Chemistry Reference
In-Depth Information
F (t)
1.0
f (t)
R (t)
0
t
FIGURE 12.1
Curves illustrating the residence time distribution F(t), residence time decay function R(t),
and residence time frequency function f(t) for a CSTR.
or
e
2
t=θ
c
out
5
F
ð
t
Þ
5
1
2
(12-23)
In this case
R
(
t
) has the form
RðtÞ
5
e
2
t=θ
(12-24)
The exponential distribution of residence times defines a
well-stirred reactor
.
Analogous expressions can be written for a plug flow tubular reactor that ide-
ally has zero mixing in the axial direction and is completely homogeneous radi-
ally. A step change imposed on
c
in
in such a system produces an identical step
change in
c
out
after a lag of
θ
sec. Thus, for
t
.
θ
for such a reactor,
R
ð
t
Þ
5
0
for
t
0
(12-25)
.
Real tubular reactors approach axial plug flow if the viscosity of the fluid
decreases with increasing rate of shearing and the resulting velocity profile is flat
across the tube.
12.6.3.2
State of Mixing in CSTRs
Note that the residence time distribution itself does not completely define the
state of mixing of the components of the reaction mixture. It actually defines the
state of mixing of volume elements which are small compared to the capacity of
the reactor. Any fluid that consists of such volume elements that do not comingle
on a molecular scale is called a
macrofluid
, and the corresponding mixing process
is termed macromixing or segregated flow mixing
[3]
. The polymer beads in a
continuous suspension polymerization process can have a distribution of residence
times with no mass transfer between them. This is then an example of macromix-
ing, with the particles corresponding to an ensemble of batch reactors operating
in parallel with a distribution of reaction times given by
Eq. (12-24)
.
