Environmental Engineering Reference
In-Depth Information
First plot log
C(L
,
t)/C(
0
)
as a function of
t
on a probability plot as shown in
Figure 6.8. The standard deviation in the data is
σ
t
=
46 min, which is the dif-
ference between the 84th and 50th percentile points,
t
84%
−
t
50%
. Hence
D
ax
=
(
1
/
2
)
σ
t
u
3
/L
=
9.3
×
10
−
5
cm
2
/s.
E
XAMPLE
6.5 P
ULSE
I
NPUT IN A
R
IVER
A conservative (nonreactive, nonvolatile, water-soluble) pollutant is suddenly dis-
charged into a river flowing at an average speed of 0.5 m/s. A monitoring station is
located 100 miles downstream from the spill. The dispersion number is 0.1. Determine
the time when the concentration at the station is 50% of the input.
D
ax
/uL
=
0.1 (intermediate dispersion).
τ =
L/u
=
(
100 miles) (1600 m/mile)/0.5
(m/s)
=
3.2
×
10
5
s
=
3.7 days. For
C(L
,
t)
=
0.5
C(
0
)
,
√
3.14
×
0.1
(t/
τ
)
exp
.
(
1
−
(t/
τ
))
2
0.4
(t/
τ
)
1
0.5
=
−
By trial and error
t
0.5
/
τ =
1.9. Hence
t
1
/
2
=
7 days.
6.1.3 D
ISPERSION AND
R
EACTION
Let us now consider the case where the flow is nonideal, and the compound entering
the reactor is undergoing reaction as it flows through the reactor. Let the reaction rate
be
r
with the stoichiometric coefficient for A being
ν
A
.
Figure 6.9 shows the reactor configuration in which we perform a material balance
over the volume between
x
and
x
x
. There are two separate inputs and outputs,
one due to bulk flow (
uC
A
A
c
)
and the other due to axial dispersion (
D
ax
A
c
∂C
A
/∂x)
.
+ Δ
Euent, C
Ae
Bulk
flow
Bulk
flow
Dispersion
Dispersion
x
=
0
x
x
+
x
x
=
L
Δ
Feed,
C
A0
Reaction
FIGURE 6.9
Material balance in a reactor with dispersion and reaction.
Search WWH ::
Custom Search