Predicting microalgae growth

Comparative Analysis of Laboratory-Based and Spectroscopic Methods Used to Estimate the Algal Density of Chlorella vulgaris

Chlorella vulgaris is of great importance in numerous exploratory or industrial applications (e.g., medicals, food, and feed additives). Rapid quantification of algal biomass is crucial in photobioreactors for the optimization of nutrient management and the estimation of production. The main goal of this study is to provide a simple, rapid, and not-resource-intensive estimation method for determining the algal density of C. vulgaris according to the measured parameters using UV-Vis spectrophotometry. Comparative assessment measurements were conducted with seven different methods (e.g., filtration, evaporation, chlorophyll a extraction, and detection of optical density and fluorescence) to determine algal biomass. By analyzing the entire spectra of diluted algae samples, optimal wavelengths were determined through a stepwise series of linear regression analyses by a novel correlation scanning method, facilitating accurate parameter estimation. Nonlinear formulas for spectrometry-based estimation processes were derived for each parameter. As a result, a general formula for biomass concentration estimation was developed, with recommendations for suitable measuring devices based on algae concentration levels. New values for magnesium content and the average single-cell weight of C. vulgaris were established, in addition to the development of a rapid, semiautomated cell counting method, improving efficiency and accuracy in algae quantification for cultivation and biotechnology applications.

Toward a modeling, optimization, and predictive control framework for fed-batch metabolic cybergenetics

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes extracellular process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, and so on. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity.

Microalgae growth rate multivariable mathematical model for biomass production

Background

The use of microalgae has been emerging as a potential technology to reduce greenhouse gases and bioremediate polluted water and produce high-value products as pigments, phytohormones, biofuels, and bioactive compounds. The improvement in biomass production is a priority to make the technology implementation profitable in every application mentioned before.

Methods

The present study was conducted to explore the use of microalgae from genus Chlorella and Tetradesmus for the generation of substances of interest with UV absorption capacity. A mathematical model was developed for both microalgae to characterize the production of microalgae biomass considering the effects of light intensity, temperature, and nutrient consumption. The model was programmed in MATLAB software, where the three parameters were incorporated into a single specific growth rate equation.

Results

It was found that the optimal environmental conditions for each genus (Chlorella T=36°C, and I<787 μmol/m²s; Tetradesmus T=23°C and I<150 μmol/m²s), as well as the optimal specific growth rate depending on the personalized values of the three parameters.

Conclussion

This work could be used in the production of microalgae biomass for the design and development of topical applications to replace commercial options based on compounds that compromise health and have a harmful impact on the environment.

Outdoor Inclined Plastic Column Photobioreactor: Growth, and Biochemicals Response of Arthrospira platensis Culture on Daily Solar Irradiance in a Tropical Place

Implementation of outdoor photobioreactors has been challenged by an extremely oversaturated daily peak of solar irradiance. This study aims to understand the role of column size and paranet shading as well as to investigate the most convenient light control in outdoor cyanobacterial culture. The photobioreactor (PBR) consisted of plastic columns with a diameter of 12.74 cm (PBRd-20) and 31.85 cm (PBRd-50) laid outdoors and inclined at 158.22° upwards against solar radiation, while paranet shading was provided at 0%, 50%, 70%, and 90% shading capacity. A semi-continuous culture of cyanobacterium Arthrospira (Spirulina) platensis was conducted for 6 weeks with weekly monitoring of the growth parameter as well as the proximate and pigments content, while the daily irradiance and culture maximum temperature were recorded. The result shows that the column diameter of 12.74 cm had a lethal risk of 44.7% and this decreased to 10.5% by widening the column diameter to 31.85 cm. This lethal risk can be eliminated by the application of a paranet at a 50% reduction level for the column diameter of 31.85 cm and a 70% reduction level for the column diameter of 12.74 cm. The highest culture productivity of 149.03 mg/(L·day) was achieved with a PBRd-20 with 50% shading treatment, but a PBRd-50 with 90% shading treatment led to an increase in the protein and phycocyanin content by 66.7% and 14.91%, respectively.

