10.37
Chemical
and
Biological
Reaction
Engineering,
Spring
2007
Prof.
K.
Dane
Wittrup
Lecture
10:
Nonideal
Reactor
Mixing
Patterns
This
lecture
covers
residence
time
distribution
(RTD),
the
tanks
in
series
model,
and
combinations
of
ideal
reactors.
NonIdeal
Mixing
PFR
CSTR
Figure
1.
Ideal
PFR
with
pulse
input.
A
pulse
input
will
yield
an
output
profile
that
is
a
pulse
input.
Figure
2.
Ideal
CSTR
with
pulse
input.
A
pulse
input
will
yield
an
output
profile
that
is
a
sharp
peak
with
a
tail.
Real
mixed
tank
stagnant
bypassing
mixing
recirculation
eddies
volumes
Figure
3.
A
real
mixed
tank.
In
a
real
mixed
tank
there
are
portions
that
are
not
well
mixed
due
to
stagnant
volumes,
recirculation
eddies,
and
mixing
bypasses.
In
a
real
PFR
there
is
backmixing
and
axial
dispersion.
In
a
packed
bed
reactor
(PBR)
channeling
can
occur.
This
is
where
the
fluid
channels
through
the
solid
medium.
Residence
Time
Distribution
A
useful
diagnostic
tool
is
the
residence
time
distribution
(RTD).
The
residence
time
is
how
long
a
particle
stays
in
the
reactor
once
entering.
E
(
t
)
dt
≡
Probability
that
a
fluid
element
entering
the
vessel
at
t=0
exits
between
time
t
and
t+dt.
Probability
density
function
for
exit
time,
t,
as
a
random
variable.
Cite
as:
K.
Dane
Wittrup,
course
materials
for
10.37
Chemical
and
Biological
Reaction
Engineering,
Spring
2007.
MIT
OpenCourseWare
(http://ocw.mit.edu),
Massachusetts
Institute
of
Technology.
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on
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YYYY].
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t
E t
dt
Probability
that
fluid
element
exits
before
time
t.
∫
( )
0
∞
E t
dt
Probability
of
exiting
at
time
later
than
t.
∫
( )
t
∞
mean
t
=
∫
tE
( )
t
dt
=
τ
0
∞
=
∫
E
( )
dt
=
1
normalized
t
0
∞
variance
=
σ
2
=
t
−
τ
2
E
t
dt
(measures
the
broadness
of
the
distribution)
∫
(
)
( )
0
E
after
t
1
before
t
1
t
1
t
Figure
4.
E(t)
versus
t.
At
a
given
time
point,
some
material
has
exited
and
some
material
will
still
exit
at
a
later
time.
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 Fall '04
 ClarkColton
 Reaction, Massachusetts Institute of Technology, residence time, K. Dane Wittrup

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