Optimum design of continuous stirred tank reactors (CSTRs) in series to biodegrade organics in wastewater was carried out. It was assumed that cell growth kinetics follows Contois model with endogenous decay. The optimal design was based on the minimum overall reactors volume required for a certain degree of substrate removal. The effect of operating parameters such as substrate inlet feed concentration to the first reactor, substrate removal efficiency, and number of CSTRs in series on the optimum design were investigated. The non-linear constrained optimisation problem was solved using the MATLAB function
. For equal CSTRs, the system of non-linear equations was solved by ‘fsolve’ MATLAB function. Results indicate that the optimum multi-stage bioreactors are beneficial only at high substrate conversion. The substrate concentration in the feed to the first reactor has little effect on the total reactors volume. Recycle of biomass to the first reactor reduces the required total reactors volume. In general, at high percentage of substrate removal the optimum reactors design requires smaller volume compared to equal-size reactors.
Keywords: optimisation of bioreactors, multi-stage bioreactors, MATLAB function fmincon, MATLAB function fsolve, wastewater treatment, Contois kinetic model, equal size-reactors in series, minimum-volume design, non-linear constrained optimisation, biomass recycle