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

Abstract

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 these pollutants must be reduced. A method which has been extensively employed to remove biodegradable organic matter is biological treatment. In this process the wastewater (or slurry) is passed through a bioreactor containing biomass which grows through consumption of the pollutants. The industrial treatment of wastewaters typically employs a reactor cascade. In a reactor cascade of n reactors the effluent stream from the ith reactor in the cascade acts as the feed stream for the (i+1)th reactor, i.e. the next reactor. The efficiency of the reactor cascade may be improved by using a settling unit. The settling unit 'captures' and concentrates the microorganisms in the effluent stream of reactor (i) and recycles it into the influent stream of reactor (j;j i). The benefit of using the settling unit is that it increases the concentration of microorganisms in reactor j, hopefully leading to an improvement in the performance of the cascade. When i=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<j the operation of the settling unit is characterised by two parameters: a concentrating factor (C) and a recycle parameter (R). The maximum value of the concentrating factor that be achieved in a specific settling unit is related to the value of the recycle parameter. We investigate how recycle affects the performance of a reactor cascade with four reactors. We consider the use of one settling unit. Steady state analysis is used to study and compare the performance for the various reactor configurations. In the first configuration we consider the scenario in which the effluent stream leaving a settling unit placed around the ith reactor enters the feed stream for the ith reactor. With even one settling unit various configurations can be utilized. For instance, the settling unit can be placed after the first, second, third or fourth reactor. We find that if the settling unit is placed around the final reactor the performance of the cascade is optimised when the settling unit operates with perfect recycle. If the settling unit is placed around one of the other reactors the performance is optimised with a value of the dimensionless recycle parameter less than one. For the second configuration we consider the scenario in which the settling unit is placed after the fourth reactor and the effluent stream from the settling unit is recycled back into the first reactor. We find that there is a critical value of the residence time. If the residence time is below the critical value then the settling unit improves the performance of the reactor cascade whereas if the residence time is above the critical value the performance of the cascade is reduced compared to that of a cascade without a settling unit. We conclude by noting that the first configuration outperforms the second configuration at high residence time. This is noteworthy as the latter is often used in industry.