Optimal steady-state design of zone volumes of bioreactors with Monod growth kinetics

This paper deals with steady-state analysis and design of bioreactors consisting of a number of completely stirred tank reactors (CSTRs) in series. The study is confined to one consumed (substrate) and one consuming constituent (biomass). The specific microbial growth rate is assumed to be described by Monod kinetics. The death of biomass is assumed to be negligible. Two optimal design problems for a large number of CSTRs in series are studied: to minimize the effluent substrate concentration for a given total volume, and to minimize the total volume for a given effluent substrate concentration. As an appealing alternative to solve these problems numerically, it is proposed to consider the asymptotic case where the number of CSTRs tends to infinity. This is shown to correspond to one CSTR in series with a plug flow reactor (PFR). A CSTR with a sufficient large volume is needed to avoid wash-out of the biomass. The main result is that both design problems for the CSTR + PFR configuration have the same solution with respect to the optimal volume of the CSTR, which is given as an explicit function of the incoming substrate concentration, the volumetric flow rate and the coefficients of the Monod growth rate function. Numerical results indicate that the plug flow approach may be used as a feasible design procedure even for a reasonably low number of CSTRs in series.