Abstract
This study presents a theoretical and mathematical analysis and modelling of the emerging microalgal membrane photobioreactors (M-MPBRs) for wastewater treatment. A set of mathematical models was developed to predict the biological performances of M-MPBRs. The model takes into account the effects of hydraulic retention time (HRT), solid retention time (SRT), and the N/P ratio of influent on the biological performance of M-MPBRs, such as microalgal biomass production and nutrient (N and P) removals. The model was calibrated and validated using experimental data from the literature. This modelling study explained that prolonged SRT could promote biomass production and nutrient removal, while prolonging HRT exhibited a negative effect. Furthermore, biomass production could be improved by augmenting nutrient loading, and nutrient removal would be limited under insufficient conditions. The modelling results demonstrated that the best performance was achieved at HRT = 1 d and SRT = 40 d for typical municipal wastewater with an influent N concentration = 40 mg/L. The modelling results are in good agreement with the experimental results from the literature. The findings suggest that the proposed models can be used as a powerful mathematical tool to optimize these parameters to improve the removal of nutrients (N and P), as well as the productivity of biomass in M-MPBRs. This study provides new insights into the use of mathematical models for the optimal design and operation of the emerging M-MPBRs for sustainable wastewater treatment.