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Kinetics of Inorganic Carbon-Limited Freshwater Algal Growth at High pH

M. K. Watson, C. M. Drapcho

Published in Transactions of the ASABE 59(6): 1633-1643 (doi: 10.13031/trans.59.11520). Copyright 2016 American Society of Agricultural and Biological Engineers.

Submitted for review in August 2015 as manuscript number NRES 11520; approved for publication by the Natural Resources & Environmental Systems Community of ASABE in August 2016.

The authors are Mary K. Watson, Assistant Professor, Department of Civil and Environmental Engineering, The Citadel, Charleston, South Carolina; Caye M. Drapcho, ASABE Member, Associate Professor, Biosystems Engineering Program, Clemson University, Clemson, South Carolina. Corresponding author: M. K. Watson, 212 LeTellier Hall, 171 Moultrie Street, Charleston, SC 29409; phone: 843-956-7686; e-mail:

Abstract.  Elevated atmospheric CO2 concentrations necessitate exploration of carbon management strategies to combat high CO2 emissions. Carbon sequestration, which includes capture and storage of inorganic carbon, is one potential component of a carbon management plan. In particular, utilization of atmospheric CO2 by algae has been proposed for carbon capture, particularly at high pH since CO2 absorption rates increase with increasing pH. The goal of this study was to quantify the growth and inorganic carbon utilization of a mixed freshwater green algal culture at high pH. Algal cultures were supplied with different initial media inorganic carbon concentrations (11 to 32 mg C L-1 as Na2CO3), maintained in a controlled environment, and adjusted to an initial pH of 10.3. Samples were taken daily to measure pH, alkalinity, inorganic carbon, and total suspended solids. Results indicated that the culture was dominated by at all inorganic carbon concentrations. Peak biomass, specific growth rate, and biomass carbon content generally increased with increasing initial inorganic carbon concentration. Nonlinear regression was used to estimate a maximum specific growth rate of 0.0727 h-1 and half-saturation constants of 5.36 × 10-4, 6.84, 10.4, and 17.5 mg C L-1 for CO2, HCO3-, CO32, and total inorganic carbon, respectively. Comparison of changes in the concentrations of inorganic carbon species due to pH increase and utilization by algae suggest that CO2, HCO3-, and CO32- (i.e., total inorganic carbon) contributed to biomass production. Overall, the determined stoichiometric and kinetic parameters can be used to facilitate modeling and optimization of algal-based carbon capture strategies.

Keywords.Algae, Carbon management, Monod kinetics.

According to the Energy Information Association (EIA, 2008), atmospheric CO2 concentrations are predicted to increase as emissions from fossil fuels remain high, although natural and anthropogenic carbon sinks can reduce this effect. Recently, atmospheric CO2 reached 400 ppm (Biello, 2015). Even with measures to abate emissions, the CO2 concentration is expected to rise to 450 ppm by 2030 (EIA, 2008). One of the major concerns of rising atmospheric CO2 is climate change, which may cause a variety of global dilemmas (e.g., sea level rise) (Meehl et al., 2005).

To address problematic CO2 emissions and atmospheric concentrations, the U.S. Department of Energy has outlined a carbon management plan that includes development of carbon sequestration technologies. Carbon sequestration refers to the capture and storage of carbon that would otherwise add to atmospheric concentrations (Figueroa et al., 2008). Specifically, cultivation of algal biomass has been proposed as an approach for carbon sequestration (Kumar et al., 2011; Reichle et al., 1999). However, since biomass decay releases CO2, biomass must be strategically stored using strategies such as direct injection into geological formations, burial as biomass, or conversion of biomass into biochar to ensure true sequestration (Sayre, 2010). Alternatively, biomass could be harvested and converted to biofuels, which would mitigate carbon emissions by reducing fossil fuel use (Nedbal et al., 2010; Sayre, 2010; Wang et al., 2008) and contribute to the economic feasibility of algal-based carbon management (Ono and Cuello, 2006). Furthermore, high pH systems, such as those that can be naturally created when algae use nitrate as a nitrogen source, can enhance CO2 diffusion and subsequently enhance mitigation (Stumm and Morgan, 1981). Ultimately, high pH environments increase the mass of atmospheric CO2 available to algae for biofixation (Reichle et al., 1999).


Enhanced Carbon Dioxide Diffusion

Film theory can be used to illustrate how pH impacts diffusion of a gas into an open system (Whitman, 1962). For CO2, the resistance to mass transfer occurs in the liquid, where a quiescent boundary layer of finite thickness (L) extends from the gas-liquid interface to the bulk solution. At the interface, the CO2 concentration is equal to the saturation value (CO2)sat. At position L, the CO2 concentration is equal to that in the bulk solution: (CO2)bulk. Based on film theory, a gas can be absorbed into a liquid via unenhanced or kinetically enhanced diffusion (Dankwerts, 1970; Emerson, 1975; House et al., 1984; Smith, 1985). During unenhanced diffusion, CO2 remains inert as it moves through the boundary layer. However, CO2 may remain in the boundary layer long enough for hydration and hydroxylation reactions to occur, which causes the CO2 gradient to vary with depth in the boundary layer (fig. 1) (Portielje and Lijklema, 1995).

Figure 1. Idealized depiction of unenhanced (dashed line) versus chemically enhanced (solid line) CO2 flux through a stagnant boundary layer. Adapted from Portielje and Lijklema (1995) and Smith (1985).

The enhancement factor (EF), which represents the ratio of enhanced flux (Fe) to unenhanced flux (F) (eq. 1), can be used to quantify the increase in diffusion rate when chemical reactions occur in the boundary layer (Smith, 1985; Zeebe and Wolf-Gladrow, 2001). The enhancement factor is also expressed as a function of the reacto-diffusive length (ak) (eq. 2), which is a measure of the relative importance of diffusion and reaction (Zeebe and Wolf-Gladrow, 2001). For CO2 diffusion, the reacto-diffusive length is a function of the diffusivity of CO2 (DCO2), the CO2 hydration rate constant (k+), and the CO2 hydroxylation rate constant (k+4) (eq. 3). Increases in pH decrease the reacto-diffusive length (and consequently increase the enhancement factor) due to an increase in hydroxyl ion concentration, which encourages hydroxylation in the boundary layer. Overall, high pH facilitates more rapid absorption of atmospheric CO2, which provides more inorganic carbon for algal growth.




