Environmental Engineering Reference
In-Depth Information
[S]
in
=
100 kg/m
3
. If the cell yield is 0.7, calculate (a) the reactor vol-
ume required for the maximum rate of production of
E
.
coli
? (b) If the
effluent from the reactor is fed to a series reactor, what is the volume of
the second reactor if the desired pollutant concentration in the exit stream
is 0.1 kg/m
3
?
6.18
3
Consider the long-term trends of PCBs in Lake Superior. It is an olig-
otrophic lake with an average depth of 145 m, surface area of 8.2
×
10
10
m
2
, volume of 1.21
×
10
13
m
3
, and a flushing time of 177 years.
The DOC content is
∼
1 mg/L.
K
SW
=
10
5
L/kg. It was reported that the
PCB content in Lake Superior has been steadily decreasing between 1978
and 1992 due to a combination of flushing, sedimentation, biodegradation,
and volatilization. A pseudo-first-order rate constant has been suggested.
The following equation was said to be applicable:
d
[
W
]
/
d
t
=
I
−
k
[
W
]
,
where [W] is the mass of PCBs in the lake (kg),
I
is the input of PCBs (both
direct and by gas absorption, kg/y), and
k
is the first-order rate constant
for disappearance of PCBs (y
−
1
). It is related to the
overall
first-order rate
constant as
k
=+
I(t)/W(t)
:
(a) Justify the equation for d[W]/d
t
given above. State all necessary
assumptions.
(b) Derive the equation for the overall rate constant
k
.
(c)
k
is given as a sum
k
=
k
flushing
+
k
sedimentation
+
k
biodegradation
+
k
volatilization
. With
k
biodegradation
=
0,
k
flushing
=
0.006 y
−
1
,
k
sedimentation
=
0.004 y
−
1
, and
k
volatilization
=
0.24 y
−
1
for a com-
bination of 82 PCB congeners, calculate the input of PCBs in the year
1986 if the 1986 PCB burden is 10,100 kg.
(d) How much PCB (in kg) is lost through volatilization in the
year 1986?
(e) Using an average Henry's constant of 1
×
10
−
4
atm m
3
/mol and a net
1986 PCB flux of 1900 kg/y, determine the air concentration of PCB
in 1986. The 1986 water concentration is 2 ng/L (
Note
: You have
to relate
k
volatilization
to the mass transfer coefficient
K
w
through
the equation
k
volatilization
=
(K
w
/h)f
w
, where
h
is the average depth
of the lake and
f
w
−
0.87 is the dissolved aqueous phase PCB
fraction.)
(f) How much PCB will remain in the lake in the year 2020?
6.19
2
The following data pertain to a local stream in Baton Rouge, Louisiana:
Average stream speed: 0.36 m/s
Average stream depth: 3 m
Average water temperature: 13 C
Flow rate of water in the stream: 1 m
3
/s
BOD of the stream: 5 mg/L
C
O
2
,w
in the stream: 8 mg/L.
At a point along the stream, a treatment plant discharges wastewater
through a pipe
∼
2 m above the water level with the following charac-
teristics:
Average flow rate: 0.1 m
3
/s
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