The anaerobic digestion ecosystem is complex, involving a broad variety of substrates and up to 140 bacterial species. This paper applies a methodology that determines the least number of macroscopic bioreactions to be taken into account in order to explain a recorded data set. We apply this methodology to model ADM1 simulations for a high rate anaerobic digestion process treating industrial wastewater. We show that: (i) a model including a single biomass only is sufficient for reproducing the COD concentration in the digester and methane flow rate in the biogas; (ii) a model with 2 biomasses is able to reproduce inorganic carbon, VFA and COD concentrations in the reactor and carbon dioxide and methane flow rates in the biogas; (iii) finally, model ADM1 allows one to make a more subtle distinction between the various volatile fatty acids, as well as to account for nitrogenous compounds when the process is monitored on a long term basis including periods of overloading.