Inorganic Carbon-Limited Algal Growth

The stoichiometry and kinetics of inorganic carbon use by algae are important for quantifying the impacts of algal growth on carbon abatement. Based on the stoichiometric work of Redfield et al. (1963), who reported C:N:P ratios of marine phytoplankton in various oceanic regions to be relatively constant at 106:16:1, algal biomass is commonly formulated as (CH2O)106(NH3)16(H3PO4). Based on CO2 as the inorganic carbon source for photosynthesis (eq. 4), production of one mole of biomass consumes 106 moles of carbon and results in a theoretical biomass yield of 2.79 mg biomass mg-1 C. In addition, use of nitrate as a nitrogen source con-sumes 18 moles of protons as one mole of algal biomass is produced. However, many authors have cited that biomass nutrient ratios can vary widely depending on species (Burkhardt et al., 1999), nutrient availability (Clark, 2001; Geider and La Roche, 2002), and growth phase (Klausmeier et al., 2004).


While CO2 is certainly the substrate used directly by ribulose-1,5 bisphosphate (RuBisCO), the enzyme that catalyzes the first reaction in CO2 fixation (Cooper et al., 1969), the debate over whether other inorganic carbon species impact algal growth is long-standing. The earliest studies support that carbon dioxide is the limiting factor for algal biomass production (e.g., Osterhout and Haas, 1918). Other authors have since agreed with the hypothesis that CO2 is the rate-limiting inorganic carbon source, including King (1970) and Novak and Brune (1985), who showed a Monod response between CO2 and specific growth rate of several green algae. In contrast, Goldman et al. (1974) supported a Monod relationship between algal growth rate and total inorganic carbon (TIC) concentration. Even earlier, Felföldy (1960) concluded that growth of several species of Scenedesmus was impacted by HCO3- and CO32- concentrations. The debate over which inorganic carbon species are used by algal cultures can be expanded based on more recent information on carbon concentrating mechanisms.

Carbon concentrating mechanisms refer to processes that organisms employ in CO2-deficient environments to achieve intracellular CO2 concentrations higher than would exist by passive diffusion alone (Thielmann et al., 1990). Price and Badger (2002) stated that low CO2 concentration in natural waters occurs due to slow diffusion of CO2, incomplete equilibrium of waters with the atmosphere, and decreasing equilibrium CO2 concentrations with increasing pH. However, the dual carboxylase and oxygenase activities of RuBisCO necessitate that CO2 be present in high concentrations to prevent photorespiration (Colman et al., 2002). As a result, organisms rely on numerous types of carbon concentrating mechanisms to enhance carbon fixation.

It is hypothesized that all cyanobacteria and most eukaryotic algae employ some type of carbon concentrating mechanism. Carbon concentrating mechanisms may include an active CO2 pump, an active HCO3- pump, and/or an external carbonic anhydrase (CA) (Bhatti and Colman, 2008; Colman et al., 2002). Transport of HCO3-, specifically, requires ATP and is therefore energy demanding (Moroney and Somanchi, 1999). Cyanobacteria generally acquire CO2 and HCO3- from the bulk medium by diffusive and active transport, respectively. Some studies have further suggested transport of CO32- by cyanobacteria (Marcus, 1997; Marcus et al., 1992). Similarly, many green algae can actively transport both CO2 and HCO3- across the cell wall (Thielmann et al., 1990) (fig. 2).

Project Scope

Given the need for innovative strategies to mitigate CO2 emissions and the potential for enhanced CO2 absorption at high pH, the goal of this project was to investigate the growth and inorganic carbon utilization of a mixed freshwater algal culture at high pH. The objectives of the research were to: (1) quantify the impact of initial TIC on biomass growth, (2) determine pertinent stoichiometric and kinetic parameters describing inorganic carbon-limited algal growth, and (3) identify inorganic carbon species influencing algal growth. Ultimately, the results from this study will provide a quantitative foundation for modeling the impacts of high pH algal systems on carbon mitigation.

Figure 2. Model for Scenedesmus carbon concentrating mechanisms (CA = carbonic anhydrase, RUBP = RuBisCO, PGA = 3-phosphoglycerate). Adapted from Thielmann et al. (1990).

Materials and Methods

Four 1 L glass vessels (7.6 cm diameter and 23.2 cm height) were used to cultivate mixed freshwater algal cultures. The reactors were fitted with No. 8 stoppers that were fabricated to provide a sampling port and connection for tubing containing 12 g Ascarite II, which was used to allow the headspace pressure to equilibrate with the atmosphere without permitting carbon dioxide to enter reactors, per Novak and Brune (1985). The reactors were kept in a controlled-environment room maintained at 25°C (model G3, Climate Technologies, Inc., Farmington Hills, Mich.) on shelves with four 40 W cool white fluorescent bulbs (ACE F40 Universal DLX) positioned 20.3 cm above the initial liquid level in the reactors. Average illuminance in the controlled-environmental chamber was measured with an environmental quality meter (model 850070, Sper Scientific, Ltd., Scottsdale, Ariz.). Average photosynthetically active radiation (PAR) was calculated to be 26.4 W m-2 (121 µE m-2 s-1) per Sager and McFarlane (1997). All cultures were mixed using stir plates set at 300 rpm and large stir bars.

Freshwater algal inoculum was obtained from Lake Hartwell in Clemson, South Carolina, and cultured using a modified BG11 media (Conwell, 2005) with 14, 20, 26, or 32 mg C L-1 as Na2CO3 during trial 1 and 11, 17, 23, of 29 mg C L-1 as Na2CO3 during trial 2. Other media components included: 1500 mg L-1 NaNO3, 40 mg L-1 K2HPO4, 75 mg L-1 MgSO4·7H2O, 36 mg L-1 CaCl2·2H2O, 6 mg L-1 citric acid, 6 mg L-1 ferric ammonium citrate, 0.0010 mg L-1 EDTA, and

1.0 mL L-1 A5 trace metal mix (2860 mg L-1 H3BO3, 1800 mg L-1 MnCl2·4H2O, 220 mg L-1 ZnSO4·7H2O, 390 mg L-1 Na2MoO4·2H2O, 79 mg L-1 CuSO4·5H2O, and 49 mg L-1 Co(NO3)2·6H2O).

