AN ANALYTICAL APPROACH TO AM2 MODEL FOR BATCH ANAEROBIC BIOREACTORS

The well-known AM2 model is commonly used for simulation of biotechnological processes of two-phases anaerobic digestions. Nevertheless, numerical simulation and graphical results usually obtained by solving the non-linear system of differential equations characterizing this model do not always enable an easy analysis of the processes as well their sensitivity to the variations of the different parameters and the initial conditions. In this paper, as an alternative to simulation, an analytical approach is proposed for batch reactors. It consists of adopting some approximations to reduce the mathematical complexity of the coupled differential equations of the AM2 model. The aim is to derive approximate analytical expressions concerning the dynamical evolution of the substrates and bacterias involved in reactions. The obtained expressions, therefore, permit a relatively easy analysis of the evolution of the main processes and their sensitivity to the different parameters and initial conditions. Moreover, it provides an explicit mathematical expression that enables to estimate the cummulative production of methane. The comparison of the obtained results by this proposed analytical approach to the numerical simulation of the AM2 model shows a satisfying qualitative convergence of the proposed approach to the AM2 model