Elemental balance based methodology to establish reaction stoichiometry in environmental modeling

Kinetic models in activated sludge, anaerobic digestion and other environmental modeling fields rely on the proper formulation of stoichiometric coefficients. Elemental balancing provides a simple and rigorous way to establish the stoichiometric coefficients of reactions represented in the Gujer matrix. The deduction of these coefficients is frequently trivial, from basic mass balancing considerations. In more complex cases, such as the Anammox growth reaction, rigorous elemental balancing is required to establish the proper formulation. This paper demonstrates the methodology based on a simple aerobic heterotrophic growth reaction where stoichiometry coefficients (such as the (1-Y_H)/Y_H term for oxygen) are well known. In the second step the methodology is applied for the Anammox growth reaction. The fraction of N₂ gas in current models originates from the NH₄⁺ and the NO₂⁻ electron donor/acceptor pair in equal proportion. This paper demonstrates that this stoichiometry is a simplification leading to elemental balance errors. The proper stoichiometric coefficients are derived.