
i
Compound
(mm Hg)
K
w
(m/h)
t
1
/
2
(
h
) for
Z
=
1m
Benzene
95.2
0.144
4.8
Biphenyl
0.057
0.092
7.5
6
×
10
−
6
3.72
×
10
−
3
Aldrin
186.3
1.3
×
10
−
3
Mercury
0.092
7.5
Note that the half-lives of both biphenyls and mercury are the same, although their
vapor pressure varies by a factor of 2. Note also that
K
w
is obtained from the individual
transfer coefficients
k
w
and
k
a
and requires a knowledge of
K
aw
as well. These can be
obtained by applying the diffusivity correction for
k
w
of oxygen (20 cm/h) and
k
a
for
water (3000 cm/h), if experimental values of individual mass transfer coefficients are
not available.
6.2.1.2
Chemicals in Surface Waters
Thesurfacewaterinafast-flowingstreamisgenerallyunmixedinthedirectionofflow,
but is laterally well mixed. This suggests that a plug-flow model will be applicable in
these cases. The appropriate equation is the advection-dispersion equation with the
axial dispersion term neglected. Figure 6.16 depicts a river stretch where we apply a
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