Optimizing a Chain of Continuous Stirred-Tank Reactors
Optimizing a Chain of Continuous Stirred-Tank Reactors
This Demonstration shows how to minimize the cost of a chain of continuous stirred-tank reactors (CSTR) where a first-order isothermal, irreversible chemical reaction takes place.
AB
k
→
The design equation for this system is -k(i)=0 for . The solution obtained by using Mathematica's built-in function Solve is =. Here and are the concentration of reactant entering the first reactor and exiting the last reactor in , is the rate constant in , is the volume of each reactor in , is the volumetric flow rate in , and stands for the number of reactors. The cost for each reactor is in dollars, and by combining the above two equations, the cost for reactors is . This function is minimized with respect to and the results are shown for =1 and user-selected values of the outlet concentration of , , the rate constant , and the flow rate .
q((i-1)-(i))
c
A
c
A
V
c
A
i=1,…,n
c
A
out
c
A
in
n
1+V
k
q
c
A
in
c
A
out
A
moles
3
m
k
-1
hr
V
3
m
q
3
m
hr
n
100000
0.6
V
n
100000
0.6
n-1
q
k
1
n
c
A
in
c
A
out
n
c
A
in
A
C
A
out
k
q