ADM1 based mathematical model of trace element precipitation/dissolution in anaerobic digestion processes

Due to the complex biogeochemistry of trace elements (TEs, e.g. Fe, Ni and Co) in anaerobic digestion processes, their role and fate is poorly understood. Challenging, time consuming and low detection limits of analytical procedures necessitate recruitment of mathematical models. A dynamic mathematical model based on anaerobic digestion model no.1 (ADM1) has been proposed to simulate the effect of TEs. New chemical equilibrium association/dissociation and precipitation/dissolution reactions have been implemented to determine TE bioavailability and their effect on anaerobic digestion. The model considers interactions with inorganic carbonate (HCO₃^- and CO₃^2-), phosphate (PO₄^3-, HPO₄^2-, H₂PO₄^-) and sulfide (HS^- and S^2-). The effect of deficiency, activation, inhibition and toxicity of TEs on the biochemical processes has been modelled based on a dose-response type inhibition function. The new model can predict: the dynamics of TEs (among carbonate, sulfide and phosphate); the starvation of TEs; and the effect of initial sulfur-phosphorus ratio in an in-silico batch anaerobic system.