Precultures containing predominately Scenedesmus (as identified by Scott Davis of Clemson University) were prepared in 4 L reactors under the same environmental conditions as the test reactors. Precultures for the experimental trials were inoculated into the test reactors while in exponential growth phase. The same mass of algal cells was inoculated into each test reactor by centrifugation and dilution to equal optical density (OD) at 750 nm. Optical density was measured with a spectrophotometer (Spectronic 20D+, Thermo Scientific; Madison, Wisc.). Prior to the experiment, a uniform pH of 10.3 was established in all reactors using a small volume of 0.1 N NaOH or 0.1 N H2SO4. The initial pH of the media ranged from 9.6 to 10.4 prior to adjustment.

Analytical Methods

The pH and alkalinity were determined in duplicate daily. The pH was monitored using a sympHony Gel 3-in-1 pH electrode and sympHony pH meter (model SP70P, VWR, Radnor, Pa.). The pH electrode was calibrated using 4.01, 7.41, and 10.40 buffers before sampling. Alkalinity was monitored per Standard Method 2320 B (APHA, 1995) with 0.02 or 0.1 N H2SO4 as titrant. Total inorganic carbon and inorganic carbon species concentrations were calculated using pH and alkalinity data per Standard Methods (APHA, 1995) and Stumm and Morgan (1981).

Biomass concentration was quantified in duplicate on each sampling day, while biomass elemental content was determined at the end of batch growth for trial 1. Biomass concentration was monitored using optical density at 750 nm. Optical densities at 750 nm were converted to total suspended solids (TSS), as defined according to Standard Method 2540 D with 0.2 µm filters (APHA, 1995) using a standard curve: OD (at 750 nm) = 9.07 × 10-4 × TSS (mg L-1), R2 = 0.979. Elemental analysis of biomass was conducted using a combustion analyzer (Elementar Vario Macro, Mt. Laurel, N.J.) for carbon and nitrogen and inductively coupled mass spectrometry (ARCOS ICP, Spectro, Mahwah, N.J.) for phosphorous.

Kinetic Evaluation

Monod kinetic parameters (eq. 5) were determined to characterize inorganic carbon-limited algal growth, per Drapcho et al. (2008). Specific growth rate (µ) was determined as the slope of a linear regression fitted to a plot of the natural log of biomass versus time data for the exponential growth phase of the batch growth curve. Monod kinetic parameters (µmax, KS) considering TIC, CO2, HCO3-, and CO32- as limiting substrates were determined by completing nonlinear regression analyses using data from reactors that demonstrated increased specific growth rate with increased concentrations of inorganic carbon source. Observed biomass yield (YX/S) for each culture was determined as the slope of a linear regression relating biomass to TIC during exponential growth. Analysis of biomass yield was completed based on TIC, rather than individual carbonate species, since pH varied throughout experiments:


where µC is the specific growth rate using inorganic carbon species (C), C is the TIC, CO2, HCO3-, or CO32- concentration, and KS,C is the half-saturation constant for inorganic carbon species (C).

Calculating the Impact of pH and Algal Growth on Inorganic Carbon

Mass balances were used to estimate the impact of algal growth on inorganic carbon species concentrations. Overall, the measured change in an individual inorganic carbon species (?Measured) was due to changes caused by pH (?pH) and algal growth (?Growth) (eq. 6). The impact of pH was estimated by calculating the difference between what the inorganic carbon species would have been at the final pH if TIC had remained unchanged and the species concentration at the initial pH of 10.3 (eq. 7). Consequently, the change in inorganic carbon species due to algal growth was estimated by solving equation 6 for ?Growth. Since TIC is independent of pH, the measured change in TIC is due only to algal growth. As a result, the sum of ?Growth for all inorganic carbon species should be equal to the measured change in TIC.



where TICinitial is the initial TIC concentration, ai,final is the ionization fraction for species i at final pH, and ai,initial is the ionization fraction for species i at initial pH (i = 0 for CO2, 1 for HCO3-, and 2 for CO32-). Ionization fractions were defined and calculated per Stumm and Morgan (1981).

Statistical Analysis

All statistical analyses were performed using IBM SPSS Statistics 22. Spearman coefficients (?) were used to quantify correlations between initial TIC and various growth-related parameters. Nonlinear regression was used to estimate Monod kinetic parameters. A significance level (a) of 0.05 was used for all hypothesis testing in order to balance the probabilities of Type I and II errors (Rajamanickam, 2001). Significant relationships were identified as those exhibiting p-values less than 0.05.

Results and Discussion

Algal genus identification revealed that Scenedesmus was dominant in all reactors. However, changes in morphology were observed, with low inorganic carbon (11 and 14 mg C L-1) reactors containing mostly single cells and high inorganic carbon (29 and 32 mg C L-1) reactors containing four-cell clusters.

Typical batch growth responses were observed for all cultures (fig. 3). In general, peak biomass concentration increased with increasing initial TIC up to 29 mg L-1, with values ranging from 48.0 to 114.7 mg TSS L-1 (? = 0.929, p = 0.001). However, at 32 mg L-1 initial TIC, the peak biomass concentration decreased as compared to the 29 mg L-1 initial TIC culture. In addition, peak biomass concentrations were reached later (approx. 90 h) in the highest initial TIC reactors (29 to 32 mg C L-1) than in the other reactors (approx. 70 h). Both trends suggest some level of inhibition in the highest TIC reactors, perhaps due to pH (see discussion below).

Figure 3. Batch growth curves for algal cultures supplied with 11 to 32 mg C L-1.

