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MBW:Modeling method for combining fluid dynamics and algal growth in a bubble column photobioreactor

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Algae are a promising candidate for regenerative life support (air revitalization, waste water treatment and food production) and fuel production. Today small laboratory bench top photobioreactors are well characterized but for gaining high productivity these systems have to be scaled up. Due to complex fluid dynamics as well as shadowing effects the results cannot be scaled to large-scale photobioreactors. By using the parameters collected from laboratory systems models are suited to predict the behavior in larger systems. Current models that predict the growth rate of large scale systems are either neglecting these effects and lead to invalid results or are time consuming due to CPU intensive CFD modeling. This paper presents a novel approach that uses a combination of fluid dynamics and algal growth models to provide a fast but accurate alga growth model. The approach uses a single CFD model of the photobioreactor geometry to create a compartment model. This simplified model can then be used repeatedly to simulate algal growth models within each compartment and the mass transfers between each compartment without recalculating the CFD. It has been shown that there is a critical grid size that has to be used for compartmentation in order to reach reliable results. By comparing this compartmental approach to models that averaged parameters over the entire photobioreactors differences in absolute values as well as time scale could be observed. Effects leading to this behavior are the lack of capability of simpler models to model the circulation of algal cells between shaded areas and the reactor walls, which are leading to longer growth. Furthermore the model is capable of simulating the behavior and effect of carbon dioxide, oxygen, and nutrients on algae in a very simple way. Compared to CFD modeling that takes a day for 10 seconds of simulation, this novel approach was able to simulate 100 hours of algal growth in 3 minutes. The model was capable of showing interactions as they are seen in experimental data. However, input parameters have been collected from literature but not been verified with an experimental setup. Also the model is lacking some parameters such as temperature and light spectrum, which can be assumed constant in a laboratory environment but should be included in future iterations of the model.


Algae are a promising candidate for reducing the environmental impact of humans. During growth algae consume carbon dioxide and nutrients to produce oxygen. This can be used to decrease the carbon dioxide emissions on Earth as well as to clean waste water by binding the nutrients. Algae also produce biomass that can be harvested and utilized for nutrition or fuel production. This functionality makes algal cultures especially suited for use as life support system in remote locations such as spacecrafts. As humans consume food and oxygen and produce carbon dioxide as well as waste products, there is potential to create a closed ecosystem out of algae and humans. Before the feasibility of such closed loop systems can be assessed by modeled it is crucial to accurately model the efficiency and productivity of large scale algal photobioreactors. For the constraint mass and volume budget of spacecrafts it is important to find the highest efficiencies of an algal photobioreactor. Furthermore, the behavior under altered environmental parameters such as nutrition, carbon dioxide and lighting is also crucial to predict. Algal systems are commonly investigated in small bench top test set ups. Here the algal can be grown in a controlled environment in order to decrease the independent variables to one. The working principles and dependencies of algae to environmental parameters learned in these experiments are important. For high productivities that can support humans or generate large amounts of fuels bigger facilities are needed. However, the results from small bench top photobioreactors cannot be scaled up to large scale photobioreactors as for example fluid dynamic behavior changes and new effects such as shading comes into play. In order to prevent expensive and time intensive experiments with large scale photobioreactors models are necessary to predict the behavior after scaling up that can then be verified in a small number of experiments. Previous attempts have tried to factor in this behavior by using average light intensity and nutrition for the entire photobioreactor volume. Due to mixing, and decreasing light intensity towards the center of the photobioreactor this approach has known deficiencies. Attempts to overcome these deficiencies include models using CFD that are capable of precisely analyzing the alga growth rate of photobioreactors. However, these CFD simulations are time consuming for analyzing a variety of first draft reactor designs and hence impractical to use. Hence, a fast but accurate model is needed.

Biological Phenomenon

As shown in Figure 1 algal cells contain chloroplasts that are responsible for the characteristic green color and are conducting photosynthesis. As part of this reaction the cells fixate carbon dioxide in glucose and produce oxygen from the consumed water as shown in the equation below.

Figure 1 Metabolism of an algal cell

This process requires light as energy source that is absorbed at a wavelength of 400–500 and 650–700nm, which represents red and blue light. It is important to note that photosynthesis occurs in 2 steps. Photosystem II (which was discovered second) occurs first. Here water is electrolyzed to oxygen, hydrogen and an electron. The electron is then excited by the red light and subsequently forms ATP while reducing itself over the electron transport chain back to the baseline level. In Photosystem (discovered first but occurs second) this same electron is excited again by blue light and bound to NADP+. Two electrons and 2 hydrogen ions together with a NADP+ complex are then creating a NADPH complex. Hence out of water and photons the energy for the carbon dioxide fixation as well as oxygen are produced. In the now following Calvin Cycle, carbon dioxide is bond to a 5 carbon Ribulose Biphosphate (RuBP) forming 2 Phosphoglycerates. 5 out of 6 times that process is occurring, the Phosphoglycerates are used to regenerate Ribulose Biphosphate. The remaining 1 out of those 6 times is used for the biomass production. By using ATP as the energy source, the hydrogen delivered by the NADPH molecule is bond to the Phosphoglycerates forming glucose. In addition nutrients such as nitrates, phosphates and silicates have to be absorbed by algal cells in order to develop amino acids and proteins. These substances are main constituent of biomass that can be utilized for nutrition of animals and humans.

