Algebraic solution of the mass balanced ADM1 to predict the steady state and to optimise the design of the anaerobic digestion of sewage sludge

This paper proposes an algebraic solution of the mass and charge balanced ADM1 model to predict the steady state performance of an anaerobic digester for sewage sludge treatment. The algebraic solution consists of three sequential stages: a kinetic stage that considers only the slowest transformations of the model, a stoichiometric stage based on the complete mass fluxes of the biological process and a physicochemical stage from which some digester outputs are calculated. The predictive capacity and the applicability of this model solution are corroborated by its comparison to the differential equation's model solution and the experimental data of a real case study. The algebraic solution is used to explore the digester response under different operational conditions. An example of application is used to verify the potential of the algebraic solution to be used, together with optimisation algorithms, for optimising the design of the digester and the operational conditions for specified performance criteria, such as effluent quality.