Sustainable production of biofuels from the algae-derived biomass

The worldwide fossil fuel reserves are rapidly and continually being depleted as a result of the rapid increase in global population and rising energy sector needs. Fossil fuels should not be used carelessly since they produce greenhouse gases, air pollution, and global warming, which leads to ecological imbalance and health risks. The study aims to discuss the alternative renewable energy source that is necessary to meet the needs of the global energy industry in the future. Both microalgae and macroalgae have great potential for several industrial applications. Algae-based biofuels can surmount the inadequacies presented by conventional fuels, thereby reducing the ‘food versus fuel’ debate. Cultivation of algae can be performed in all three systems; closed, open, and hybrid frameworks from which algal biomass is harvested, treated and converted into the desired biofuels. Among these, closed photobioreactors are considered the most efficient system for the cultivation of algae. Different types of closed systems can be employed for the cultivation of algae such as stirred tank photobioreactor, flat panel photobioreactor, vertical column photobioreactor, bubble column photobioreactor, and horizontal tubular photobioreactor. The type of cultivation system along with various factors, such as light, temperature, nutrients, carbon dioxide, and pH affect the yield of algal biomass and hence the biofuel production. Algae-based biofuels present numerous benefits in terms of economic growth. Developing a biofuel industry based on algal cultivation can provide us with a lot of socio-economic advantages contributing to a publicly maintainable result. This article outlines the third-generation biofuels, how they are cultivated in different systems, different influencing factors, and the technologies for the conversion of biomass. The benefits provided by these new generation biofuels are also discussed. The development of algae-based biofuel would not only change environmental pollution control but also benefit producers' economic and social advancement.

Graphical abstract

Stochastic LCA Model of Upscaling the Production of Microalgal Compounds

Microalgae are currently being investigated for their promising metabolites but assessing the environmental impact of producing these compounds remains a challenge. Microalgae cultivation performance results from the complex interaction of biological, technological, geographical, and physical factors, which bioengineers try to optimize during the upscaling process. The path from the discovery of a microalgal compound to its industrial production is therefore highly uncertain. Nonetheless, it is key to anticipate the potential environmental impacts associated with the future production of a microalgal target compound. This is achieved in this study by developing an ex-ante, parameterized, and consequential LCA model that performs dynamic simulations of microalgae cultivation. The model is applied to calculate the environmental impacts of 9000 stochastically generated combinations of photobioreactor geometries and operational setups. The demonstration of the model is done for a fictive microalgal strain, parameterized to resemble Chlorella vulgaris, and a fictive target compound assumed to be a carbohydrate. The simulations are performed in Aalborg, Denmark, and Granada, Spain to appreciate geographical variability, which highly affects the requirements for thermoregulation. Open-source documentation allows full reproducibility and further use of the model for the ex-ante assessment of microalgal products.

Biodiesel production potential of microalgae, cultivated in acid mine drainage and livestock wastewater

The adaptability and biofuel production potential of two strains of microalgae isolated and cultivated in livestock wastewater effluent (LWE) with acid mine drainage (AMD) were investigated. The isolated strains of microalgae from samples obtained from LWE and AMD, two microalgal strains (Nephroselmis sp. KGE2 and Autodesmus obliquus KGE17) were selected based on their growth rate and lipid productivity. The dry cell weight of Nephroselmis sp. KGE2 and Autodesmus obliquus KGE17 after 20 days of cultivation in AMD increased from 0.05 to 0.59 g/L and from 0.05 to 0.55 g/L, respectively. These findings revealed a significant accumulation of fatty acids with increasing AMD content. Nephroselmis sp. KGE2 in LWE with 5% AMD demonstrated a higher growth rate (0.59 ± 0.03 g/L) and fatty acid production (401.5 ± 47.3 mg/L) than Autodesmus obliquus KGE17 with 5% AMD. Additionally, Nephroselmis sp. KGE2 had C16-C18 fatty acid content (92.4%) in LWE with AMD. Biodiesel produced from Nephroselmis sp. KGE2 had a higher cetane number (52.31) and iodine value (88.26 g I₂/100 g oil). Consequently, Nephroselmis sp. KGE2 can be considered a potential candidate for biodiesel production using AMD as an iron source.