The concentrations of the substances listed above has effects on photosynthesis and hence on algal growth. They are listed below:

Light intensity, spectrum, and cycle The light intensity has been shown to yield maximum growth rate of chlorella vulgaris at 140 µE m-2 s-1 [1]. It has to be noted that other studies have found varying results due to different measurement units and methods. Values of optimum growth vary from 1370 lux over 2691 lux to 27397 lux [2]. Before the innovation of LED’s and still today for terrestrial applications most studies use light sources that have a comparable spectrum to the sun. Pigments within chlorella vulgaris consist mainly of chlorophyll and carotenoids, which mainly capture the light with wavelengths of 400–500 and 650–700nm, which represents red and blue light. [3]. In accordance with this Lee and Palsson (1994) have shown that the same growth rates can be achieved using LED lights with a very narrow spectrum around 680 nm (red) [2]. Most of terrestrial research is using the sun as light source and hence try to mimic the natural light with a day/night cycle ranging from 12/12 to 16/8. It has however been shown that algae yield a greater growth rate at a light cycle of about 100 Hz [4]. This is called the flashing light effect.

Carbon Dioxide concentration It is shown that the growth rate is carbon dioxide level dependent with a single maximum that is above ambient (0.004 %) carbon dioxide concentration. The exact location of that maximum however is still under discussion. Studies have exposed microalgae to levels between 0 and 20 % carbon dioxide. Studies have experimentally found it at 4 % and 6 % [5][6] .

Oxygen concentration Richardson et al. have shown that above an oxygen partial pressure 13.75 the growth rate decreases in a linear fashion and ceased at 2 atmospheres, whereas between 2.53 and 13.75 psia the growth rate was not affected [7] by changing oxygen levels. Most interestingly however is that the growth rate was accelerated about 12 % below 2.53 psia.

Pressure While total pressures above ambient seem to have no influence on the growth rate, reduced rates are thought to be slightly stimulatory [8]. Other studies have looked at altered pressures under pure carbon dioxide atmospheres [9]. Hereby they have seen a maximum growth rate at 300 mbar. Low survivability at lower pressures is thought to be caused by desiccation, whereas low survivability at higher pressure is due to carbon dioxide toxicity.

pH-Level An experimental study has shown that chlorella vulgaris is capable of growing over a wide range of pH values. The optimum has been found between 6.4 and 6.8 [10].

Temperature In specific the growth rate of chlorella vulgaris increases with increasing temperatures from 10 °C until its optimum temperature of 30 °C. At the 35 °C the growth quickly drops off [5][11]. This is also in alignment with the optimum temperature of 32.4 °C shown in a different study [10].

Mathematical Model

The mathematical model is split up into 3 sub models.

Light intensity modeling

Algal growth is dependent on the available light energy and given in the following equation. The light source intensity will be decrease due to distance as well as absorption due to water and biomass. In order to gain the light intensity over a certain volume, the center of that volume will be taken to estimate the needed parameters.


Algal kinetics modeling

Algal cells can exist in 3 distinct states as shown in Figure 2: The resting state, where algal cells have to little resources to grow, the active state where algal cells grow and split into new cells that belong to the resting state and the inhibited states that have too much resources that inhibit growth. At initialization of the model all cells start in the resting state. The model and the conversion of cells between those states is mainly dependent on the lighting level. These equations represent fractions so that x1+x2+x3=1

Figure 2 The structure of the PSF model[12]

There is not just transfer between states but there also is growth in the entire population, which is described with the following equation.


Cell growth just occurs in the active state and its dynamics are described by the factor mu. However, algal growth can also be limited by lack or inhibition of carbon dioxide, lack of nutrients as well as oxygen toxicity. Every one of those limitations is modeled by a multiplication factor. As stated earlier newly grown cells are starting in the resting state as shown below. The unchanged cells can just be separated by the fractions calculated earlier.


The final step is modeling the behavior of the carbon dioxide, nutrient and oxygen concentrations. Carbon dioxide as well as nutrient decay are dependent on the growth rate of the algal cells.


