In this work, we are interested in the mathematical analysis of a model of a bioreactor based on the results of a model already implemented ADM1. It is an observability analysis and estimation scheme for specific growth rates for an anaerobic digestion process of cow dung. A 1- stage model of 3 dynamic states is assumed describing all anaerobic digestion with a different population of microorganisms, and the evaluation of biogas production (methane + carbon dioxide). The result of specific growth rates (µmax = 0.44d-1) of bacterial populations (24gL-1 ± 2.3%) and substrate (6.5gL-1± 0.5%) are estimated from the dilution rate and biogas. The dynamics of anaerobic digestion appear to depend on the type of organic matter contained in cow substrates.