Modeling and Simulation of Photobioreactors with Computational Fluid Dynamics—A Comprehensive Review

Computational Fluid Dynamics (CFD) have been frequently applied to model the growth conditions in photobioreactors, which are affected in a complex way by multiple, interacting physical processes. We review common photobioreactor types and discuss the processes occurring therein as well as how these processes have been considered in previous CFD models. The analysis reveals that CFD models of photobioreactors do often not consider state-of-the-art modeling approaches. As a comprehensive photobioreactor model consists of several sub-models, we review the most relevant models for the simulation of fluid flows, light propagation, heat and mass transfer and growth kinetics as well as state-of-the-art models for turbulence and interphase forces, revealing their strength and deficiencies. In addition, we review the population balance equation, breakage and coalescence models and discretization methods since the predicted bubble size distribution critically depends on them. This comprehensive overview of the available models provides a unique toolbox for generating CFD models of photobioreactors. Directions future research should take are also discussed, mainly consisting of an extensive experimental validation of the single models for specific photobioreactor geometries, as well as more complete and sophisticated integrated models by virtue of the constant increase of the computational capacity.

Growth parameter estimation and model simulation for three industrially relevant microalgae: Picochlorum, Nannochloropsis, and Neochloris

Multiple models have been developed in the field to simulate growth and product accumulation of microalgal cultures. These models heavily depend on the accurate estimation of growth parameters. In this paper growth parameters are presented for three industrially relevant microalgae species: Nannochloropsis sp., Neochloris oleoabundans, and Picochlorum sp. (BPE23). Dedicated growth experiments were done in photobioreactors to determine the maximal biomass yield on light and maintenance rate, while oxygen evolution experiments were performed to estimate the maximal specific growth rate. Picochlorum sp. exhibited the highest specific growth rate of 4.98 ± 0.24 day⁻¹ and the lowest specific maintenance rate of 0.079 day⁻¹, whereas N. oleoabundans showed the highest biomass yield on light of 1.78 g_x·mol_ph⁻¹. The measured growth parameters were used in a simple kinetic growth model for verification. When simulating growth under light conditions as found at Bonaire (12 °N, 68° W), Picochlorum sp. displayed the highest areal biomass productivity of 32.2 g.m⁻²·day⁻¹ and photosynthetic efficiency of 2.8%. The presented growth parameters show to be accurate compared to experimental data and can be used for model calibration by scientists and industrial communities in the field.

Dynamic Optimization Approach to Estimate Kinetic Parameters of Monod-Based Microalgae Growth Models

The biomass concentration of microalgae growth in photobioreactor was predicted using the Monod-based growth models. Kinetic parameters such as maximum specific growth rate and saturation constant of light intensity were evaluated by nonlinear least squares methods that focused on minimizing the sum of squares error (SSE). The importance of good initial guess for the nonlinear least squares method was also discussed. The optimal control problem of the microalgae growth model was determined based on parameter sensitivity. Therefore, a dynamic optimization approach was used where an optimal input design method was formulated to obtain a control function of a problem. The dynamic state equations, additional state equations, cost function, and Hamiltonian function were used to establish a control function of microalgae growth in a photobioreactor. Hence, the biomass production of microalgae can be predicted using numerical methods such as the Taylor series method.

Stochastic simulation of phytoplankton biomass using eighteen years of daily data - predictability of phytoplankton growth in a large, shallow lake

