Bioprocess Engineering 15 (1996) 257—264  Springer-Verlag 1996 Optimal design for CSTR’s in series using reversible Michaelis — Menten reactions I.M. Abu-Reesh Abstract An analytical expression is derived for the optimal design of a series of CSTR’s performing reversible Michaelis—Menten kinetics in the liquid phase. The optimal design is based on minimum overall volume of N reactors in series required to achieve a certain degree of substrate conversion. The reversible Michaelis—Menten equation is also able to explain competitive product inhibition and irreversible Michaelis—Menten kinetics. The reversible Michaelis—Menten kinetics covers three types of enzymatic reactions depending on the values of the rate constant for the forward (k s ) and reverse (k p ) reactions. An optimum design is obtained in the three cases of K s K p , K s K p and K s K p . The minimum overall reactors volume is compared with the more convenient equal-sized CSTR’s. The effect of enzyme deactivation on the minimum overall reactors volume is investigated. The perfor- mance of a series of CSTR’s is compared with plug-flow reactor. Glucose isomerization which exhibits reversible Michaelis—Menten kinetics is used as a model system for optimization. List of symbols E [mg/l] concentration of active enzyme E 0 [mg/l] initial concentration of active enzyme F [l/h] volumetric flow rate K  [h1] pseudo-first order reaction rate constant K d [h1] first order thermal deactivation rate constant K e [] equilibrium constant K 1 , K 2 [h1] rate constants K 1 , K 2 [l/mg h] rate constants K m [mole/h] apparent Michaelis constant K  m [] dimensionless Michaelis—Menten con- stant (K m / S 0 ) K p [mole/l] Michaelis constant for product K s [mole/l] Michaelis constant for substrate N [] number of reactors in series P [mole/l] product concentration P e [mole/l] product concentration at equilibrium Received: 23 January 1996 I.M. Abu-Reesh Chemical Engineering Department, The University of Jordan, Amman-11942, Jordan R (s) [mole/lh] reaction rate S [mole/l] substrate concentration S e [mole/l] substrate concentration at equilibrium S 0 [mole/l] substrate concentration at reactor inlet of the first reactor S M [mole/l] reduced substrate concentration (SS e ) t [h] time V [l] reactor volume V m [mole/lh] maximum apparent reaction rate V p [mole/lh] maximum reaction rate for product V s [mole/lh] maximum reaction rate for substrate X [] substrate conversion X e [] substrate conversion at equilibrium X r relative substrate conversion (X/X e ) Greek symbols  [] dimensionless substrate concentration (S/S 0 )  [] dimensionless holding time (V m /S 0 ) or (K )  [h] holding time  [] normalized deactivation rate constant (K d S 0 / V m ) Subscripts eq equal size reactors i refer to i th reactor j refer to j th reactor N refer to N th reactor o initial opt optimum (minimum) size p plug-flow tot total 1 Introduction In recent years, a number of investigators have studied the optimum design of continuous stirred tank reactors (CSTR’s) in series for the performance of enzyme-catalyzed reactions. Although plug-flow reactor is more efficient than mixed reactor for Michaelis—Menten type kinetics, CSTR offer a number of advantages over plug-flow reactor. It has better mixing (temperature and composition are uniform throughout the reactor). It has lower construction cost and easy to control various parameters. Also, CSTR can operate at steady state in 257