Anaerobic membrane bioreactor modeling in the presence of Soluble Microbial Products (SMP) – the Anaerobic Model AM2b☆
Introduction
The objectives of a wastewater treatment plant (WWTP) are to reduce the volume of pollutants in discharges, take advantage of the energy that can potentially be produced (such as CH4 in anaerobic treatment) and provide purified effluents for recycling in agriculture and/or industry. The technology of Anaerobic Membrane BioReactors (AnMBR) appears promising for achieving these aims. However, the risk of membrane fouling limits the development of these systems. The use of models coupling the fouling phenomena together with biotic characteristics should enable such fouling to be more predictable and thus, by means of a control, to act in order to limit their impact on system performance.
Among the soluble organic compounds in WWTP effluent, it has been shown that the Soluble Microbial Products (SMP) play a crucial role in the membrane fouling (pore blocking) and their presence in a MBR affects the process performance (effluent quality). It is therefore essential to integrate the SMP into the modeling of bioprocesses.
Most efforts to couple biotic phenomena with membrane models have been primarily directed at improving aerobic systems. They have been based on the modification of activated sludge models (ASM) to include SMP formation and degradation. Concerning anaerobic conditions, in contrast, only a few papers are available [4]. Yet anaerobic digestion systems offer many advantages, including the possible use of the resulting biogas as an energy source. Usually, two categories of SMP are considered: BAP (Biomass Associated Products), associated with biomass mortality, and UAP (Utilization Associated Products), associated with substrate degradation and the growth of biomass [5].
In their review [5], Barker and Stuckey noted that the first model to characterize only the SMP formation in a fermentation system was proposed in 1959 by Luedeking and Piret [6]. Later on, this incomplete model was further refined. But the first model to predict both the production and the degradation of SMP in an anaerobic chemostat was proposed by [7], in considering the two categories of SMP (UAP and BAP). It integrated the UAP production but starting from the initial organic matter alone and considered only their degradation by acidogenic bacteria. The BAP were considered to be produced by the decay of acidogenic bacteria and also slowly degraded by them. The model did not take into account either the UAP or BAP production starting from the intermediate product of the reaction (a two step model was considered), nor the decay of methanogenic biomass.
This model was further developed by [8] who have added: (i) the concept of UAP production in the consumption of both the initial organic matter and the intermediate products by acidogenic and methanogenic bacteria respectively; (ii) BAP production starting from the decay of acidogenic and methanogenic bacteria; and (iii) BAP degradation by acidogens which grow and give intermediate products.
Later on, [9] proposed a unified theory for the production and the degradation of the UAP and the BAP by envisaging the combination of three types of compound: Extracellular Polymeric Substances (EPS), SMP and inert biomass. They organized their theory through six hypothetical interactions between SMP, EPS, active and inert biomass.
Recently, Aquino and Stuckey [10] in order to predict SMP production, have refined the model suggested in [8] by taking into account the concept of EPS formation and degradation as suggested in [9].
It should be stressed that the majority of the studies cited above relate to conventional systems for anaerobic digestion (chemostat-like systems) and not to membrane reactors. In addition, the most recently developed models are rather complex and clearly unsuited for observer synthesis and/or control system design.
This paper proposes a model which includes the formation and degradation of SMP in an AnMBR, and should prove simple enough to be used for control purposes while capturing the main features related to SMP dynamics. To this end, we propose the AM2b model which we study equilibria and their bifurcations.
This paper is structured as follows: first, we present the model with SMP. Its equilibria are then determined for different generic cases using a graph-based approach. Finally, simulation results are presented which point out different qualitative behavior according to model parameters values. These simulations are discussed before conclusions and perspectives are drawn.
Section snippets
Hypotheses
The compartments included in the model are represented in Fig. 1. The process considered here is a side-stream MBR, where S1 is the organic matter concentration (COD), S1in the input concentration, S2 the Volatile Fatty Acid concentration (VFA), S2in the input concentration, X1 the acidogenic biomass, X2 the methanogenic biomass and S = UAP + BAP i.e. the Soluble Microbial Products (SMP) concentration.
A full model of an AnMBR should integrate a biological model of bioreactions taking place in the
Characterization of equilibria
The kinetics μ1, μ2 and μ are assumed to be dependent on S1, S2 and S, respectively. The model analysis given in this paper is valid for all kinetics verifying the following qualitative properties whose patterns are represented as graphs in Fig. 3:
- 1.
μ1(S1) and μ(S) are increasing functions for S1 ⩾ 0 and S ⩾ 0 respectively, with μ1(0) = μ(0) = 0, and μ1(+∞) = m1 and μ(+∞) = m.
- 2.
μ2(S2) is an increasing function for ; it has a maximum for and it is decreasing for , with μ2(0) = 0 and μ2
Numerical simulations
In this section, we analyze the three generic cases illustrated by Fig. 5, Fig. 6, Fig. 7. We characterize the number and the nature of equilibria according to the bifurcation parameter m. In addition, we highlight the capability of the AM2b model to predict a number of qualitative features of interest from a practical point of view.
Conclusion
In this paper, we have developed and studied a mathematical model for an AnMBR. The new model, named AM2b, was developed by modifying the AM2 model [1] to integrate SMP production and degradation. The mass balance equations are proposed in considering a new reaction network taking into account certain assumptions about the functioning of the AnMBR, in particular the behavior of the different variables with respect to the presence of a membrane. A graph-based approach to study the developed
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