Mathematical Modeling of Microalgal Growth during Anaerobic Digestion Effluent Bioremediation

The development of kinetic models aims at predicting the behavior of a system or analyzing the underlying mechanisms. This process is essential for understanding microalgal growth and optimizing culture conditions. In the case of microalgal cultivation in wastewater, the analysis becomes even more difficult as growth is often inhibited by several factors, such as nutrient limitation and light inadequacy. In this context, a mathematical model was developed to describe the microbial growth of the species Parachlorella kessleri in different reactor setups using either sterile or non-sterile anaerobic digestion effluent as a substrate. Three different mass balances were taken into consideration to describe biomass growth, phosphorus, and nitrogen consumption. Concerning biomass growth, the logistic model was applied to evaluate the inhibition in biomass formation due to lack of illumination. The maximum optical density under which these species could grow was quantified with an ODmax parameter, which was estimated at 4.07 AU/cm for the Erlenmeyer flask and 2.79 AU/cm for cylindrical photobioreactors. Regarding the nitrogen mass balance, two different terms concerning microalgal assimilation and ammonia stripping were implemented into the equation. The proposed model predicted biomass growth with high accuracy in model training (R-2 = 0.90) and validation (R-2 = 0.89).