Optimum Temperature Policies for Consecutive and Parallel Reactions

Example 8JJh-2 Optimum Temperature Policies for Consecutive and Parallel Reactions 

The two basic complex reaction schemes, consecutive and parallel, were considered in an interesting and useful simple way by Millman and Katz [12], and illustrates 

The rigorous optimization could be done with several mathematical techniques— see Beveridge and Schechter [16], and for a concise discussion of the Pontiyagin maximum principle see Ray and Szekely [17] also see Aris [10] for specific chemical reactor examples. Millman and Katz found that the formal optimization techniques were rather sensitive during the calculations and devised a simpler technique whose results appeared to be very close to the rigorous values it should have further possibilities for practical calculations. 

The basic idea was to assume that the temperature trajectory to be determined could be approximated as a linear function of the desired product concentration to be maximized specifically  

Then the two parameters, co and Cj, are determined for the optimal condition max xg(z). This still requires a search technique to obtain the values of Cq and Cl, but it was found that these computations were much simpler than the completely rigorous optimization. Actually, further terms in dx /dr and J Xqdx gave better results than the linear function, and are based on standard three-mode process controller actions however, we will not pursue this further here. 

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OPTIMUM TEMPERATURE POLICIES FOR CONSECUTIVE AND PARALLEL REACTIONS... 

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