Exact analytical expressions are derived for the optimal design (minimum overall reaction volume) of N CSTRs in series carrying out an enzyme catalysed Michaelis-Menten one-substrate one-product reversible reaction. These equations enable the direct calculation of the smallest total reactor volume (holding time) needed for a given overall conversion degree, as well as the individual reactor volume and conversion degrees. Results are also compared with the ones obtained for a single tank and for a plug flow reactor.