Optimization of an Unstructured First-Order Kinetics Model of Cyclically Operated Bioreactors

A procedure for the optimization of an unstructured first-order kinetics model of cyclically operated biological reactors for the biodegradation of a single pollutant is developed using a combination of analytical and numerical tools. Asymptotic analytical profiles for the substrate and biomass for each steady cycle are obtained, which allow the formulation of an analytical design equation that relates the concentration of the pollutant at the end of a steady cycle to all the operating parameters of the bioreactor such as space-time, pollutant feed concentration, filling time, and ratio of minimum to maximum reactor volume. This analytical design equation is used for the systematic construction of practical bifurcation diagrams showing the variations of the pollutant concentration at the end of a cycle with the bioreactor operating parameters. The design equation also allows the formulation of a variety of optimization problems such as the maximization of volumetric efficiency as well as the minimization of the end-of-cycle pollutant concentration. In all cases it is shown that optimal parameter value sets exist. Implications of these results for the optimization of waste-treatment facilities are discussed.