In silico study of the microalgae−bacteria symbiotic system in a stagnant pond

•A rigorous model for the microalgae-bacteria symbiosis in a stagnant pond is proposed.•A combined Lagrangian Particle Tracking−Cubic Spline Collocation method is applied.•The effect of operating conditions on the behavior of co-culture is analyzed.•A strong symbiotic interaction between growth of microalgae and bacteria is observed.•Pond depth exerts the most significant effect on the bioprocess kinetics. A rigorous mathematical modeling of the symbiotic interaction between microalgae and bacteria in a stagnant pond is applied to analyze the effect of the operating conditions on the bioprocess kinetics. The microbial co-culture is described by a partial differential equations system, which is solved by a combined numerical method based on the Lagrangian Particle Tracking for microalgae transport equation and the Orthogonal Cubic Hermite Collocation for remaining transport equations. The effect of the temperature and light intensity, alkalinity, turbidity, initial ratio of biomasses, algal cell size, pond depth on the algal biomass productivity and the substrates removal is analyzed. It was found that all of them significantly affect the biomass production and the substrates removal, which is discussed in detail. Besides, a strong symbiotic interaction between cell growth of microalgae and bacteria is observed; specifically, bacterial growth was restricted by the microalgal growth, due to the limitation of dissolved oxygen.