Economic criteria in the design of cascades of CSTR's for the performance of enzyme‐catalyzed reactions

The mass balances on substrate in each unit of a series of CSTRs performing an enzyme‐catalyzed reaction described by Michaelis‐Menten kinetics (with parameter K m ) are written and the necessary and sufficient condition that must besatisfied by the intermediate concentrations in order to obtain a minimum overall capital investment is found on the assumption that the cost of each reactor unit scales up on its capacity according to a fractional factor exponential rule (with parameter n ). The asymptotic situations of pseudo‐zero order and pseudo‐first order behavior are explored. The ratio between consecutive concentrations leading to a minimum overall capital investment decreases as K m decreases at a rate that is slower for higher n , and tends to unity as the pseudo‐first order situation is approached. If fractional values of n are considered, local minima of the capital investment associated with the overall reactor cascade exist only in certain ranges of substrate conversion; below the lower limits of such ranges, the number of reactor units should actually be decreased. A graphical procedure aimed at obtaining the intermediate optimal concentrations is presented.