Anaerobic membrane BioReactor modeling in the presence of Soluble Microbial Products (SMP) - the Anaerobic Model AM2b

In this paper, we develop a mathematical model of anaerobic membrane bioreactors (AnMBR) for control design purposes. In particular, we integrate into this model the production and the degradation of Soluble Microbial Products (SMP), which are known to play an important role in the membrane fouling phenomenon. The proposed model, named AM2b, is based on the modification of the AM2 two step model initially proposed in [1]. We present a graph-based approach to determinate its equilibria and discuss three different generic cases. We show that under general assumptions (case A), the model developed has the same number of equilibria as the AM2 model and operates in bi-stability [2]. However, under certain operating conditions or if biological parameters values are slightly modified (cases B and C), the AM2b model exhibits equilibria bifurcation and multi-stability property. It is also shown that the AM2b model can provide interesting qualitative information to the user, such as the influence on some equilibria of the variation in the concentration of organic matter in the influent concentration