Optimal temperature policy for reversible reactions with deactivation: Applied to enzyme reactors

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Abstract
The optimal temperature policy which will maximize the final 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 Szepé 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 first‐order 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 10% 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.
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