Environmental Engineering Reference
In-Depth Information
therefore
c
e
is also negligible. Under these circum-
stances, Equation (4.49) becomes
25
22.7 mg/L
20
dc
dt
(4.50)
= −
k c
v
15
which indicates that volatization of voCs in streams
can be accounted for by a first-order decay process with
a decay factor equal to
k
v
. Therefore, downstream con-
centrations resulting from the spill of a mass
M
of voC
in a river can be estimated using Equation (4.37) as
10
5
0
0
1
2
3
4
5
6
7
8
9
10
Me
−
v
k t
(
x Vt
K t
−
)
2
c x t
( , )
=
exp
−
(4.51)
time (hours)
4
A
4
π
K t
L
L
Figure 4.4.
Concentration 2 km downstream of spill.
where
A
is the cross-sectional area of the river (L
2
),
K
L
is the longitudinal dispersion coefficient (LT
−2
),
x
is the
distance downstream from the spill (L), and
V
is the
mean velocity in the stream (LT
−1
). It is important to
keep in mind that Equation (4.51) assumes that the
spilled mass,
M
, is initially well mixed across the river.
Using the
two-film model
proposed by Lewis and
Whitman (1924) and further explored by Rathbun
(1998), the volatization coefficient,
k
v
(d
−1
), can be esti-
mated using the semiempirical relation
location. The actual travel time to the downstream loca-
tion is equal to
x
/
V
= 2.77 hours compared with the spill
duration of 1 hour. If the time to peak were assumed to
be 3.66 hours and substituted into Equation 4.48, the
estimated maximum concentration would be 16.9 mg/L,
compared with the actual peak of 22.7 mg/L.
4.3.2 Spills of Volatile Organic Compounds
Contamination of a stream by volatile organic com-
pounds (voCs) can be by spills directly into the stream,
spills in the drainage area that are subsequently washed
off into the stream, or from voC-contaminated base
flow that enters the stream (LaSage et al., 2008). The
fate and transport of voCs in rivers and streams are
affected by several processes, including advection, dis-
persion, volatization, microbial degradation, sorption,
hydrolysis, aquatic photolysis, chemical reaction, and
bioconcentration. In most cases, volatization and disper-
sion are the dominant processes affecting the concen-
trations of voCs in streams (Rathbun, 1998).
Dispersion is parameterized by the longitudinal dis-
persion coefficient,
K
L
, which can be calculated using
any of the formulas listed in Table 4.1.
Volatization
is
the movement of a substance from the bulk water phase
across the water-air interface into the air, and can be
described by the first-order relation
−
1
1
1
RT
H k
(4.52)
k
=
+
v
d
Φ
k d
Ψ
a
3
where
d
is the mean depth of the stream (m),
k
a
is the
reaeration coefficient for oxygen in water (d
−1
), Φ and
Ψ are constants that depend on the particular voC
(dimensionless),
R
is the ideal gas constant (J/K·mol),
T
is the temperature (K),
H
is the Henry's law constant of
the voC (Pa·m
3
/mol), and
k
3
is the mass-transfer coef-
ficient for evaporation of water from a stream (m/d).
The reaeration coefficient for oxygen in water,
k
a
, can
be estimated using empirical equations such as those
listed in Table 4.6; Φ, Ψ, and
H
for several voCs
are listed in Table 4.3. The ideal gas constant,
R
, is
8.31 J/K·mol, and the mass-transfer coefficient,
k
3
(m/d),
can be estimated using the empirical equation (Rathbun
and Tai, 1983)
k
=
(416 156
+
V
w
exp
)
[0.00934(
T
−
26.1)]
(4.53)
dc
dt
3
=
k c
(
−
c
)
(4.49)
v
e
where
V
w
is the wind speed over the stream (m/s), and
T
is the temperature (°C). It should be noted that
Henry's law is given by
where
c
is the concentration of the voC in water (ML
−3
),
t
is time (T),
k
v
is the volatization coefficient (T
−1
), and
c
e
is the concentration of the voC in the water if the
water were in equilibrium with the partial pressure of
the voC in the air (ML
−3
). In most cases, voC concen-
trations in the air above streams are negligible, and
p Hc
e
=
(4.54)
e
where
p
e
is the equilibrium partial pressure of the sub-
stance in the gas phase (Pa), and
c
e
is the equilibrium
Search WWH ::
Custom Search