A new method to calculate the periodic steady state of sequencing batch reactors for biological wastewater treatment: model development and applications

This paper describes a new mathematical procedure to calculate the periodic steady state of the sequencing batch reactor (SBR). This new procedure allows the direct calculation of the steady state profiles of biomass and substrate in the SBR without calculating the dynamics of the system from start up to steady state. The procedure is based on the mass balances of biomass (X) and substrate (S) and the steady state profiles are obtained by imposing the condition that the integrals of dX and dS over a complete cycle are both equal to 0. The results obtained by the proposed technique are compared against the steady state results obtained by dynamic simulation. The numerical accuracy of the procedure is discussed and the procedure is applied to show the effect of the operating parameters (solids residence time (SRT), hydraulic residence time (HRT), length of the phases and number of cycles) on the steady state biomass and substrate concentrations. We show how the model can be used for various applications like: optimisation of operating parameters for a minimum reactor volume; simulation of the competition between filamentous and floc-forming bacteria for bulking control; calculation of the minimum volumetric mass transfer coefficient required to maintain a desired oxygen concentration. It is hoped that the procedure described in this paper will facilitate the use of mathematical models for the design of SBR’s. Of course, it will be the responsibility of the users of this new method to use it with the appropriate kinetic model and parameter values.