During the past decades, on-line monitoring of freshwater lakes has developed rapidly. To use high frequency time-series in lake management, novel models are needed that are simple and provide insight into the complexity of phytoplankton dynamics. Chlorophyll a (Chl), a proxy for phytoplankton biomass and environmental drivers were monitored on-line in large, shallow Lake Balaton during the vegetation periods between 2001 and 2018. Growth and non-growth (G and non-G) states of algae were deduced from daily change in Chl. Random forests (RF) were used to find stochastic response rules of phytoplankton to growth-supporting environmental habitat templates. The stochastic G/non-G state was translated into long-term daily biomass dynamics by a deterministic biomass model to assess uncertainty and to distinguish between inevitable and unpredictable blooms. A biomass peak was qualified as inevitable or unpredictable if the lower 95% confidence limit of simulations exceeded or remained at the baseline Chl level, respectively. Compared to a stochastic null model based on monthly Markovian transition probabilities, RF-based models captured wax and wane of biomass realistically. Timing of peaks could be better simulated than their magnitude, likely because habitat templates were primarily determined by light whereas peak sizes might depend on unmeasured processes, such as phosphorus availability. In general, algal growth was favored by wind-induced sediment resuspension that decreased light availability but simultaneously enhanced the P supply. Seasonal temperature and an integral of departures from the "normal" seasonal temperature over 2 to 3 generations were important drivers of phytoplankton growth, whereas short-term (diel and day to day) changes in water temperature appeared to be irrelevant. Four types of years could be distinguished during the study period with respect to algal growth conditions. The present modeling approach can reasonably be used even in highly variable aquatic environments when 3 to 4 years of daily data are available.

Photobiological Effects on Biochemical Composition in Porphyridium cruentum (Rhodophyta) with a Biotechnological Application

This study describes the relation of photosynthetic capacity, growth and biochemical compounds in the microalgae Porphyridium cruentum under saturated irradiance (200 μmol m^-2  s^-1 ) by white light (WL) and low-pressure sodium vapor lamps (SOX lamps-control) and supplemented by fluorescent lamps (FLs) with different light qualities (blue: λ_max = 440 nm; green: λ_max = 560 nm; and red: λ_max = 660 nm). The maximum photosynthetic efficiency (F_v / F_m ) showed a positive correlation with the light quality by saturating light SOX in mixture with stimulating blue light than the white light (WL) at the harvest day (10 days). The production, that is maximal electron transport rate (ETR_max ), and energy dissipation, that is maximal nonphotochemical quenching (NPQ_max ), had the same pattern throughout the time (3-6 days) being the values higher under white light (WL) compared with SOX and SOX plus supplemented different light qualities. Total protein levels increased significantly in the presence of SOX light, while phycoerythrin (B-PE) showed significant differences under SOX+ blue light. Arachidonic acid (ARA) was higher under SOX and SOX plus supplemented different light qualities than that under WL, whereas eicosapentaenoic acid (EPA) was the reverse. The high photomorphogenic potential by SOX light shows promising application for microalgal biotechnology.

Outdoor scale-up of Leptolyngbya sp.: Effect of light intensity and inoculum volume on photoinhibition and -oxidation

The effect of light intensity and inoculum volume on the occurrence of photooxidation for Leptolyngbya sp. QUCCCM 56 was investigated, to facilitate the transition from small‐scale laboratory experiments to large‐scale outdoor cultivation. Indoor, the strain was capable of growing at light intensities of up to 5600 µmol photons/m²/s, at inoculation densities as low as 0.1 g/L (10% inoculation volume vol/vol). Levels of chlorophyll and phycocyanin showed a significant decrease within the first 24 h, indicating some level of photooxidation, however, both were able to recover within 72 h. When cultivated under outdoor conditions in Qatar during summer, with average peak light intensities 1981 ± 41 μmol photons/m²/s, the strain had difficulties growing. The culture recovered after an initial adaptation period, and clear morphological differences were observed, such as an increase in trichome length, as well as coiling of multiple trichomes in tightly packed strands. It was hypothesized that the morphological changes were induced by UV‐radiation as an adaptation mechanism for increased self‐shading. Furthermore, the presence of contaminating ciliates could have also affected the outdoor culture. Both UV and contaminants are generally not simulated under laboratory environments, causing a mismatch between indoor optimizations and outdoor realizations.

