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WOLFRAM|DEMONSTRATIONS PROJECT

Optimizing a Chain of Continuous Stirred-Tank Reactors

​
concentration
c
A
out
,
moles
3
m
0.005
rate constant k,
-1
hr
0.5
flow rate q,
2
m
hr
8
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
A
k
→
B
takes place.
The design equation for this system is
q(
c
A
(i-1)-
c
A
(i))
V
-k
c
A
(i)=0
for
i=1,…,n
. The solution obtained by using Mathematica's built-in function Solve is
c
A
out
=
c
A
in
n
1+
k
q
V
. Here
c
A
in
and
c
A
out
are the concentration of reactant
A
entering the first reactor and exiting the last reactor in
moles
3
m
,
k
is the rate constant in
-1
hr
,
V
is the volume of each reactor in
3
m
,
q
is the volumetric flow rate in
3
m
hr
, and
n
stands for the number of reactors. The cost for each reactor is
100000
0.6
V
in dollars, and by combining the above two equations, the cost for
n
reactors is
100000
0.6
n
q
k
1
n
c
A
in
c
A
out
-1
. This function is minimized with respect to
n
and the results are shown for
c
A
in
=1
and user-selected values of the outlet concentration of
A
,
C
A
out
, the rate constant
k
, and the flow rate
q
.
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