Equilibria of an anaerobic wastewater treatment process and their stability ⋆ B. Benyahia ∗ T. Sari ∗∗ B. Cherki ∗∗∗ J. Harmand ∗∗∗∗ ∗ Laboratoire d’Automatique, Tlemcen University, Algeria and EPI MERE, INRIA, Montpellier, France (e-mail: benyahiab@yahoo.fr). ∗∗ LMIA, Mulhouse University and EPI MERE, INRIA, Montpellier, France, (e-mail: tewfik.sari@sophia.inria.fr) ∗∗∗ Laboratoire d’Automatique, Tlemcen University, Algeria (e-mail: b cherki@yahoo.fr) ∗∗∗∗ LBE-INRA, UR050, Narbonne, and EPI MERE, INRIA, Montpellier, France(e-mail: harmand@supagro.inra.fr) Abstract: This paper deals with the analysis of the equilibria and their stability of the so-called AMOCO model developed by Bernard et al. (2001) to describe the dynamical behavior of an anaerobic fixed-bed wastewater treatment process. Depending on the model parameters, the steady states are analytically characterized and their stability is analyzed. Following this study, it is shown that the overloading tolerance (denoted herein OT), a parameter proposed in Hess and Bernard (2007) to monitor anaerobic processes on-line, may be not adapted under certain operating conditions and even lead to bad operating decisions. Keywords: Biotechnology, steady state analysis, equilibrium, model approximation, risk analysis. 1. INTRODUCTION In a very near future, water resources around the Mediter- ranean will not be sufficient to meet demands. Solutions to alleviate water shortages exist with their advantages and drawbacks: obviously, all should be employed in a com- plementary manner. One solution, largely used in several areas, notably in South East Asia, in the United States and in Europe is the reuse of wastewater for agricultural pur- poses. This solution consists in recovering the wastewater (generated by industries and domestic use) by processing them so that they can be safely reused in agriculture. One innovative technical approach to do so is to couple the conventional treatment plants with membranes that filter out microorganisms and Suspended Solids. This techni- cal solution, however, requires lot of energy (to minimize the clogging of membranes) and therefore is not, a pri- ori, suited to countries with low average incomes as in Northern African Mediterranean countries. However, when coupled with remediation process producing energy such as the “anaerobic digestion” able to generate potentially valuable biogas, a membrane process could provide an interesting alternative solution within a reuse policy. The anaerobic digestion process is the biological conver- sion of the organic matter into gaseous methane, carbonic gas (the biogas) and biomass. Its main advantage is to produce methane that can precisely be used to recover energy. Thus, coupling the anaerobic process with the membrane technology appears to be a promising solution ⋆ This work was supported by TREASURE (an INRIA Euromed 3+3 project, http://www.treasure.fr) and COADVISE (project FP7- PEOPLE-IRSES-2008 No. 230833). for countries under arid climates. Most Membrane BioRe- actors (or MBR) are aerobic systems. Thus, the recent modeling efforts to couple models of biological phenomena together with models of membrane modules have been essentially proposed for aerobic treatment plants. Within the framework of the TREASURE Euro-Mediterranean research network 1 , we are interested in the modeling and in the optimal control of Anaerobic MBRs (denoted AnMBR). In order to study the coupling of anaerobic bi- ological phenomena with the membrane characteristics, it is necessary to modify the existing models of the anaerobic digestion in order to take into account new variables such as the soluble microbial products that have been shown to play an important role in the membrane fouling process, Le Clech et al. (2006). Recently, such a model has been proposed by Benyahia (2009). It is based on a slight mod- ification of the so-called AMOCO model to which a new variable has been added. The so-called AMOCO model is a simple two-step mass balance model of the anaer- obic process. It has been specifically developed within the AMOCO European project (and thus its name 2 ) for automatic control and diagnosis purposes. Its main asset is to capture the main features of the anaerobic process, that is the possibility of unstability after an organic or hydraulic overload by the accumulation of volatile fatty acids (VFA) during the methanogenic stage. To do so, it includes Haldane kinetics for modeling the methanogenic step. Furthermore, it takes into account very simply a 1 Acronym for TREAtment and SUstainable Reuse of Effluents in semiarid climates 2 Acronym for Advanced MOnitoring and COntrol System for anaerobic processes, European FAIR project No. ERB-FAIR-CT96- 1198 Proceedings of the 11th International Symposium on Computer Applications in Biotechnology (CAB 2010), Leuven, Belgium, July 7-9, 2010 Julio R. Banga, Philippe Bogaerts, Jan Van Impe, Denis Dochain, Ilse Smets (Eds.) FrMT1.5 Copyright held by the International Federation of Automatic Control 371