Due to the importance of anaerobic digestion as a treatment process, different dynamic models exist, such as the AM2 which was developed jointly by researchers of the INRA of Narbonne and the INRIA of Sophia-Antipolis in 2001 (Olivier et al., 2001). It is based on experimental results obtained on the fixed bed reactor of the INRA of Narbonne. This model is made of two steps: acidogenesis and methanogenesis corresponding to acido-acetogens and methanogens bacteria populations, respectively. As a more recent and elaborate model, the ADM1, was developed by an IWA group (Batstone et al., 2002). Its main feature is the consideration of the principal steps of anaerobic digestion process that are, respectively, substrate disintegration (non biological step), hydrolysis, acidogenesis, acetogenesis and finally the methanogenesis with seven different bacteria groups.

Since its development in 2002 and up to now, the ADM1 has been tested and used on different substrates where a great number of research works are reported in the literature. As examples, one can cite (Blumensaat and Keller, 2005) who modified the initial version of ADM1 for the simulation of a dynamic behaviour of a pilot scale digester using sludge, in order to ensure a faultless model implementation. They obtained accurate results for the cases of low to medium loading rates. However the accuracy showed a decline with the increase of the loading rate.

Wayne and Parker, 2005) considered the application of the ADM1 to a variety of anaerobic digestion configurations where the results showed, in most of the considered cases, that the model was able to reproduce the trends of the experimental results.

(Feng et al., 2006) found that the ADM1 is not sensitive to the distribution ratio of carbohydrates, proteins and lipids, whereas the fraction of short chain fatty acids (SCFA) in the influent is rather more important.

Consequently, the great capabilities of ADM1 in modelling different types of substrates and calculations have been the motivating factor to use it in the present work to evaluate the performances of a co-digestion process for the treatment of organic municipal solid waste and waste activated sludge in the above mentioned 2000 m3 reactor working at a temperature of 37°C.

As mentioned above the ADM1 (Anaerobic Digestion Model No. 1) was developed by the IWA group (Batstone et al., 2002) with the objective to build a full mathematical model based intimately on the phenomenological model in order to simulate, at best, anaerobic reactors. It includes, as a first step, the disintegration of solid complexes (non biological step) into carbohydrates, lipids, proteins and inert material (soluble and particulate inert). The second step is the hydrolysis process of the disintegration products under an enzymatic action to produce sugars, amino acids and long chain fatty acids (LCFA), successively. Then, amino acids and sugars are fermented to produce VFA, hydrogen and carbon dioxide (acidogenesis). Then LCFA, proprionic acid, butyric acid and valeric acid are anaerobically oxided into acetate, carbon dioxide and hydrogen (acetogenesis). Finally, methane can be produced through two paths: the first one is based on acetate whereas the second one is through the reduction of carbon dioxide by molecular hydrogen. The organic species and molecular hydrogen, in this model, are expressed as COD (Chemical Oxygen Demand), whereas inorganic nitrogen and inorganic carbon species are expressed through their molecular concentrations.

Extensions and modifications were brought to ADM1 to enlarge its prediction capabilities by, taking into account other factors such as, for instance, the sulfato-reductors or the degradation of certain substrates (Wolfsberger and Halubar, 2006) and (Batstone and Keller, 2003). Moreover, Usama Zaher (Usama, 2005) considered the toxic effects of cyanide as an inhibition process for acetate.