Microalgae-based biomass has been extensively studied because of its potential to produce several important biochemicals, such as lipids, proteins, carbohydrates, and pigments, for the manufacturing of value-added products, such as vitamins, bioactive compounds, and antioxidants, as well as for its applications in carbon dioxide sequestration, amongst others. There is also increasing interest in microalgae as renewable feedstock for biofuel production, inspiring a new focus on future biorefineries. This paper is dedicated to an in-depth analysis of the equilibria, stability, and sensitivity of a microalgal growth model developed by Droop (1974) for nutrient-limited batch cultivation. Two equilibrium points were found: the long-term biomass production equilibrium was found to be stable, whereas the equilibrium in the absence of biomass was found to be unstable. Simulations of estimated parameters and initial conditions using literature data were performed to relate the found results to a physical context. In conclusion, an examination of the found equilibria showed that the system does not have isolated fixed points but rather has an infinite number of equilibria, depending on the values of the minimal cell quota and initial conditions of the state variables of the model. The numerical solutions of the sensitivity functions indicate that the model outputs were more sensitive, in particular, to variations in the parameters of the half saturation constant and minimal cell quota than to variations in the maximum inorganic nutrient absorption rate and maximum growth rate.

The world’s human population is increasing as is the demand for new sustainable sources of energy. Accordingly, microalgae-based carbohydrates for biofuel production are being considered as an alternative source of raw materials for producing biofuels. Microalgae grow in photobioreactors under constantly changing conditions. Models improve our understanding of microalgae growth. In this paper, a photoacclimated model for continuous microalgae cultures in photobioreactors was used to study the time-varying behavior and sensitivity of solutions under optimal productivity conditions. From the perspective of dynamic simulation in this work, light intensity was found to play an influential role in modifying metabolic pathways as a cell stressor. Enhancing carbohydrate productivity by combining nutritional deficiency and light intensity regulation modeling strategies could be helpful to optimize the process for the highest yield in large-scale cultivation systems. Under the proposed simulation conditions, a maximum carbohydrate productivity of 48.11 gCm−3d−1 was achieved using an optimal dilution rate of 0.2625 d−1 and 350 μmolm−2s−1 of light intensity. However, it is important to note that, a particular set of manipulated inputs can generate multiple outputs at a steady state. A numerical solution of the sensitivity functions indicated that the model outputs were especially sensitive to changes in parameters corresponding to a minimum nitrogen quota, maximum nitrogen intake rate, dilution rate, and maximum nitrogen quota compared to to other model parameters.

Increasing the use of solar irradiation by the photosynthetic metabolism of green microalgae is necessary to exploit its potential as a source of lipids, carbohydrates, pigments or aromatic compounds as a source of biofuels or products of interest. Microalgae exposed to sunlight are able to adapt by synthesizing a greater amount of pigment to dissipate the incident light energy, controlling the supersaturation of cellular photosystems but reducing the efficiency of the use of light. The photoacclimation is described by the content of chlorophyll mass in relation to the carbon content in the biomass (g Chl / g C). In an outdoor photobioreactor, irradiance depends upon geographical location, time of year and atmospheric conditions. In the present proposal, the generation of biomass is established as a dynamic function of the nutrients, represented as C: N:Chl and the primary assimilation of nutrients as Nitrate (N) and Ammonium (A). The results of this research show an evolution of G: C, N: C, Chl: C and biomass as C (carbon) in different scenarios of parameterization showing consistent results.