# 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