OPTIMIZATION OF AUTOCATALYTIC REACTIONS

The problem of maximizing product (catalyst) mass was formulated for irreversible autocatalytic reactions of any order power law kinetics, A + nB --> (n + 1)B, mB --> C. The feed strategy for a well-mixed isothermal semi-batch reactor was determined using singular control theory. The product concentration or the net product mass produced per total charge of reactant is maximized. The feedback singular feedrate and singular switching functions were developed for free final-time problems with final-time-independent performance functions. The generalized feedback singular feedrate and singular switching functions were simplified for cubic autocatalysis (n = 2) with first-order decay (m = 1). Analysis of the singular feedrate, singular switching function, and the net rate of catalyst mass and concentration change trajectories allowed determination of the practical operating limitations of singular control and provided an insight into the best initial and feed compositions to use. Multiple converging and/or diverging critical compositions exist on the singular arc. The numerical optimization was performed using initial conditions which lie on the singular arc for a feed containing reactant and catalyst and a feed containing reactant only. A minimum of 15% improvement, depending upon the initial conditions used, over semi-batch with constant feedrate followed by batch operation with an addition of fresh feed was observed when the optimal semibatch feedrate scheme was used. The global optimization problem, in which the total amounts of catalyst and reactant are fixed, was solved to determine the best initial and feed compositions to use in conjunction with the feedback singular control.