According to the photosynthetic equation the oxygen production is dependent on the carbon dioxide fixation. Hence, it is just a multiplication of the carbon dioxide reduction.



The flow field was calculated once by CFD. From there compartments of similar properties where formed[13]. The main factor that was emphasized with a weighing factor was lighting intensity. In addition the compartments where further shaped due to turbulence intensity and pressure. Due to the cylindrical geometry of the photobioreactor and the circumferential lighting these compartments mainly are tubular. In order to automatically determine these departments, the photobioreactor has to be divided into a grid of evenly sized compartments. The developed algorithm then starts at a random cell and determines whether the neighboring cells have the described properties of similar range. If no more cells that fulfill that requirement are found the compartment is finished and the algorithm jumps to a new random cell and continuous there. From the calculated flow field the liquid flow volume between the compartments was determined. Together with the surface area between neighboring compartments, their volume as well as their acceleration, a complete mass flow within the photobioreactor could be established from the produced geometry. These compartments where then used to run the light intensity and algal kinetics modeling for each compartment separately. The results of each incremental iteration were then used to model the mass transfers between the compartments before the algal kinetics model was continuing to its next iteration.

Results from the paper

The CFD resulted in a flow field that is carrying the liquid upwards in the center and back down on the sides of the bubble column to replace the lost liquid at the bottom. The algorithm divided the photobioreactor successfully into 77 compartments. 5 additional compartments had to be added at the top and bottom boundary layer. The simulation was conducted for 3 different cases. Case 1 has the division of the photobioreactor into 82 compartments as deemed representable of the fluid dynamics in the analysis. In order to show the importance of the compartmentalization two other cases where introduced. Firstly a single compartment with volume average distance to the light source was assumed. Secondly a maximum case was assumed with the shortest pathway between light source and algal cells. In these 3 cases the mass fraction of the resting and active state where shown. The mass fraction of the inhibited state is negligible low in all cases. On top of that there is also the growth rate plotted, that shows the total growth of the culture.

Figure 3 Growth rate of biomass and the mass fractions of biomass in the resting (1) and active (2) states in a batch cultivation calculated (A) with division to 82 compartments, (B) for ideal mixing with average intensity, and (C) for ideal mixing with maximum intensity. The fraction of the inhibited state (3) was negligible in all cases.[12]

It can be seen in figure 3 that in all cases the growth rate is reaching a maximum and decreasing afterwards. This is caused due to continuously increasing shadowing of the photobioreactor due to the produced biomass. As the light intensity suddenly decreases with distance from the reactor wall, more cells are going into the resting state and hence decreasing the growth rate. Differences can however be seen in the time dependency. At average intensity the maximum is reached much earlier than in the compartmental model as the algal cells in the model are static and hence cannot absorb the light at the walls of the photobioreactor. It can be seen that in the compartment model the growth is almost an order of magnitude faster than in the average intensity case and an order of magnitude lower than in the maximum intensity case. It can further be seen that the time dependencies between the maximum case and the compartment case are comparable whereas the average intensity case introduces a significant error. Absolute values however differ substantially and would have to be corrected leading to an unreliable model. It can be seen in Figure 4 that mass transfer in bubble column photobioreactors has limiting effects on the growth rates. As the transfer rate is slower than the consumption and production of carbon dioxide the concentration of both substances changes dependent on the growth rate. Hence even though the input air stream is in the favorable composition for efficient growth the oxygen level increases approximately 100 % whereas the carbon dioxide concentration decreases by about 15 %. As previously described lower carbon dioxide levels as well as increased oxygen levels inhibit algal growth which in this model can be calculated to about 5 %.

Figure 4 The oxygen and carbon dioxide concentrations in the liquid phase as a function of time.[12]

Important to note is that CFD modeling takes a day for 10 seconds of behavior, whereas with the compartment model 100 hours could be solved in 3 minutes.


