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Dynamics of a Nonadiabatic Continuously Stirred Tank Reactor

​
time t
3000
residence time θ
200
inlet temperature
T
0
300
coolant temperature
T
c
300.
feed concentration
c
A
0
2.
heat transfer coefficient U
30
This Demonstration shows the dynamics of a non-isothermal continuously stirred tank reactor (CSTR) where a first-order irreversible chemical reaction
A
k(T)
→
B
takes place. The dynamics of the system are described by the equations [1]
dx
dt
=-x/θ+k(T)(1-x)
,​
dT
dt
=
(
T
0
-T)
θ
-
ΔH
ρ
C
p
c
A
0
(1-x)+
U
ρ
C
p
(
T
c
-T)
,​
x(0)=0
,
T(0)=
T
0
,
where
x
and
T
are the conversion and temperature at the reactor outlet,
T
0
and
T
c
represent the reactor fluid inlet temperature and cooling temperature,
ΔH
is the heat of reaction,
U
is the heat transfer coefficient,
ρ
and
C
p
are the average density and heat capacity of the reactants,
c
A
0
is the feed concentration,
k(T)=
k
0
-ΔE
1
T
-
1
T
m
e
is the reaction rate as a function of temperature,
ΔE
is the activation energy, and
k
0
and
T
m
are constants. The solution shows multiple stationary states. These values determine the number of steady states possible: the feed concentration
c
A
0
, the inlet temperature of the reactive and cooling fluid, the residence time, and the heat transfer coefficient. A single steady state is most common, but two and even three steady states can occur. When three steady states occur only two of them are stable, whereas the other stationary point (the middle one) is unstable. Qualitative and mathematical proofs of this complex behavior can be found in standard chemical engineering texts [1], [2], and [3].
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