A comparative study of mechanistic and hybrid model structures for microalgae-based tertiary wastewater treatment systems

Abstract

Microalgae-based wastewater treatment (WWT) systems are a sustainable approach to nutrient removal with biomass valorisation. However, accurately modelling these systems remains complex due to the intricate relations between environmental input variability and biological processes. This study conducts a systematic comparison of mechanistic and hybrid modelling methodologies for predicting biomass growth and nutrient dynamics (ammonia, nitrate, phosphate) in pilot-scale systems operated under natural conditions with real municipal effluent after secondary treatment. Mechanistic models included Monod-, Droop-, and Caperon-Meyer-type nutrient kinetics, with variations that incorporated light, temperature, and biomass decay factors. Additionally, two hybrid modelling approaches were tested, residual-corrected hybrids, where machine learning (ML) algorithms adjust the residuals of mechanistic model predictions, and factor-prediction hybrids, where ML techniques estimate values for environmental limitation factors. Models were calibrated and validated with experimental data for microalgae biomass (X alg ), ammonia (S NH4 ), nitrate (S NO3 ), and phosphate (S PO4 ), and assessed with R 2 and root mean squared error (RMSE) metrics. Findings indicate that mechanistic models incorporating internal nutrient storage and biomass decay provide superior predictive accuracy when compared to those based solely on external nutrient concentrations. Residual-corrected hybrid models enhanced prediction accuracies for X alg by 0.15–0.42 in R 2 and for S PO 4 and S NO 3 by 4–62% in RMSE, depending on the base model. Factor-prediction hybrids performed similarly to mechanistic models, considering light limitations, although with a lower number of calibrated parameters. This study discusses trade-offs between model complexity, interpretability, and predictive capability, offering a framework for integrating mechanistic and data-driven methodologies in microalgal WWT systems.