Inorganic Carbon, pH, and Alkalinity

TIC declined in the reactors as carbon was consumed to form new algal biomass (fig. 4a). Final TIC (9.60 ±1.63 mg C L-1) did not vary based on initial TIC (? = 0.571, p = 0.139). Since there was substantial TIC remaining after peak biomass production, it is likely that some limiting condition existed within the reactors (see discussion of pH below). Indeed, other researchers have stated that “only a portion of the total inorganic carbon can be extracted during intense algal activity,” since complete conversion of CO32- to CO2 would cause the pH to increase near 14 (Goldman et al., 1974, p. 560).

Due to uptake of hydrogen ions by algal cells, pH increased over time in all closed reactors (fig. 4e). Peak pH, ranging from 10.8 to 11.4, generally increased with increasing initial TIC (? = 0.976, p = 0.001). Increased initial TIC led to increased biomass production (fig. 3), which caused increased utilization of protons (eq. 4) and ultimately an in-crease in pH. Final pH of above 11 was also observed by Felföldy (1960), who studied photosynthesis of numerous Scenedesmus strains supplied with 36 mg C L-1 as KHCO3.

Figure 4. (a) Total inorganic carbon, (b) carbon dioxide, (c) bicarbonate, (d) carbonate, (e) pH, and (f) alkalinity within freshwater algal batch reactors initially containing 11 to 32 mg C L-1.

The high pH reached in cultures with high initial TIC may have caused growth inhibition, since the optimum pH is 7.4 to 8.0 for Scenedesmus (Maraskolhe et al., 2012). However, a continuous-flow, mixed algal reactor supplied with natural freshwater as media to study carbon capture reached a pH of 10.3, which indicates that a high pH may be representative of some natural systems (Ramaraj et al., 2014). Systems may also reach high pH naturally during nitrate-dependent algal growth due to uptake of protons (eq. 4). In addition, use of external enzymes, such as carbon concentrating mechanisms to convert HCO3- to CO2 and OH-, is also known to alkalize the system (Shiraiwa et al., 1993). Consequently, the high pH observed in this study may also occur in some natural systems.

CO2 (fig. 4b) and HCO3- (fig. 4c) decreased in closed reactors, while trends in CO32- (fig. 4d) varied based on initial TIC concentration. Nearly all available CO2 and HCO3- were consumed during algal growth. Final CO2 concentrations generally decreased with increasing initial TIC and ranged between 4.25 × 10-6 and 5.54 × 10-5 mg C L-1 (? = -0.952, p = 0.001). Similarly, Novak and Brune (1985) reported the CO2 threshold (i.e., minimum CO2 concentration required for growth) to be 2.40 × 10-6 to 5.64 × 10-6 mg C L-1 between 21°C and 27°C. Within lower initial TIC reactors (11 to 20 mg C L-1), CO32- remained relatively constant, while within higher initial TIC reactors (23 to 32 mg C L-1), CO32- declined after 75 to 100 h.

Alkalinity remained constant, ranging from 81 to 218 mg CaCO3 L-1 (fig. 4f). In general, alkalinity was higher in reactors with higher initial TIC (? = 1.000, p = 0.001). The decrease in HCO3- and CO32- (figs. 4c and 4d), which would tend to decrease alkalinity, was somewhat balanced by consumption of H+ (fig. 4e) and subsequent increase in OH- (which contributes to alkalinity). King (1970) noted that increased consumption of inorganic carbon could cause production of OH- and subsequently little change in alkalinity. Utilization of NO3- as a nitrogen source (NaNO3 was provided in growth media) typically increases alkalinity (Brewer and Goldman, 1976); however, no increase in alkalinity was observed, likely due to relatively low peak biomass concentrations.

Stoichiometric and Kinetic Parameters

Biomass elemental composition was determined to characterize the stoichiometry of inorganic carbon-limited algal growth. Ranging from 19.1% to 25.7% on a mass basis, biomass carbon composition increased linearly with increasing initial TIC (fig. 5). Ranging from 3.67% to 4.49% on a mass basis, biomass nitrogen composition increased linearly with increasing initial TIC (fig. 5). Ranging from 6.54% to 8.96%, phosphorous concentration varied nonlinearly with initial TIC (fig. 5).

Similarities and differences were observed between stoichiometric relationships of carbon, nitrogen, and phosphorous and Redfield ratios (Redfield et al., 1963) (table 1). Notably, the phosphorous content of the algal biomass was quite high, which led to N:P ratios well below the Redfield benchmarks. Conversely, the C:N ratios were similar to the Redfield ratios (Redfield et al., 1963). Indeed, Klausmeier et al. (2004) suggested that biomass phosphorous content may be increased during exponential growth, as was the case in the current study. Furthermore, Geider and La Roche (2002) summarized that, under nutrient-rich conditions, the N:P ratios of biomass are often well below the Redfield ratio, while the C:N ratios tend to remain close to the Redfield ratio. Even still, Burkhardt et al. (1999) also reported that low CO2 conditions leads to wide variations in biomass elemental composition. Consequently, the stoichiometric relationships reported in the current study differ from the Redfield ratios (Redfield et al., 1963), likely due to exponential growth in a CO2-limited and otherwise nutrient-rich environment.

Figure 5. Biomass elemental composition for algal cultures supplied with 14 to 32 mg C L-1.
Table 1. Empirical formulas and C:N ratios for algal cultures supplied with 14 to 32 mg C L-1.
Initial TIC
(mg C L-1)
Biomass Empirical FormulaC:N
(mol C/
mol N)
(mg X
mg-1 C)

From linear regressions of biomass formed versus TIC utilized, the average observed biomass yield for the cultures was 6.62 ±1.45 mg TSS mg-1 TIC (table 2). No significant correlation was found between observed biomass yield and initial TIC (? = -0.405, p = 0.320). Similarly, Pipes (1962) and Goldman et al. (1974) reported biomass yield to be constant with varying inorganic carbon concentration. However, the average observed biomass yield was higher than calculated theoretical biomass yields (table 1), likely because TSS (used in determination of observed biomass yield) is an overestimate of actual biomass concentration (Grady et al., 1999).

