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WOLFRAM|DEMONSTRATIONS PROJECT

Multiple Reactions in a Continuous Stirred-Tank Reactor with Heat Effects

​
ΔQ
Q
in
and
Q
out
list of steady states
T
0
298
β
298
Consider a continuous stirred-tank reactor (CSTR) with multiple reactions:
A
k
1
→
B
k
2
→
C
. Only species
A
is fed to the reactor with an inlet concentration equal to
C
A0
=1
.
The Demonstration finds the steady states using both the mass and energy balance equations. From snapshot 1, up to five steady states can be obtained.
The mass balance equations for the species
A
and
B
are:
C
A
(T)=
C
A0
/(1+
k
1
(T)τ)
,
C
B
(T)=
k
1
(T)τ
C
A
(T)/(1+
k
2
(T)τ)
,
where
τ
is the residence time and
k
1
(T)
and
k
2
(T)
are the reaction rate constants given by the Arrhenius law.
The energy balance can be written as
Q
in
(T)=
Q
out
(T)
,
where
Q
in
(T)=-Δ
H
1
V
k
1
(T)
C
A
(T)-Δ
H
2
V
k
2
(T)
C
B
(T)
,
and
Q
out
(T)=Fρ
C
P
T-F
ρ
0
C
P,0
T
0
+UAT-
T
j
.
Here,
Δ
H
1
and
Δ
H
2
are the heat of reactions,
F
is the molar flow rate,
C
P
is the heat capacity,
ρ
is the density, the subscript
0
indicates inlet conditions,
U
and
A
are the overall heat transfer coefficient and the area of the cooling jacket, respectively,
T
j
=278K
is the temperature of cooling, and
V
is the reactor's volume.
The two heat quantities
Q
in
(T)
and
Q
out
(T)
are plotted versus
T
in red and blue;
Q
out
(T)
is a simple linear function (shown by the blue line).
The steady states are shown by the green dots in two different plots: (1)
Q
in
(T)
and
Q
out
(T)
versus
T
; and (2)
Q
out
(T)-
Q
in
(T)=ΔQ(T)
. You can vary the inlet temperature
T
0
and the parameter
β=Fρ
C
P
+UA
.
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