A mathematical model for the kinetics of concurrent volatile solids destruction and water evaporation during aerobic and anaerobic digestion of wastewater sludge under mesophilic and thermophilic temperatures

Abstract

Experimental and computational approaches were employed to model kinetics of volatile solids destruction in the presence of water evaporation during biological digestion of wastewater sludge. Water evaporation occurred in both anaerobic and aerobic laboratory digesters with a much higher intensity in the latter. The water evaporation followed a linear trend over time. By inclusion of the linear equation for water evaporation rate, new kinetic models were developed to predict volatile solids (VS) and volatile suspended solids (VSS) concentrations of batch biological digesters. Modelled results using a first-order model were in good agreement with the measured VS concentrations of the anaerobic reactors operated at 35 °C and 55 °C (AnD.55) with coefficients of determination (R2) 0.92 and 0.84, respectively. VS degradation of AnD.55 was slightly more consistent with zero-order kinetics (R2 = 0.86). VS and VSS concentrations measured for batch aerobic digesters also agreed with the first-order model. R2 values were 0.91, 0.75 and 0.99 for reactors operated at 35 °C (AD.35), 45 °C and 55 °C, respectively. As for the progression in terms of VSS concentration, the highest R2 and lowest sum of squared error values belonged to AD.35. This is the first study that developed kinetic models for simultaneous VS degradation and water evaporation under both mesophilic and thermophilic conditions. The outcomes of this study indicate that water evaporation needs to be considered for accurate determination of the kinetic rate constant and solids reduction in laboratory and full-scale sludge digesters.