In addition, the average observed yield was higher than reported in previous studies. Specifically, Goldman et al. (1974) reported an observed biomass yield of 2.24 mg biomass mg-1 TIC for Scenedesmus cultures supplied with 7.8 to 13.1 mg C L-1 (as a combination of NaHCO3 and Na2CO3). Perhaps the biomass yield in the current study is different from that of Goldman et al. (1974) due to differing culture conditions and resulting C:N:P ratios, as discussed above. For instance, Goldman et al. (1974) cultivated Scenedesmus in a continuous culture, while batch reactors were used in the current study. Indeed, Klausmeier et al. (2004) reported that growth phase (e.g., exponential versus stationary) altered biomass nutrient content, which could impact biomass yield. Specifically, accumulation of inorganic phosphorous-rich storage compounds within cells during exponential growth (Klausmeier et al., 2004) could increase the weight of biomass per the amount of inorganic carbon utilized, which would result in a higher biomass yield. In addition, the provided TIC differed between the current study and Goldman et al. (1974), which could also lead to varying biomass elemental compositions (Burkhardt et al., 1999) and subsequently biomass yields.

From linear regressions of biomass concentration versus time, specific growth rates were determined to range from 0.0220 to 0.0458 h-1 (table 2). A positive correlation was found between specific growth rate and initial TIC (? = 0.714, p = 0.047). However, in trial 1, there was no increase in specific growth rate when initial TIC was increased from 26 to 32 mg C L-1, perhaps due to high pH.

Table 2. Biomass yields and specific growth rates for freshwater algal cultures supplied with 11 to 32 mg C L-1.
Initial TIC
(mg C L-1)
mg TSS
mg-1 TIC
Trial 1145.130.7630.03260.943
Trial 2119.810.8440.02200.997

Nonlinear regression was used to estimate Monod kinetic parameters for all potential inorganic carbon substrates (CO2, HCO3-, CO32-, and TIC) (table 3). With an average of 0.0727 h-1, the maximum specific growth rate did not vary based on inorganic carbon source (or pH), as was also demonstrated by Goldman et al. (1974). However, half-saturation constants varied greatly based on inorganic carbon source, with the highest values for TIC and lowest values for CO2.

Table 4. Mass balances for inorganic carbon sources, considering overall depletion of TIC and inorganic carbon species (?Measured) to be due to pH (?pH) and algal growth (?Growth).
Initial TIC
(mg C L-1)
Carbon Dioxide
(× 10-4 mg C L-1)
(mg C L-1)
(mg C L-1)
Total Inorganic Carbon
(mg C L-1)
Trial 114-6.5-6.0-0.5-5.8-4.1-1.7-1.74.1-5.8-7.5-7.5
Trial 211-4.7-4.3-0.4-3.5-2.5-

Estimates of the Monod kinetic parameters are similar to those reported in previous studies, although some discrepancies exist due to differences in culture conditions. Bhatti and Coleman (2008) reported TIC half-saturation constants for a variety of eukaryotic algal species that ranged from 0.76 to 24.49 mg C L-1, with values generally increasing with increasing culture pH. Similarly, Goldman et al. (1974) reported TIC half-saturation constants to be 0.3 to 0.7 mg C L-1 for pH 7.05 to 7.59, with values increasing greatly with even small increases in pH. Indeed, the TIC half-saturation constant reported in the current study is near the high end of the Bhatti and Coleman (2008) range and well above the Goldman et al. (1974) range, which is expected given the high culture pH.

Similarities and differences between the current study and the literature were also observed for CO2 and HCO3- half-saturation constants. Chen and Durbin (1994) reported the CO2 half-saturation constant for two marine phytoplankton as 5.40 × 10-3 to 5.88 × 10-3 mg C L-1, although the pH range of the marine cultures was much lower (7.0 to 9.4) than the current study. Novak and Brune (1985) also reported the CO2 half-saturation constant for Scenedesmus to be somewhat higher (1.32 × 10-3 to 2.04 × 10-3 mg C L-1) than the current study, although the light availability was slightly lower (600 ft-candles) than in the current study (831 ft-candles). The HCO3- half-saturation constant for the two marine phytoplankton in the Chen and Durbin (1994) study was 11.99 to 25.75 mg C L-1, which is higher than the current study (6.84 mg L-1), perhaps due to differing culture conditions.

The estimated maximum specific growth rate was also similar to previous studies. Novak and Brune (1985) reported maximum specific growth rates for Scenedesmus of 0.046 to 0.057 h-1 between 21°C and 27°C, which is only slightly lower than the current study, perhaps due to differences in light availability. Even still, Spirulina grown under very high TIC conditions (600 mg C L-1) exhibited an average maximum specific growth rate of 0.071 h-1, which is very similar to the current study (Richmond et al., 1982). Phytoplankton cultivated under lower pH conditions exhibited higher maximum specific growth rates (0.141 to 0.283 h-1) than the current study, as expected (Chen and Durbin, 1994).

Table 3. Nonlinear estimation of Monod kinetic parameters for potential inorganic carbon substrates.
SubstrateTrial 1Trial 2Average
(mg C L-1)
(mg C L-1)
(mg C L-1)
CO20.07563.55 × 10-40.0110**0.07007.18 × 10-40.0065**0.07285.36 × 10-4

    [a]    Asterisks indicate statistical significance: * = p < 0.05, and ** = p < 0.01.

Figure 6. Total suspended solids, TIC, and inorganic carbon species in batch reactors supplied with (a) 17 and (b) 29 mg C L-1.

Relationship Between Algal Growth and Inorganic Carbon Species

As expected, concentrations of CO2 and HCO3- decreased as new algal biomass was formed (fig. 6). The decline in CO2 and HCO3- was not only due to algal growth because increasing pH would also tend to shift the inorganic carbon equilibrium toward CO32-. Increase in pH accounted for over 90% of the measured decline in CO2 and 70% to 89% of the meas-ured decline in HCO3-, depending on initial TIC (table 4). Algal growth, by extension, accounted for less than 10% of the measured decline in CO2 and 11% to 30% of the meas-ured decline in HCO3- (table 4). Overall, increase in pH was the primary factor impacting CO2 and HCO3- concentrations during batch growth.