The author shows a simplified way to repeatedly model algal growth in bubble column photobioreactors using a combination of CFD modeling and compartmentalization instead of time intensive CFD modeling. By comparing the traditional approach of averaging the entire photobioreactor to this novel approach, which takes into account the flow field and light availability, he showed that there are differences in growth rate as well as state dynamics. By carefully determining the number of compartments of the photobioreactor a good approximation can be achieved in a fraction of the time that is required for the more precise CFD modeling. With this a new tool was created that helps to quickly analyze a variety of design for photobioreactors, before they have been built. As no experimental verification of that model has been performed, the absolute values are unreliable. However, comparative analysis between the different cases as well as growth dynamics are justified. It was further shown with this model that algal growth is maintained as shadowed algal cells in the inner part of the photobioreactors are transported to the outer walls and still receive light, necessary for growth. Other approaches are incapable of showing this behavior together with mass transfer of nutrients, oxygen and carbon dioxide. This approach of modeling the algal growth in a bubble column photobioreactor is not geometry dependent. The algorithms are solely based on flow field and light distribution and hence can be applied to all photobioreactors where these 2 items can be calculated. Important to note is that the model is lacking some important influential factors for algal growth. It simplifies photosynthesis to nutrients, carbon dioxide, oxygen and light supply. However algal growth is also dependent on the temperature and light spectrum, which have not been modeled as they have been assumed constant. For laboratory environments this approach is justified but as algal photobioreactors are often used outdoors an update of the model would be favorable. Finally photosynthesis as previously described consists out of the light dependent Photosystem I and II but also the light independent Calvin-Cycle. It has been shown that algal cells are also active for short times of darkness. That is not considered in this model and might demand a compartment model at a lower more detailed level as this approach might simplify the correlation between carbon dioxide consumption and oxygen production too much.

External Links

  1. Dauta, A., Devaux, J., Piquemal, F., & Boumnich, L. (1990). Growth rate of four freshwater algae in relation to light and temperature. Hydrobiologia, 207(1), 221–226. doi:10.1007/BF00041459
  2. 2.0 2.1 Lee, C., & Palsson, B. (1994). High density algal photobioreactors using light emitting diodes. Biotechnology and Bioengineering, 44, 1161–1167. Retrieved from
  3. Ravelonandro, P. H., Ratianarivo, D. H., Joannis-Cassan, C., Isambert, A., & Raherimandimby, M. (2008). Influence of light quality and intensity in the cultivation of Spirulina platensis from Toliara (Madagascar) in a closed system. Journal of Chemical Technology & Biotechnology, 83(6), 842–848. doi:10.1002/jctb.1878
  4. Liao, Q., Li, L., Chen, R., & Zhu, X. (2014). A novel photobioreactor generating the light/dark cycle to improve microalgae cultivation. Bioresource Technology, 161, 186–91. doi:10.1016/j.biortech.2014.02.119
  5. 5.0 5.1 Chinnasamy, S., Ramakrishnan, B., Bhatnagar, A., & Das, K. C. (2009). Biomass production potential of a wastewater alga Chlorella vulgaris ARC 1 under elevated levels of CO2 and temperature. International Journal of Molecular Sciences, 10(2), 518–32. doi:10.3390/ijms10020518
  6. Bhola, V., Desikan, R., Santosh, S. K., Subburamu, K., Sanniyasi, E., & Bux, F. (2011). Effects of parameters affecting biomass yield and thermal behaviour of Chlorella vulgaris. Journal of Bioscience and Bioengineering, 111(3), 377–82. doi:10.1016/j.jbiosc.2010.11.006
  7. Richardson, B., Wagner, F. W., & Welch, B. E. (1969). Growth of Chlorella sorokiniana at Hyperbaric Oxygen Pressures. Applied Microbiology, 17 (1 ), 135–138.
  8. Orcutt, D. M., Richardson, B., & Holden, R. D. (1970). Effects of Hypobaric and Hyperbaric Helium Atmospheres on the Growth of Chlorella sorokiniana. Applied Microbiology, 19(1), 182–3. Retrieved from
  9. Thomas, D. J., Eubanks, L. M., Rector, C., Warrington, J., & Todd, P. (2008). Effects of atmospheric pressure on the survival of photosynthetic microorganisms during simulations of ecopoesis. International Journal of Astrobiology, 7(3-4), 243. doi:10.1017/S1473550408004151
  10. 10.0 10.1 Mayo, A. W. (1997). Effects of Temperature and pH on the Kinetic Growth of Unialga Chlorella vulgaris Cultures Containing Bacteria. Water Environment Research, 69(1), 64–72. Retrieved from
  11. Converti, A., Casazza, A. A., Ortiz, E. Y., Perego, P., & Del Borghi, M. (2009). Effect of temperature and nitrogen concentration on the growth and lipid content of Nannochloropsis oculata and Chlorella vulgaris for biodiesel production. Chemical Engineering and Processing: Process Intensification, 48(6), 1146–1151. doi:10.1016/j.cep.2009.03.006
  12. 12.0 12.1 12.2 Nauha, E. K., & Alopaeus, V. (2013). Modeling method for combining fluid dynamics and algal growth in a bubble column photobioreactor. Chemical Engineering Journal, 229, 559–568. doi:10.1016/j.cej.2013.06.065
  13. Laakkonen, M. (2006). Development and Validation of Mass Transfer Models for the Design of Agitated Gas-Liquid Reactors Development and Validation of Mass Transfer Models for the Design of Agitated Gas-Liquid Reactors.