Dynamical Model for Stigeoclonium nanum in Thin-Layer Photobioreactors Considering Abiotic Losses and Logistics Constraints

This paper presents a mechanistic model for a thin-layer microalgal bioreactor cultivating Stigeoclonium nanum, with a comprehensive analysis of its dynamics and stability. Unlike most bioreactor studies that assume simple Monod or linear growth, our model rigorously explores the nonlinear interplay between logistic constraints and multiple nutrient limitations. We introduce a coupled Logistic–Monod system of nonlinear ordinary differential equations that captures sigmoidal transitions and steady states of Stigeoclonium nanum under simultaneous nitrogen and phosphorus depletion and incorporates abiotic nutrient removal to ensure mass conservation. Qualitative analysis proves positive invariance and boundedness of solutions using the Localization of Compact Invariant Sets method. Asymptotic stability of the biologically relevant equilibrium is established. Experimental validation in a thin-layer photobioreactor using three-fold cross-validation yielded high correlation coefficients (0.78–0.96) for biomass, nitrate, and phosphate concentrations, confirming predictive accuracy. The model thus provides a robust framework for process control and optimization in industrial-scale applications.