Consider the batch reactor system simulated by Aziz et al.^3 The two reactions, A + B → C and A+ C → D, are carried out in a jacketed batch reactor, where C is the desired product and D is a waste product. The manipulated variable is the temperature of the coolant in the cooling jacket. There are

Question

Consider the batch reactor system simulated by Aziz et al. ${ }^{3}$ The two reactions, $A + B \rightarrow C$ and $A + C \rightarrow D$ , are carried out in a jacketed batch reactor, where $C$ is the desired product and $D$ is a waste product. The manipulated variable is the temperature of the coolant in the cooling jacket. There are two inequality constraints: upper and lower bounds on the coolant temperature and an upper limit on the maximum reactor temperature. Using the model parameters specified by Aziz et al., evaluate the following control strategies for a set-point change from $20^{\circ} C$ to $92^{\circ} C$ .

(a) PID controller

(b) Batch unit

(c) Batch unit with preload

(d) Dual-mode controller

(a) PID controller

(b) Batch unit

(c) Batch unit with preload

(d) Dual-mode controller

Accepted Answer

[latex]T_{r}=[/latex] Reactor temperature profile

[latex]T_{j p}=[/latex] Jacket set-point temperature profile (manipulated variable)

a) PID controller:

[latex]\begin{aligned}&K_{c}=26.5381 \& au_{I}=2.8658 \& au_{D}=0.4284\end{aligned}[/latex]

b) Batch unit

[latex]\begin{aligned}&K_{c}=10.7574 \& au_{I}=53.4882\end{aligned}[/latex]

c) Batch unit with preload

[latex]\begin{aligned}&K_{c}=10.7574 \& au_{I}=53.4882\end{aligned}[/latex]

d) Dual mode controller

1.- Full heating is applied until the reactor temperature is within [latex]5 \%[/latex] of its set point temperature.

2.- Full cooling is then applied for [latex]2.8 min[/latex]

3.- The jacket temperature set point [latex]T_{j s p}[/latex] of controller is then set to the preload temperature [latex]\left(46^{\circ} C ight)[/latex] for [latex]2.4 min[/latex].

[latex]{ }^{3} N[/latex]. Aziz, M. A. Hussain, and I. M. Mujtaba, Performance of Different Types of Controllers in Tracking Optimal Temperature Profiles in Batch Reactors, Comput. Chem. Eng, 24, 1069 (2000).

Question 22.13: Consider the batch reactor system simulated by Aziz et al.^3...

This Question has been Answered.

Already have an account?

Login

Related Answered Questions