In this study, a simple dynamic model of a submerged Membrane BioReactor (sMBR) is proposed, which would be suitable for process control. The system dynamics is first analyzed showing the existence of three different time scales. The existence of slow-fast dynamics is central to the development of a dedicated parameter estimation procedure. The proposed model structure is validated using realistic simulation data from a detailed simulator built in a well-established environment, namely GPS-X. Finally, a nonlinear model predictive control is designed to illustrate the potential of the developed model within a model-based control structure. The problem of water treatment in a recirculating aquaculture system is considered as an application example.