Within higher initial TIC reactors, CO32- decreased, as would be expected for an inorganic carbon source (fig. 6a); however, concentrations remained relatively constant in lower initial TIC reactors (fig. 6b). In the absence of algal growth, as pH increases, CO32- would also be expected to increase. In fact, holding initial TIC constant and increasing the pH to final measured values would have caused an increase in CO32- of 2.5 to 12.3 mg C L-1, depending on initial TIC (table 4). To match trends of decreasing or constant CO32-, algal growth had to deplete 2.2 to 21.7 mg L-1, depending on initial TIC (table 4). Consequently, CO32- (in addition to CO2 and HCO3-) was substantially impacted by algal growth.

As biomass was formed, TIC decreased in all reactors (fig. 6). Unlike individual inorganic carbon species, changes in TIC were due only to algal growth, since TIC is not pH-dependent. Accordingly, the estimated changes in CO2, HCO3-, and CO32- due to algal growth were roughly equal to the measured TIC decline within each reactor. The percent of TIC utilized varied between 24% and 71% and generally decreased with increasing initial TIC. It is likely that higher pH in the higher initial TIC reactors contributed to use of a lower fraction of available TIC, since pH inhibition has been suggested or demonstrated by other authors (e.g., Chen and Durbin, 1994). In addition, as initial TIC increased, the CO32- fraction of consumed TIC increased, while the HCO3- fraction of consumed TIC decreased (fig. 7). Since more CO32- was available in higher initial TIC reactors (due to higher pH), it is reasonable that use of CO32- was higher than in lower initial TIC reactors.

Figure 7. CO2, HCO3-, and CO32- utilization (as a percentage of TIC used for algal growth) in batch reactors supplied with (a) 11, (b) 20, and (c) 32 mg C L-1.

While it is clear that TIC and all inorganic carbon species were depleted by algal growth, there are three potential scenarios for inorganic carbon species utilization. First, CO2 was used directly and replenished as equilibrium was re-established among inorganic carbon species (e.g., Novak and Brune, 1985). Second, both CO2 and HCO3- were used directly and replenished as equilibrium was re-established among inorganic carbon species (fig. 2) (e.g., Thielmann et al., 1990). Third, CO2, HCO3-, and CO32- were all used directly, and equilibrium was re-established based on pH and relative usage of each individual species (e.g., Marcus, 1997). While clear identification of the actual inorganic carbon source that crossed algal cell walls is beyond the scope of this kinetic study, the data can be used to make several observations.

The data reported above, as well as previous studies, support that CO2 was not the only inorganic carbon source directly used by algal cultures. Given that the pH was 10.3 or higher throughout the experiments, it is unlikely that the extremely low CO2 concentrations were able to sustain the documented biomass production. Even as early as 1960, Felföldy (1960) suggested that if culture pH rises above 9.0, then it is likely that CO2 is not the sole inorganic carbon source.

Consider the results from the 20 mg C L-1 reactor where there was substantial growth between 70 and 90 h, despite the fact that very little CO2 was present (fig. 6b). Although the specific growth rate between 70 and 90 h was 0.021 h-1 (29% of the maximum specific growth rate, 0.0727 h-1), there was only an average of 2.88 × 10-5 mg C L-1 as CO2 (KS,CO2 = 5.36 × 10-4 mg C L-1) and 1.7 mg C L-1 as HCO3- (KS,HCO3 = 6.84 mg C L-1) available. Given that the CO2 and HCO3- concentrations were too low to account for the observed growth rate, it is plausible that CO32- served as an additional inorganic carbon source. In fact, between 70 and 90 h, 12.4 mg C L-1 as CO32- (KS,CO3 = 10.44 mg L-1) was available. Under optimal environmental conditions, there was enough CO32- available to support growth at over one-half of the maximum specific growth rate. Given that the actual growth rate (0.021 h-1) was less than one-half of the maximum specific growth rate (0.037 h-1), it is likely that the high pH in the reactor inhibited full utilization of CO32-. Chen and Durbin (1994) also demonstrated decreased growth rates in high pH environments when CO2 and HCO3- concentrations were low. Nevertheless, it is likely that all three inorganic carbon species (i.e., TIC) contributed to growth of algal cultures, whether directly or indirectly, as was suggested by previous authors (e.g., Felföldy, 1960; Goldman et al., 1974).

Implications and Future Work

Ultimately, cultivation of algae has the potential to contribute to future carbon abatement plans. As algae grow, in natural or engineered systems, they utilize inorganic carbon from their aqueous environment. Depletion of inorganic carbon leads to diffusion of atmospheric CO2 into the system, a process that is accelerated at high pH. Conditions of high pH do not have to be induced. Rather, when algae use nitrate as a nitrogen source, the pH of the medium can naturally increase as protons are depleted from the medium (eq. 4). Indeed, the pH of natural systems rich with algae has been shown to be quite high (nearly 10.0), especially in summer months (Hansen, 2002). For engineered systems, an additional advantage of allowing high pH is natural control of protozoa and other organisms that may cause contamination (Touloupakis et al., 2016). Overall, future work entails developing a quantitative model for describing how algae use inorganic carbon at high pH to aid in understanding and design of carbon management strategies.

Modeling how algal cultures utilize and differentiate between each inorganic carbon species will be a significant challenge. Indeed, determining which species (CO2, HCO3-, and/or CO32-) are directly depleted by algal growth is a long-standing point of debate (e.g., Novak and Brune, 1985). A significant contribution of this work is the determination that the mixed culture composed primarily of Scenedesmus responded kinetically to all three inorganic carbon species, with estimates of maximum specific growth rate and half-saturation constants provided. Subsequently, future work will focus on how to model the utilization of multiple inorganic carbon species. For instance, are growth rates for each of the three potential inorganic carbon sources additive (µtotal,single) (eq. 8) (Keymer et al., 2014) or substitutable (µtotal,sub) (eq. 9) with CO2 as the preferred inorganic carbon source (Drapcho et al., 2008)?