Models of microalgal cultivation for added-value products - A review

Microalgae are considered a promising feedstock for biorefineries given that their chemical composition - rich in carbohydrate and lipid - can be directed towards the co-production of various value-added fuels and chemicals. Production of microalgal biomass for biorefinery purposes requires the identification and establishment of optimal cultivation systems, a crucial yet complicated task due to the numerous factors (e.g. media composition, light, temperature) that simultaneously regulate biomass growth and intracellular composition. Modelling these biological processes, taking into account a single or multiple growth-limiting factors, offers a valuable tool to simulate, design and optimise the dynamics of microalgae cultivation. This review provides an overview of existing models developed to describe microalgal growth processes at the macroscopic scale (also termed black-box models) and discusses their formulation in detail. The black-box kinetic modelling frameworks are compiled into single-factor (6 formulations) and multiple-factor (32 formulations - further divided into non-interactive, additive, and interactive) growth kinetic models, as reported in more than 80 studies, for the prediction of biomass growth as a function of major operational factors such as media composition (e.g. nutrient concentration) and environmental factors (e.g. transient light and temperature). In addition, the review focuses on those models that further account for the production dynamics of two microalgal intracellular products with renowned potential as biorefinery substrates: carbohydrate and lipid molecules. Models of microalgal cultivation dynamics offer a robust engineering tool to understand the natural yet complex responses of microalgae to their growing environment and can help - if used appropriately - to optimise microalgae cultivation and increase the economic viability and sustainability of microalgal systems.

Experimental and Model-Based Analysis to Optimize Microalgal Biomass Productivity in a Pilot-Scale Tubular Photobioreactor

A dynamic coarse-grained model of microalgal growth considering light availability and temperature under discontinuous bioprocess operation was parameterized using experimental data from 15 batch cultivations of Nannochloropsis granulata in a pilot-scale tubular photobioreactor. The methodology applied consists of a consecutive two-step model parameter estimation using pooled, clustered and reorganized data to obtain initial estimates and multi-experiment fitting to obtain the final estimates, which are: maximum specific growth rate μ_max = 1.56 d⁻¹, specific photon half-saturation constant K_S,ph = 1.89 molphgX-1d-1, specific photon maintenance coefficient m_ph = 0.346 molphgX-1d-1 and the cardinal temperatures T_min = 2.3°C, T_opt = 27.93°C and T_max = 32.59°C. Biomass productivity prediction proved highly accurate, expressed by the mean absolute percent error MAPE = 7.2%. Model-based numerical optimization of biomass productivity for repeated discontinuous operation with respect to the process parameters cultivation cycle time, inoculation biomass concentration and temperature yielded productivity gains of up to 35%. This optimization points to best performance under continuous operation. The approach successfully applied here to small pilot-scale confirms an earlier one to lab-scale, indicating its transferability to larger scale tubular photobioreactors.

The use of a natural substrate for immobilization of microalgae cultivated in wastewater

The methods of separation of microalgae has a significant impact in the economic aspects of their cultivation. In this study, pine bark was used as a substrate for immobilization of microalgal biomass cultivated in raw municipal sewage. The experiment was conducted in cylindrical photobioreactors (PBRs) with circulation of wastewater. Biomass was cultivated for 42 days. After that time, abundant growth of the biofilm with microalgae on the surface of pine bark as well as improvement of the quality of treated sewage were observed. The efficiency of removal of nutrients from wastewater was 64-81% for total nitrogen and 97-99% for total phosphorus. Moreover, the concentration of suspended solids in sewage was reduced, which resulted in a decrease in turbidity by more than 90%. Colorimetric analysis and Volatile Matter (VM) content in the substrate showed a decrease in the Higher Heating Value (HHV) and concentration of VM due to the proliferation of biofilm.

Effect of Light Intensity and Quality on Growth Rate and Composition of Chlorella vulgaris

In this research, the effect of solar irradiance on Chlorella vulgaris cultivated in open bioreactors under greenhouse conditions was investigated, as well as of ratio of light intensity in the 420–520 nm range to light in the 580–680 nm range (I_420–520/I_580–680) and of artificial irradiation provided by red and white LED lamps in a closed flat plate laboratory bioreactor on the growth rate and composition. The increase in solar irradiance led to faster growth rates (μ_exp) of C. vulgaris under both environmental conditions studied in the greenhouse (in June up to 0.33 d⁻¹ and in September up to 0.29 d⁻¹) and higher lipid content in microalgal biomass (in June up to 25.6% and in September up to 24.7%). In the experiments conducted in the closed bioreactor, as the ratio I_420–520/I_580–680 increased, the specific growth rate and the biomass, protein and lipid productivities increased as well. Additionally, the increase in light intensity with red and white LED lamps resulted in faster growth rates (the μ_exp increased up to 0.36 d⁻¹) and higher lipid content (up to 22.2%), while the protein, fiber, ash and moisture content remained relatively constant. Overall, the trend in biomass, lipid, and protein productivities as a function of light intensity was similar in the two systems (greenhouse and bioreactor).

