A mathematical model for the biological treatment of industrial wastewaters in a cascade of four reactors

Many industrial processes, particularly in the food industry, produce slurriesor wastewaters containing high concentrations of biodegradable organicmaterials. Before these contaminated wastewaters can be dischargedthe concentration of these pollutants must be reduced. A method which has beenextensively employed to remove biodegradable organic matter is biologicaltreatment. In this process the wastewater (or slurry) is passed through abioreactor containing biomass which grows through consumption of thepollutants.The industrial treatment of wastewaters typically employs a reactor cascade.In a reactor cascade of n reactors the effluent stream from the ith reactor inthe cascade acts as the feed stream for the (i+1)th reactor, i.e. the nextreactor. The efficiency of the reactor cascade may be improved by using asettling unit. The settling unit `captures' and concentrates themicroorganisms in the effluent stream of reactor (i) and recycles it into theinfluent stream of reactor (j, j≤i). The benefit of using the settling unitis that it increases the concentration of microorganisms in reactor j,hopefully leading to an improvement in the performance of the cascade. Wheni=j the operation of the settling unit is characterised by a single parameter,the dimensionless recycle parameter, which can take values between zero(no recycle) and one (perfect recycle). When i