(Solved): 9 Consider a tubular catalytic reactor where an endothermic reaction \( A \ri ...

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9 Consider a tubular catalytic reactor where an endothermic reaction \( A \rightarrow B \) takes place (Figure PI.7a). The reacting mixture is heated with steam flowing in a jacket around the tubular reactor. The stream of the raw material \( A \) includes a chemical \( C \) which poisons the catalyst over a period of five days. As the catalyst decays, the conversion of \( A \) to \( B \) decreases. We can make up for this decrease by increasing the temperature of the reacting mixture, which can be achieved by increasing the supply of heat to the reactor through higher pressure steam. Let us assume that the reactor is isothermal along its length. Figure PI.7b (a) Figure PI.7 shows the temperature in the reactor during the reaction period that maximizes the profit from the operation of the tubular reactor. (a) Formulate the optimization problem that yields the temperature profile of Figure PI.7b as its solution. (b) Develop a feedback control system that will regulate the temperature of the reactor to that shown in Figure PI.7b. What is the control objective here? (c) Draw a control system that uses a digital computer for the implementation of the feedback system in part (b). Include measuring devices, transmission lines, final control elements, and whatever else is necessary.