### Lecture 34 - Optimization

As part of the review on optimization, homework problem 19.14 was covered in class.

**Homework Problem 19.14** from Process Dynamics and Control (Seborg, Edgar, Mellichamp, Doyle)

A reversible chemical reaction, A->B and B->A, occurs in an isothermal continuous stirred-tank reactor. The rate expressions for the forward and reverse reactions are:

- r1 = k1 CA
- r2 = k2 CB

Using the information given below, use a numerical search procedure to determine the value of Fb (L/hr) that maximizes the production rate of Cb (i.e. the amount of Cb that leaves the reactor, mol B/hr). The allowable values of Fb are 0 <= Fb <= 200 L/hr.

Available information

- The reactor is perfectly mixed.
- The volume of liquid, V, is maintained constant using an overflow line (not shown in the diagram).
- The following parameters are kept constant at the indicated numerical values:

- V = 200 L
- FA = 150 L/hr
- CAF = 0.3 mol A/L
- CBF = 0.3 mol B/L

The solution to this problem is possible with a number of numerical or analytical techniques. One solution approach that we covered in class was with the APMonitor software through the web interface.

Equations and Solution to HW19.14

**Equations for HW19.14**

**Solution to HW19.14**

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