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The optimal temperature policy which will maximize the h a 1 catalyst activity that gives a fixed conversion of reactants in a specified time for batch operation was determined by the formulation of a calculus of variations problem following the technique of Szepk and Levenspiel (1968). The method was applied to the general case of first-order reversible reactions which occur in the presence of catalysts deactivating by an irreversible firstorder mechanism. To reduce trial and error estimations and circumvent numerical instabilities, the two-point boundary value variational problem was reformulated in terms of an initial value problem with a parameter which includes the initial value of temperature. This initial value problem was solved by a regression technique.These techniques were applied to the industrially important enzymatic reaction of the isomerization of D-glucose to D-fructose catalyzed by glucose isomerase in solution. Kinetic and deactivation data are available for this endothermic reaction which obeys first-order reversible kinetics and for the isomerase denaturation which appears to be first order. The optimal temperature operational policy as stated above maximized final enzyme activity such that 1% less denaturation of glucose isomerase occurred when compared to final isomerase activity yielding the same conversion for the same reaction time when the reactor is operated at the optimal isothermal temperature. SCOPEThe problem of the optimal operation policy for chemical reactors is important when it is desired to improve the operational economics and product yield. Accordingly these problems have received attention in the recent literature where investigators have employed calculus of variations methods to the analysis of batch and tubular plug flow reactors. Irreversible nth order reactions with concentration independent and recently concentration dependent deactivation models were examined. Numerical methods and theoretical developments treated in the format of Pontryagin's Maximum Principle were applied to the problem of reversible reactions with concentration independent decaying catalysts in a tubular reactor. Biochemical reactions catalyzed by denaturable enzymes which may be in solution or immobilized on inert supports are of emerging interest in recent literature. The determination of the optimal policies of reactor operation for these biochemical reaction systems is as important as in previous needs because of the high costs of enzyme catalysts and the temperature sensitivity of enzyme denaturation.The work described herein applies the calculus of variations formulation to the problem of determining the optimal temperature policy which will maximize the final Correspondence concerning this paper should be addressed to L. T. catalyst activity that gives a fixed conversion of reactants in a specified time for a batchwise operated reactor. The technique can also be applied to the mathematically equivalent problem of maximizing conversion with a specified final catalyst activity in a given rea...

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