Light–temperature–nutrient dependent Monod modeling of optimized Isochrysis galbana growth in a PV-integrated photobioreactor

Abstract

A reliable growth-prediction model is essential for optimizing outdoor cultivation of Isochrysis galbana, particularly under rapidly changing light and temperature conditions induced by photovoltaic (PV) shading. In this study, an extended Monod-type kinetic model integrating the combined effects of light intensity, temperature, and nutrient (nitrate) availability, specifically designed for a PV-integrated photobioreactor (PBR), is developed and validated. A 19 experimental runs Central Composite Design (CCD) was employed to examine how PV–PBR spacing and LED supplementation influence biomass accumulation and specific growth rate. The experimental data highlighted clear interactions among light, temperature, and nutrient uptake. LED supplementation enhanced growth at sub-optimal PV–PBR distances, but its impact diminished as natural irradiance increased. The extended Monod model showed strong predictive capability, outperforming the classical model with lower RMSE and higher R² values. Parameter fitting showed that μ_max, Ks, and light-related coefficients responded sensitively to diurnal irradiance dynamics, reflecting the physiological behavior of Isochrysis galbana exposed to mixed natural–artificial illumination. Model validation across all CCD conditions further confirmed its robustness, with residuals indicating no systematic deviation. Overall, the multi-factor Monod framework developed here provides an accurate and scalable approach for predicting outdoor Isochrysis galbana growth in solar-integrated systems. These findings offer practical direction for refining PV–PBR layouts, boosting biomass productivity, and guiding future efforts to build dynamic, real-world microalgal cultivation models.