An additional element of this work will include characterization and modeling of the algal culture in open systems. The closed algal growth model will be expanded to include enhanced diffusion of carbon dioxide at elevated pH. In addition, experimental work will be completed to quantify carbon abatement and provide data for model verification. Once completed, the dynamic algal growth model will facilitate understanding and optimization of carbon abatement strategies, especially those at high pH.


A study was completed to analyze the growth of mixed freshwater algal cultures supplied with 11 to 32 mg C L-1 as Na2CO3 at high pH (10.3 initially). Cultures composed of primarily Scenedesmus were maintained in a controlled environment and sampled daily for pH, alkalinity, inorganic carbon, and total suspended solids. A summary of the results is given below.

Conclusions from this work are as follows:

Ultimately, this study provides insights into the kinetics and stoichiometry of algal growth, specifically at high pH. While the debate surrounding which inorganic carbon species kinetically impacts algal growth is long-standing, no earlier work specifically addressed high experimental pH. Conditions of high pH are especially interesting because high pH is known to enhance abatement of atmospheric CO2. In natural aquatic systems, high pH (and enhanced diffusion of carbon dioxide) may exist in warm months when there is excess algal growth. In engineered systems, there may be some advantage to allowing pH to naturally drift upward for both contamination control and carbon dioxide abatement.

The kinetic and stoichiometric data presented and analyzed in this work can be used to develop a dynamic mathematical model to aid in design and better understanding of algal-based carbon abatement strategies. Specifically, modeling of the simple closed systems analyzed in the current work will allow more detailed analysis of the impact of CO2, HCO3-, and CO32- on algal growth. In turn, verified kinetic expressions capturing inorganic carbon-limited algal growth can serve as the basis for models of more complex carbon management systems with potentially significant impacts on the global carbon cycle. Overall, cultivation of algae for carbon capture and subsequent carbon abatement or sequestration is one potential component of a carbon management plan, especially when algae are grown in high pH systems that enhance the availability of atmospheric CO2 for biofixation.


Financial support for Dr. M. K. Watson was provided by a Stackhouse Fellowship awarded by the College of Agriculture, Forestry, and Life Sciences at Clemson University. The authors would also like to thank Scott Davis of the Clemson Aquaculture Center for algal species identification and Kathy Moore of the Agricultural Service Laboratory at Clemson University for analysis of biomass carbon, nitrogen, and phosphorous content.



APHA. (1995). Standard methods for the examination of water and wastewater. 19th Ed. Washington, DC: American Public Health Association.

Bhatti, S., & Colman, B. (2008). Inorganic carbon acquisition in some synurophyte algae. Physiol. Plant., 133(1), 33-40.

Biello, D. (2015). CO2 levels for February eclipsed prehistoric highs. Scientific American (5 March 2015). Retrieved from

Brewer, P. G., & Goldman, J. C. (1976). Alkalinity changes generated by phytoplankton growth. Limnol. Oceanogr., 21(1), 108-117.

Burkhardt, S., Zondervan, I., & Riebesell, U. (1999). Effect of CO2 concentration on C:N:P ratio in marine phytoplankton: A species comparison. Limnol. Oceanogr., 44(3), 683-690.

Chen, C. Y., & Durbin, E. G. (1994). Effects of pH on the growth and carbon uptake of marine phytoplankton. Mar. Ecol. Prog. Ser., 109, 83-94.

Clark, D. R. (2001). Growth rate relationships to physiological indices of nutrient status in marine diatoms. J. Phycol., 37(2), 249-256.

Colman, B., Huertas, I. E., Bhatti, S., & Dason, J. S. (2002). The diversity of inorganic carbon acquisition mechanisms in eukaryotic microalgae. Funct. Plant Biol., 29(3), 261-270.

Conwell, K. L. (2005). Green algal production of sulfoquinovosyl diacylglycerol under various light intensities. MS thesis. Clemson, SC: Clemson University.

Cooper, T. G., Filmer, D., Wishnick, M., & Lane, M. D. (1969). The active species of CO2 utilized by ribulose diphosphate carboxylase. J. Biol. Chem., 244(4), 1081-1083.

Dankwerts, P. V. (1970). Gas-liquid reactions. New York, NY: McGraw-Hill.

Drapcho, C. M., Nhuan, N. P., & Walker, T. H. (2008). Biofuels engineering process technology. New York, NY: McGraw-Hill.

EIA. (2008). International energy outlook. Washington, DC: U.S. Energy Information Association.

Emerson, S. (1975). Chemically enhanced CO2 gas exchange in a eutrophic lake: A general model. Limnol. Oceanogr., 20(5), 743-753.

Felföldy, L. J. M. (1960). Comparative studies on photosynthesis in different Scenedesmus strains. Acta Botanica Hungarica, 6(1-2), 1-13.

Figueroa, J. D., Fout, T., Plasynski, S., McIlvried, H., & Srivastava, R. D. (2008). Advances in CO2 capture technology: The U.S. Department of Energy’s carbon sequestration program. Intl. J. Greenhouse Gas Control, 2(1), 9-20.

Geider, R., & La Roche, J. (2002). Redfield revisited: Variability of C:N:P in marine microalgae and its biochemical basis. European J. Phycol., 37(1), 1-17.

Goldman, J. C., Oswald, W. J., & Jenkins, D. (1974). The kinetics of inorganic carbon-limited algal growth. J. Water Pollut. Control Fed., 46(3), 554-574.

Grady, C. P. L., Daigger, G. T., & Lim, H. C. (1999). Biological wastewater treatment. New York, NY: Marcel Dekker.

Hansen, P. J. (2002). Effect of high pH on the growth and survival of marine phytoplankton: Implications for species succession. Aquat. Microb. Ecol., 28(3), 279-288.

House, W. A., Howard, J. R., & Skirrow, G. (1984). Kinetics of carbon dioxide transfer across the air/water interface. Faraday Disc. Chem. Soc., 77, 33-46.

Keymer, P. C., Lant, P. A., & Pratt, S. (2014). Modelling microalgal activity as a function of inorganic carbon concentration: accounting for the impact of pH on the bicarbonate system. J. Appl. Phycol., 26(3), 1343-1350.

