(194af) Modeling of Stationary Phase in Microalgae Growth Using the Population Balance Equation

Microalgae are being widely studied because of their versatility to some of the main needs of humanity such as energy, food and fine chemicals [1]. These kinds of cells can be found in every corner of the globe and they are considered among the fastest growing plants on Earth. Sometimes, they are unwanted and, for that reason, defining what happens in the stationary phase could play an important role in a better understanding of how these species survive in very adverse conditions.

Microalgae growth can be classified into different phases, commonly named lag, exponential, linear, stationary and decaying phases [2]. To maximize the production, it is necessary to define which are the best living conditions. For that purpose, experiments can be performed and the best environmental conditions (temperature, nutrients and light intensity to mention some) can be defined. However, experiments are quite time consuming and, often, require expensive instruments. Therefore, it is useful to develop models able to predict the growth of microalgae. This can be particularly useful for a further optimization of the production process.

Many models have been utilized to predict the growth, but most of them can’t give much information about the life cycle of microalgae [2]. Population balance has been utilized on numerous fields of engineering and science [3]. Recently the population balance equation (including the breakage equation) has been applied to cellular growth and microalgae growth in particular [4]-[6]. Especially, having more information about the growth, the division rate as well as the size distribution can be quite advantageous when the objective is to optimize the whole system. For example, knowing the size of the cells can enhance the harvesting technology, which is among the most energy consuming steps before obtaining any final product from microalgae [7]. Therefore, it can be useful to know the behavior of the population during the stationary phase, in which the highest concentration of cells is reached. At this point the growth rate of the whole population is close to zero, considering also that part of the population would die. For that reason, a better understanding of the growth of living cells as well as the content of dead cells may give some valuable information related to the life cycle of microalgae. Differently from the exponential and linear phases, where the number of dead cells can be neglected, in the stationary phase that number plays an important role. In particular, maintaining the stationary phase for a prolonged period can give indication about this phase and explain why the decaying period does not occur immediately after the linear phase.

Numerous methods can be used to solve the population balance equation (PBE) [3], [8]. In our case, to solve the PBE, which is a integro-partial differential equation, a discretized method has been applied. The model considers dead cells and living population and it can predict the total population (alive and not) as well as the size distribution dynamically. Other than that, it can provide additional parameters such as the growth rate, the division rate at different cellular sizes and the number of daughter cells. The model has been validated experimentally using some batch photobioreactors, in which a unicellular species of microalgae (Chlorococcum) was grown. The temperature was maintained constant using a temperature controller, while nutrients were introduced only in the beginning of the experiment. Cell concentration and size distribution was measured daily; the experimental data were then utilized for parameter estimation applying the population balance equation. The results are in agreement with experiments and additional investigation will be performed in the future.

References

[1] E. M. Grima et al, "Recovery of microalgal biomass and metabolites: process options and economics," Biotechnol. Adv., vol. 20, pp. 491-515, 2003.

[2] E. Lee, M. Jalalizadeh and Q. Zhang, "Growth kinetic models for microalgae cultivation: a review," Algal Research, vol. 12, pp. 497-512, 2015.

[3] D. Ramkrishna, Population Balances: Theory and Applications to Particulate Systems in Engineering. Academic press, 2000.

[4] M. A. Hjortsø, Population Balances in Biomedical Engineering. McGraw-Hill, 2006.

[5] A. Bertucco et al, "Population balance modeling of a microalgal culture in photobioreactors: Comparison between experiments and simulations," AIChE J., vol. 61, pp. 2702-2710, 2015.

[6] E. Pahija et al, "Microalgae growth determination using modified breakage equation model," Computer Aided Chemical Engineering, vol. 37, pp. 389-394, 2015.

[7] A. Concas, M. Pisu and G. Cao, "A novel mathematical model to simulate the size-structured growth of microalgae strains dividing by multiple fission," Chem. Eng. J., vol. 287, pp. 252-268, 2016.

[8] R. J. LeVeque, Finite Volume Methods for Hyperbolic Problems. Cambridge university press, 2002.