Environmental Engineering Reference
In-Depth Information
Reactor volume
V
Concentration
[A]
E
uent
Feed
F
j
0
F
j
Accumulation
Reaction
FIGURE 6.2
Mass balance for a reactor.
Note that
N
j
is the total moles of
j
in the reactor. The above equation is the basis
for reactor design. Note that if there are additional source terms within the system,
they are included in the input term. Specifically, we can determine either the time or
the reactor volume required for a specified conversion of the reactants to products.
6.1.1.1
Batch Reactor
Since both
F
j
0
and
F
j
are zero in this case, we have
d
N
j
d
t
=
Vv
j
r
.
(6.2)
Consider a first-order reaction A
→
B for which
r
=
kC
A
and
v
A
=−
1. Hence,
d
N
A
d
t
=−
kC
A
V
,
(6.3)
where
V
is the total volume of the reactor. Further, since
N
A
=
C
A
V
in a constant-
volume batch reactor, we can write
d
C
A
d
t
=−
kC
A
.
(6.4)
Thus, for this case the rate of change in concentration ofA in the reactor,
C
A
(t)
,is
given by the rate of the reaction. We can substitute the appropriate expression for the
rate (
r
A
)
as given in Chapter 5 and solve the resulting differential equation for
C
A
(t)
.
A batch reactor is an unsteady-state operation, where the concentration changes with
time, but is the same throughout the reactor.
6.1.1.2
Continuous-Flow Stirred Tank Reactor
A common type of reactor encountered in environmental engineering is the
continuous-flow stirred tank reactor
(CSTR) in which the effluent concentration is
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