Approximate expressions of a SBR for wastewater treatment: Comparison with numeric solutions and application to predict the biomass concentration in real cases

• Analytical equations to represent the performance of SBR were developed.
• The proposed equations represented the change of substrates as a function of time.
• Based on real SBR data biomass growth yield and decay factor were obtained.
• The proposed equations represented the change of the biomass concentration in a SBR.

Most industrial wastewater treatment systems often operate under transient conditions, causing several operational problems. An effective solution is the use of Sequencing Batch Reactors (SBR). In general, a great number of simulations are necessary to solve SBRs mathematical models in order to evaluate the effect of the operational conditions on the performance of the reactor. In this work, a set of analytical equations that represent the effect of the operational parameters on the performance of a SBR was developed. The obtained equations adequately represent the change of the organic substrate, ammonia, biomass, oxygen and soluble microbial products as a function of time within a single operation cycle of the SBR. The equations also predict the steady-state concentrations as a function of several operational parameters, avoiding the problem of performing a great number of simulations. Based on real SBR data, the biomass growth yield and the decay factor for two synthetic wastewaters were obtained. Using these coefficients, the proposed equations adequately predicted the biomass concentration in real cases.