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Abstract: Mathematical modelling of membrane bioreactors (MBRs) for wastewater treatment has targeted either the biological processes (treatment quality target) as well as various aspects of system management. However, the high number of interactions among the involved physical–chemical processes, hampers a straightforward mathematical modelling. This circumstance is much more emphasized for submerged MBR systems where the membrane is immersed in an aeration tank. One of the main crucial points that prevents a comprehensive understanding is the interpretation of the fouling phenomenon and its connections with the biological processes. An overall mathematical model for MBR has not been completely established yet. Indeed, existing MBR models are generally focused only on some of the involved processes (e.g. biological, physical, chemical, etc.) to analyze limited MBR aspects. However, a comprehensive integrated mathematical approach aimed at an in-depth analysis is warmly recommended in order to optimize the whole MBR system. Seeking the development of the area, the paper presents an integrated MBR model that simulates and takes into account both biological and physical processes. An innovative calibration protocol was applied to evaluate the model parameter values as well. This protocol is based on a preliminary global sensitivity analysis to reduce the number of model parameters to be calibrated to the most influential ones. The calibration protocol consists of a novel step-wise Monte Carlo based calibration of the subset of influential parameters. The key point of the step-wise procedure is that calibration is carried out for sub-groups of variables instead of solving a complex multi-objective function. The model results compare fairly well with the experimental results of a MBR pilot plant. [Copyright &y& Elsevier]

Abstract: The paper presents the setting up of a mathematical model for membrane bioreactor able to simulate physical-biological wastewater organic removal. The model is basically divided into two sub-models: the first sub-model is basically devoted for the simulation of the biological features and the second one for the physical processes. In particular regarding the biological aspects, the ASM concept has been employed. On the other hand, the physical processes have been modelled considering the deep-bed theory taking into account not only the effect of the physical membrane filtration but also the cake layer effect. This latter operates as a biological membrane leading to a further reduction of the effluent COD. The model was applied to a SMBR pilot plant characterized by hollow fibre membrane module in submerged configuration. The SMBR was fed by raw wastewater collected from the Palermo (IT) WWTP and it was in operation for a total period of 130 days. During the whole experimentation the TSS was maintained meanly constant with periodic sludge withdrawal, in order to analyse the role of cake layer on organic removal. The model results are interesting and confirm the importance of cake deposition in the filtration process. The developed model can be employed as a useful tool in optimizing operation conditions as well as design issues for SMBR systems. [Copyright &y& Elsevier]