Chemistry Reference
In-Depth Information
controlled at relatively low conversions (high [M]) where the viscosity of the
medium presents less of a problem. This is particularly true of bulk polymeriza-
tions such as those in the high-pressure polyethylene processes.
12.6.3.1
Residence Time Distributions
The polymerization time in continuous processes depends on the time the reac-
tants spend in the reactor. The contents of a batch reactor will all have the same
residence time, since they are introduced and removed from the vessel at the
same times. The continuous flow tubular reactor has the next narrowest resi-
dence time distribution, if flow in the reactor is truly plug-like (i.e., not lami-
nar). These two reactors are best adapted for achieving high conversions, while
a CSTR cannot provide high conversion, by definition of its operation. The resi-
dence time distribution of the CSTR contents is broader than those of the former
types. A cascade of CSTRs will approach the behavior of a plug flow continu-
ous reactor.
The residence times in a continuous flow reactor have a distribution that can
be characterized by any of a trio of functions. One of these is the cumulative
probability function
F
(
t
), which is the fraction of exiting material that was in the
reactor for a time less than
t
.
Physically,
F
(
t
) represents the time dependence of the concentration of a non-
reactive tracer that was instantaneously injected as a slug into the flowing reac-
tion medium. A related expression gives
R
(
t
), the decay function,
R
ð
t
Þ
5
1
:
0
2
F
ð
t
Þ
(12-19)
If a nonreactive tracer were being continuously and steadily injected into the
stream and then abruptly turned off,
R
(
t
) would represent its relative concentration
in the reactor effluent. The frequency function
f
(
t
) defines the fraction of exiting
material that had residence times between
t
and
t
dt
in the reactor. It is given by
1
f
ð
t
Þ
5
dF
ð
t
Þ
52
dR
ð
t
Þ
(12-20)
Figure 12.1
illustrates these functions for a general CSTR.
Now imagine a perfectly mixed CSTR operating with a tracer material with
inlet concentration
c
in
and effluent concentration
c
out
. The mass balance for this
system is
Vdc
out
=
dt
5
νð
c
in
2
c
out
Þ
(12-21)
If a step change is imposed on
c
in
, so that
0 t
t
0
,
c
in
5
1 t
t
0
.
then for
t
0 the preceding equation gives
in
.
ð
1
c
out
Þ
52
ν
t
=
V
t
=θ
(12-22)
2
52
