Mathematical Model for Meso- and Thermophilic Anaerobic Sewage Sludge Digestion

A mathematical model is developed to describe the dynamic behavior of mesophilic (35 ± 5 °C) and thermophilic digestion (55 ± 5 °C). Special emphasis is given to acetotrophic methanogenesis and propionate degradation, as the steps that determine the stability of anaerobic digestion, as well as to hydrolysis rate, which determines the degradation efficiency of particulate degradable organic carbon. Within the range of 6−20 (mesophilic) and 2−8 d (thermophilic) hydraulic retention time (HRT), the observed maximum growth rates for acetotrophic methanogens are 0.33 and 1.3 d^-1, respectively, with a 15% decay rate. Temperature and pH dependence as well as ammonia inhibition of acetate and propionate conversion are determined and included in the model, which allows us to simulate the effect of protein- and nitrogen-rich waste addition and the consequences of temporarily increased free ammonia at high pH. No inhibition of hydrogen conversion was observed in the same free ammonia range. The pH optimum is between 6.6 and 7.3. Acetotrophic methanogenesis is strongly inhibited below pH 6.2, whereas above pH 7.4 it can be inhibited by free ammonia. For digesters fed with ordinary municipal sewage sludge, free ammonia inhibition of acetate conversion leads to an increase in acetate at about 35 and 140 mg of N/L for mesophilic (HRT = 20 d) and thermophilic (HRT = 6 d) conditions, respectively. The hydrolysis rate constant is 0.25 and 0.4 d^-1 respectively for these two conditions. The model is validated with load variation experiments in laboratory and full-scale digesters for step and shock loads.