Microalgal kinetics - a guideline for photobioreactor design and process development

Kinetics generally describes bio‐(chemical) reaction rates in dependence on substrate concentrations. Kinetics for microalgae is often adapted from heterotrophs and lacks mechanistic foundation, e.g. for light harvesting. Using and understanding kinetic equations as the representation of intracellular mechanisms is essential for reasonable comparisons and simulations of growth behavior. Summarizing growth kinetics in one equation does not yield reliable models. Piecewise linear or rational functions may mimic photosynthesis irradiance response curves, but fail to represent the mechanisms. Our modeling approach for photoautotrophic growth comprises physical and kinetic modules with mechanistic foundation extracted from the literature. Splitting the light submodel into the modules for light distribution, light absorption, and photosynthetic sugar production with independent parameters allows the transfer of kinetics between different reactor designs. The consecutive anabolism depends among others on nutrient concentrations. The nutrient uptake kinetics largely impacts carbon partitioning in the reviewed stoichiometry range of cellular constituents. Consecutive metabolic steps mask each other and demand a maximum value understandable as the minimum principle of growth. These fundamental modules need to be clearly distinguished, but may be modified or extended based on process conditions and progress in research. First, discussion of kinetics helps to understand the physiological situation, for which ranges of parameter values are given. Second, kinetics should be used for photobioreactor design, but also for gassing and nutrient optimization. Numerous examples are given for both aspects. Finally, measuring kinetics more comprehensively and precisely will help in improved process development.

Enhanced biomass and lipid production of Neochloris oleoabundans under high light conditions by anisotropic nature of light-splitting CaCO3 crystal

The aim of this work was to study the anisotropic effect of crystalline CaCO₃ nanoparticles (CN)-driven multiple refraction/scattering from the CN-coated agglomerated cells on the rate of photosynthesis and the product yield under high light conditions in the freshwater microalgae Neochloris oleoabundans. The CN-coating via biomineralization significantly improved the biomass and lipid production of N. oleoabundans during second stage of autotrophic induction by sustaining relatively high rate of photosynthesis at high irradiance using the multiple-splitting effect of the anisotropic polymorphism. The CN were successfully produced, adsorbed and grown on the external cells under conditions of mild alkalinity (pH 7.5-8.0), mild CaCl₂ concentration (0.05 M) and under nitrogen starvation with strong light (400 µE m^-2 s^-1). Consequently, lipid content and productivity of N. oleoabundans cells cultured with 0.05 M CaCl₂ increased by 18.4% and 31.5%, respectively, compared to the cells cultured with 0.05 M CaCl₂ and acetazolamide to inhibit calcification.

Theory of turbid microalgae cultures

Microalgae can be cultivated in closed or open photobioreactors (PBR). In these systems, light rapidly decreases as it passes through the culture due to the turbidity of the medium. Thus, microalgae experiment different light intensities depending on their position in the medium. In this paper, we study theoretically how the growth rate of microalgae is affected by different factors; incident light intensity, form of the PBR, microalgae population density, turbidity of non-microalgae components, and light path-length of the reactor. We show that for different types of PBR the average growth rate is completely determined by the incident light intensity and the optical depth. In the case of vertical cylindrical PBRs illuminated from above (e.g. race-way or panel-type reactors), we described (and we prove under general assumptions) in details the dependence of the AGR on the aforementioned factors. Finally, we discuss some implications of our analysis; the occurrence of the Allee effect, if light ostensibly limits or inhibits the growth rate in outdoor cultures, and how the geometry of the PBR affects microalgae growth rate and productivity.