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 be satisfied 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-tent 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 stower for higher nt 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.