Environmental Engineering Reference
In-Depth Information
ascertained. Warneck (1988) has listed values of mixing time for several radioactive
tracers. A similar approach can also be used for appropriate tracers to calculate mixing
times within the troposphere and stratosphere, if the two boxes are further subdivided
into a north and south hemisphere. The average values obtained are summarized in
Table 6.5.
E
XAMPLE
6.16 A
TMOSPHERIC
R
ESIDENCE
T
IME
Atmospheric residence time is important in atmospheric models. This tells us the dura-
tion a molecule spends in the atmosphere before it is removed by either wet or dry
deposition to the surface of the earth.This is based on the perfectly mixed box approach.
Starting with 1 cubic volume of the lower atmosphere, we have the following mass
balance (Seinfeld and Pandis, 2006; Warneck, 1999):
input rate by flow
−
output rate by flow
+
rate of production
−
rate of removal
=
accumulation.
d
m
A
d
t
,
F
i
A
−
F
out
A
+
S
A
−
R
A
=
(6.141)
where
m
A
is the total mass of speciesA in the unit volume of air considered.The average
residence time is defined as
τ
A
=
m
A
/(S
A
+
F
out
)
=
m
A
/(S
A
+
F
i
A
)
, since at steady
A
state
R
A
+
F
out
A
=
S
A
+
F
i
A
. For the entire atmosphere at steady state,
F
i
A
=
F
ou
A
=
0
and
S
A
=
R
A
.Atmospheric concentrations are expressed in mass per unit volume of air,
C
A
,(
μ
g/m
3
)
,orasa
mixing ratio
,
ξ
i
=
C
A
/C
tot
, where
C
A
is the molar concentration
of A in air and
C
tot
is the total molar concentration of air. Note that since the ideal gas
law applies
ξ
A
=
P
A
/P
.
C
A
(
μ
g/m
3
)
and
ξ
A
(ppmv) are related as follows:
ξ
A
=
8.314
(T/PM
A
)
C
A
(see also Appendix 4). For sulfur, which has a total rate of production of
2
×
10
14
g/y and an average mixing ratio of 1 ppb, we find the total mass at steady state
to be (1
×
10
−
9
g/g) (5
×
10
21
g), where 5
×
10
21
g is the total mass of the atmosphere.
Hence
m
=
5
×
10
12
g.Thus the average residence time is
τ
A
=
5
×
10
12
/
2
×
10
14
=
0.025 y. Note that if
τ
A
=
G/R
A
and
R
A
=
k
A
G
,wehave
τ
A
=
1
/k
A
.
6.3.1.2
Dispersion Models
When pollutant sources are not widely distributed across a large area, and mixing
is insufficient, the CSTR box model described above becomes inapplicable. Exam-
ples are point source emissions from smokestacks, episodic spills on the ground,
explosions, or accidental releases of air pollutants. We shall use the general case of a
continuous smokestack emission to illustrate the principles of air pollution modeling
from point sources.
We saw in Chapter 2 that temperature gradient in the atmosphere determines
whether the atmosphere is stable or unstable. The variation in temperature with height
determines the extent of buoyancy-driven mixing within the atmosphere. To do so, we
Search WWH ::
Custom Search