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