Modelling and simulation of membrane bioreactors for wastewater treatment

The work presented in this thesis leads to the formulation of a dynamic mathematical model of an immersed membrane bioreactor (iMBR) for wastewater treatment. This thesis is organised into three parts, each one describing a different set of tasks associated with model development and simulation. In the first part, the Author qualitatively and quantitatively compares various published activated sludge models, i.e. models of biochemical processes associated with bacterial growth, decay, lysis and substrate utilisation in activated sludge systems. As the thesis is focused on modelling membrane bioreactors (MBRs) which are known to experience membrane fouling as a result of adsorption of biopolymers present in the bulk liquid onto and within the membrane, all activated sludge models considered in this thesis are able to predict, with various levels of accuracy, the concentrations of biopolymeric substances, namely soluble microbial products (SMP) and extracellular polymeric substances (EPS). Some of the published activated sludge models dedicated to modelling SMP and EPS kinetics in MBR systems were unable to predict the SMP and EPS concentrations with adequate levels of accuracy, without compromising the predictions of other sludge and wastewater constituents. In other cases, the model equations and the assumptions made by their authors were questionable. Hence, two new activated sludge models with SMP and EPS as additional components have been formulated, described, and simulated. The first model is based on the Activated Sludge Model No. 1 (ASM1) whereas the second model is based on the Activated Sludge Model No. 3 (ASM3). Both models are calibrated on two sets of data obtained from a laboratory-scale system and a full-scale system and prove to be in very good agreement with the measurements. The second part of this thesis explains the development of two membrane fouling models. These models are set to describe the loss of membrane permeability during filtration of various solutions and suspensions. The main emphasis is placed on filtration of activated sludge mixtures, however the models are designed to be as general as feasibly possible. As fouling is found to be caused by a large number of often very complex processes which occur at different spatial as well as temporal scales, the two fouling models developed here have to consider a number of significant simplifications and assumptions. These simplifications are required to balance the model's accuracy, generality and completeness with its usability in terms of execution times, identifiability of parameters and ease of implementation in general purpose simulators. These requirements are necessary to ascertain that long term simulations as well as optimisation and sensitivity studies performed in this thesis either individually on fouling models or on the complete model of a MBR can be carried out within realistic time-scales. The first fouling model is based on an idea that fouling can be subdivided into just two processes: short-term reversible fouling and long-term irreversible fouling. These two processes are described with two first order ordinary differential equations (ODEs). Whilst the first model characterises the membrane filtration process from an observer's input-output point of view without any rigorous deterministic description of the underlying mechanisms of membrane fouling, the second model provides a more theoretical and in-depth description of membrane fouling by incorporating and combining three classical macroscopic mechanistic fouling equations within a single simulation framework. Both models are calibrated on a number of experimental data and show good levels of accuracy for their designated applications and within the intended ranges of operating conditions. In the third part, the first developed biological model (CES-ASM1) is combined with the behavioural fouling model and the links between these two models are formulated to allow complete simulation of a hollow fibre (HF) immersed membrane bioreactor (iMBR). It is assumed that biological processes affect the membrane through production of mixed liquor suspended solids (MLSS), SMP and EPS which cause pore blockage, cake formation, pore diameter constriction, and affect the specific cake resistance (SCR). The membrane, on the other hand, has a direct effect on the bulk liquid SMP concentration due to its SMP rejection properties. SMP are assumed to be solely responsible for irreversible fouling, MLSS is directly linked to the amount of cake depositing on the membrane surface, whereas EPS content in activated sludge affects the cake's SCR. Other links provided in the integrated MBR model include the effects of air scouring on the rate of particle back-transport from the membrane surface and the effects of MLSS concentration on oxygen mass transfer. Although backwashing is not described in great detail, its effects are represented in the model by resetting the initial condition in the cake deposition equation after each backwash period. The MBR model was implemented in Simulink® using the plant layout adopted in the MBR benchmark model of Maere et al. [160]. The model was then simulated with the inputs and operational parameters defined in [36, 160]. The results were compared against the MBR benchmark model of Maere et al. [160] which, contrary to this work, does not take into account the production of biopolymers, the membrane fouling, nor any interactions between the biological and the membrane parts of an MBR system.