Optimal temperature policies for reactors subject to catalyst deactivation—I Batch reactor

Abstract For a single irreversible reaction A → R subject to catalyst deactivation, the problem of finding the optimal temperature policy in a batch reactor was formulated as a Bolza problem of the calculus of variations. For reaction and deactivation kinetics described by Eqs. (2–10), an analytical solution was obtained for the optimal policy. Accordingly, depending on the relative sizes of the activation energies E (for reaction) and ϵ (for catalyst decay), the optimal policy is either to operate at the maximum allowable temperature (if ϵ E ), or with a rising temperature policy characterized by d k eff /d t = d( ka )/d t = 0 (if ϵ > E ). This result is applicable for arbitrary orders of reaction and deactivation. A simple equation was derived for the optimal temperature policy itself, and finally the effect of temperature constraints was examined.