King, D. L. (1970). The role of carbon in eutrophication. J. Water Pollut. Control Fed., 42(12), 2035-2051.

Klausmeier, C. A., Litchman, E., Daufresne, T., & Levin, S. A. (2004). Optimal nitrogen-to-phosphorus stoichiometry of phytoplankton. Nature, 429(6988), 171-174.

Kumar, K., Dasgupta, C. N., Nayak, B., Lindblad, P., & Das, D. (2011). Development of suitable photobioreactors for CO2 sequestration addressing global warming using green algae and cyanobacteria. Bioresour. Tech., 102(8), 4945-4953.

Maraskolhe, V. R., Warghat, A. R., & Charan, G. (2012). Carbon sequestration potential of Scenedesmus species (microalgae) under the fresh water ecosystem. African J. Agric. Res., 7(18), 2818-2823.

Marcus, Y. (1997). Distribution of inorganic carbon among its component species in cyanobacteria: Do cyanobacteria in fact actively accumulate inorganic carbon? J. Theor. Biol., 185(1), 31-45.

Marcus, Y., Berry, J. A., & Pierce, J. (1992). Photosynthesis and photorespiration in a mutant of the cyanobacterium Synechocystis PCC 6803 lacking carboxysomes. Planta, 187(4), 511-516.

Meehl, G. A., Washington, W. M., Collins, W. D., Arblaster, J. M., Hu, A., Buja, L. E., ... Teng, H. (2005). How much more global warming and sea level rise? Science, 307(5716), 1769-1772.

Moroney, J. V., & Somanchi, A. (1999). How do algae concentrate CO2 to increase the efficiency of photosynthetic carbon fixation? Plant Physiol., 119(1), 9-16.

Nedbal, L., Cervenż, J., Keren, N., & Kaplan, A. (2010). Experimental validation of a nonequilibrium model of CO2 fluxes between gas, liquid medium, and algae in a flat-panel photobioreactor. J. Ind. Microbiol. Biotech., 37(12), 1319-1326.

Novak, J. T., & Brune, D. E. (1985). Inorganic carbon-limited growth kinetics of some freshwater algae. Water Res., 19(2), 215-225.

Ono, E., & Cuello, J. L. (2006). Feasibility assessment of microalgal carbon dioxide sequestration technology with photobioreactor and solar collector. Biosyst. Eng., 95(4), 597-606.

Osterhout, W. J. V., & Haas, A. R. (1918). On the dynamics of photosynthesis. J. Gen. Physiol., 1(1), 1-16.

Pipes, W. O. (1962). Carbon dioxide-limited growth of Chlorella in continuous culture. Appl. Microbiol., 10(4), 281-288.

Portielje, R., & Lijklema, L. (1995). Carbon dioxide fluxes across the air-water interface and its impact on carbon availability in aquatic systems. Limnol. Oceanogr., 40(4), 690-699.

Price, G. D., & Badger, M. R. (2002). Advances in understanding how aquatic photosynthetic organisms utilize sources of dissolved inorganic carbon for CO2 fixation. Funct. Plant Biol., 29(3), 117-121.

Rajamanickam, M. (2001). Statistical methods in psychological and educational research. New Delhi, India: Concept Publishing.

Ramaraj, R., Tsai, D. D.-W., & Chen, P. H. (2014). Freshwater microalgae niche of air carbon dioxide mitigation. Ecol. Eng., 68, 47-52.

Redfield, A. C., Ketchum, B. H., & Richards, F. A. (1963). The influence of organisms on the composition of sea-water. In The sea, volume 2: The composition of seawater: Comparative and descriptive oceanography, (pp. 26-77). Cambridge, MA: Harvard University Press.

Reichle, D., Houghton, J., Kane, B., & Ekmann, J. (1999). Carbon sequestration research and development. Oak Ridge, TN: Oak Ridge National Laboratory.

Richmond, A., Karg, S., & Boussiba, S. (1982). Effects of bicarbonate and carbon dioxide on the competition between Chlorella vulgaris and Spirulina platensis. Plant Cell Physiol., 23(8), 1411-1417.

Sager, J. C., & McFarlane, J. C. (1997). Radiation. In R. W. Langhans, & T. W. Tibbits (Eds.), Plant growth chamber handbook (pp. 1-29). Ames, IA: Iowa Agricuture and Home Economics Experiment Station.

Sayre, R. (2010). Microalgae: The potential for carbon capture. BioScience, 60(9), 722-727.

Shiraiwa, Y., Goyal, A., & Tolbert, N. E. (1993). Alkalization of the medium by unicellular green algae during uptake of dissolved inorganic carbon. Plant Cell Physiol., 34(5), 649-657.

Smith, S. V. (1985). Physical, chemical, and biological characteristics of CO2 gas flux across the air-water interface. Plant Cell Environ., 8(6), 387-398.

Stumm, W., & Morgan, J. J. (1981). Aquatic chemistry: An introduction emphasizing chemical equilibria in natural waters. Hoboken, NJ: John Wiley & Sons.

Thielmann, J., Tolbert, N. E., Goyal, A., & Senger, H. (1990). Two systems for concentrating CO2 and bicarbonate during photosynthesis by Scenedesmus. Plant Physiol., 92(3), 622-629.

Touloupakis, E., Cicchi, B., Benavides, A. M. S., & Torzillo, G. (2016). Effect of high pH on growth of Synechocystis sp. PCC 6803 cultures and their contamination by golden algae (Poterioochromonas sp.). Appl. Microbiol. Biotech., 100(3), 1333-1341.

Wang, B., Li, Y., Wu, N., & Lan, C. Q. (2008). CO2 bio-mitigation using microalgae. Appl. Microbiol. Biotech., 79(5), 707-718.

Whitman, W. G. (1962). The two-film theory of gas absorption. Intl. J. Heat Mass Transfer, 5(5), 429-433.

Zeebe, R. E., & Wolf-Gladrow, D. A. (2001). CO2 in seawater: Equilibrium, kinetics, isotopes. Elsevier Oceanography Series Vol. 65. Amsterdam, The Netherlands: Elsevier.