CE 561 Lecture Notes
Fall 2009
p. 1 of 20
Days 24 and 25: The ideal continuous stirred tank reactor (CSTR)
The third idealized reactor type that we will consider is the continuous stirred tank reactor
(CSTR).
This idealized reactor is also called the continuous flow stirred tank reactor (CFSTR),
the backmix reactor, mixed flow reactor, ideal stirred tank reactor, etc.
It is, in some sense, the
opposite of the PFTR.
In the PFTR, we assumed that there was no mixing among fluid elements
within the reactor.
In the CSTR, we assume that there is perfect mixing.
The entire reactor is
assumed to be at the same temperature and composition as the outlet stream from the reactor.
Because there is no spatial dependence of the concentrations, this reactor’s steadystate behavior
is described by algebraic equations rather than differential equations.
This feature allows us to
explore in more detail the temporal behavior of the reactor and the stability of steady state
operating conditions.
This same feature makes it relatively simple to analyze kinetic data taken
in a CSTR.
The reaction rate can be obtained directly from measured concentrations in the inlet
and outlet streams without assuming a reaction order or performing an integration of the model
or differentiation of the data.
The Governing Equations:
We derived the species mole balances and the energy balance for the CSTR previously.
If
the density of the inlet and outlet streams are the same, and we can assume constant heat capacity
and other physical properties, then the equations are
( )
( ) ( )
1
*
1
ˆˆ
M
k
o
ko
k
ik i
i
M
p
po o
i i
H
i
dC
V
QC C V
r
dt
dT
CV
CQ T T
V
H r Q
dt
α
ρρ
=
=
=
−+
=
−
+
−∆
∑
∑
where
V
is the reactor volume (assumed constant),
Q
o
is the inlet volumetric flow rate (which is
equal to the outlet flow rate for a constant density, constant volume reactor),
Q
H
*
is the total heat
addition rate to the reactor (positive for heating, negative for cooling), and the other terms have
their usual meanings.
The heat addition rate can vary with time, and will often have a form like
Q
H
=
UA
(
T
–
T
f
).
Accounting for variation in density and physical properties can be done as a
straightforward extension of what we will do here, and may be necessary for quantitative
description of a particular system.
However, doing so would introduce no qualitatively different
reactor behavior, so we will focus on these relatively simple equations.
We can define the
residence time in terms of the reactor volume and volumetric flow rate through it, as we did for
the PFTR
o
V
Q
τ
=
Then the equations become
( )
( )
( )
1
*
1
M
k
ko
k
ik i
i
M
i
H
oi
p
po
i
dC
CC
r
dt
H
Q
dT
TT
r
dt
C
CQ
τα
ττ
=
=
=
=
+
∑
∑
To simplify the notation of the energy balance, we will define
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Fall 2009
p. 2 of 20
( )
*
and
ˆˆ
i
H
iH
p
po
H
Q
JQ
C
CQ
ρρ
−∆
=
=
Then we have
1
1
M
k
ko
k
ik i
i
M
o
H
ii
i
dC
C
C
r
dt
TT
Q
dT
Jr
dt
α
τ
ττ
=
=
−
=
+
−
=
++
∑
∑
The steadystate balances are the algebraic equations
1
1
0
0
M
ko
k
ik i
i
M
o
H
i
CC
r
T
T
Jr Q
τα
=
=
−+
=
+ =
∑
∑
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 Fall '09
 Thermodynamics, Steady State, Chemical reaction

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