A mathematical model for the biological treatment of industrial wastewater in a reactor cascade

Many industrial processes, particularly in the food industry, produce slurries or wastewaters containing high concentrations of biodegradable organic materials. Before these contaminated wastewaters can be discharged the concentration of the biodegradable organic pollutant must be reduced. One way to do this is to pass the wastewater through a bioreactor containing biomass which grows through consumption of the pollutant. Anaerobic conditions are often favoured for the processing of waste materials with high levels of biodegradable organic pollutants as these can be removed with low investment and operational costs. We investigate the steady state effluent concentration leaving a cascade of two reactors. Our particular concern is the improvement in performance that can be achieved through the use of one or two recycling units. With even one settling unit various configurations can be utilized. For instance, the unit can be placed after the first reactor and recycle back to the feed stream of the reactor. Alternatively, the unit can be placed after the second reactor and recycle back to the feed stream of this reactor. Finally, the settling unit can be placed after the second reactor and recycle back to the feed stream of the first reactor. Which of these configurations minimizes the effluent concentration leaving the cascade? Surprisingly, we find that in the general the first of these configurations produces the best results and the third configuration, which is the one more often mentioned in the literature, the worst.