Optimization by distributed control of reactors with decaying catalyst Part II: First-order catalyst deactivation

The problem of optimally choosing the temperature T(z, t) as a function of time t and position z in a tubular fixed bed chemical reactor, so as to minimize the total yield of product over a fixed time period for a reaction-deactivation system with a slow decaying catalyst has been formulated for the case where the rate of catalyst decay is linearly dependent upon activity. Several characteristics of extremal control policies which supplement the theoretical characterization obtained for the case of general reaction-deactivation kinetics using Sirazetdinov and Degtyarev's maximum principle are indicated. Results are that the supplementary properties of the extremal controls for linear catalyst deactivation kinetics may be used to advantage to reduce the computational dimensionality in synthesizing the control policies. Numerical calculations are presented to illustrate this fact in the case of initial catalyst activity profiles which are not uniform nor continuous along the reactor bed.