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Laurent Pilon, Mechanical and Aerospace Engineering Department, Henry Samueli School of Engineering and Applied Science, University of California Los Angeles, Los Angeles, CA 90095, USA. E-mail: firstname.lastname@example.org
Aims: The objective of this study is to develop kinetic models based on batch experiments describing the growth, CO2 consumption, and H2 production of Anabaena variabilis ATCC 29413-UTM as functions of irradiance and CO2 concentration.
Methods and Results: A parametric experimental study is performed for irradiances from 1120 to 16100 lux and for initial CO2 mole fractions from 0·03 to 0·20 in argon at pH 7·0 ± 0·4 with nitrate in the medium. Kinetic models are successfully developed based on the Monod model and on a novel scaling analysis employing the CO2 consumption half-time as the time scale.
Conclusions: Monod models predict the growth, CO2 consumption and O2 production within 30%. Moreover, the CO2 consumption half-time is an appropriate time scale for analysing all experimental data. In addition, the optimum initial CO2 mole fraction is 0·05 for maximum growth and CO2 consumption rates. Finally, the saturation irradiance is determined to be 5170 lux for CO2 consumption and growth whereas, the maximum H2 production rate occurs around 10 000 lux.
Significance and Impact of the Study: The study presents kinetic models predicting the growth, CO2 consumption and H2 production of A. variabilis. The experimental and scaling analysis methods can be generalized to other micro-organisms.
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Increased amounts of greenhouse gas emissions as well as the exhaustion of easily accessible fossil fuel resources are calling for effective CO2 mitigation technologies and clean and renewable energy sources. Hydrogen, for use in fuel cells, is considered to be an attractive alternative fuel since water vapour is the only byproduct from its reaction with oxygen. Hydrogen production by cultivation of cyanobacteria in photobioreactors offers a clean and renewable alternative to thermochemical or electrolytic hydrogen production technologies with the added advantage of CO2 mitigation. In particular, Anabaena variabilis is a cyanobacterium capable of mitigating CO2 and producing H2. The objective of this study is to investigate experimentally the CO2 mitigation, growth, and H2 production of A. variabilis ATCC 29413-UTM in BG-11 medium under atmosphere containing argon and CO2. Parameters investigated are the irradiance and the initial CO2 mole fraction in the gas phase.
Table 1 summarizes previous studies on H2 production by A. variabilis. It indicates the strain used, the gas phase composition, irradiance and the medium used during growth and H2 production stages, as well as the specific growth, CO2 consumption, and H2 production rates. Briefly, Tsygankov et al. (1998) and Sveshnikov et al. (1997) studied the hydrogen production by A. variabilis ATCC 29413 and by its mutant PK84, lacking the hydrogen uptake metabolism. On the other hand, Markov et al. (1993) proposed a two stage photobioreactor alternating between (i) growth and (ii) H2 production phases for attaining high H2 production rates. During the growth phase cyanobacteria fix CO2 and nitrogen from the atmosphere to grow and produce photosynthates. In the H2 production phase, they utilize the photosynthates to produce H2. In addition, Yoon et al. (2002) used a two stage batch process and suggested an improvement on the first stage by incorporating nitrate in the growth medium for faster growth of A. variabilis. As opposed to using a two stage photobioreactor, Markov et al. (1997b) demonstrated a single stage photobioreactor using A. variabilis PK-84 in a helical photobioreactor. More recently, Tsygankov et al. (2002) demonstrated a single stage photobioreactor operation for H2 production using A. variabilis PK-84 in an outdoor photobioreactor similar to that of Markov et al. (1997b).
Table 1. Summary of experimental conditions used and associated maximum specific growth, CO2 consumption and H2 production rates reported in the literature using various strains of Anabaena variabilis
Most previous studies using A. variabilis have used a two stage photobioreactor with relatively limited ranges of CO2 concentrations and light irradiance. In addition, to the best of our knowledge, there has been no reported study simultaneously varying irradiance and the initial CO2 mole fraction in the gas phase to assess quantitatively the CO2 mitigation, growth, and H2 production of A. variabilis in a single stage process. The objectives of this work are (i) to develop kinetic models based on batch experiments describing the growth, CO2 consumption and H2 production of A. variabilis ATCC 29413-UTM as functions of irradiance and CO2 concentration and (ii) to provide recommendations on the optimum irradiance and the gas phase CO2 mole fraction for achieving rapid growth, high CO2 uptake and H2 production rates.
Materials and methods
A cyanobacterial suspension was prepared from a 7-day-old culture. The micro-organism concentration denoted by X was adjusted to 0·02 kg dry cell m−3 by diluting the culture with fresh medium and was confirmed by monitoring the optical density (OD). Then, 60 ml of the prepared suspension was dispensed in 160-ml serum vials. The vials were sealed with butyl rubber septa, crimped and flushed through the septa with industrial grade argon, sterilized with 0·2 μm pore size syringe filter, for 10 min with a needle submerged in the liquid phase. The initial CO2 mole fraction in the head-space, denoted by xCO2,g,o, was set at 0·03, 0·04, 0·08, 0·15 and 0·20. This was achieved first by adjusting the gauge pressure in the vials to −7·09, −10·13, −20·27, −30·40 and −40·53 kPa respectively. Then, 7, 10, 20, 30 and 40 ml of industrial grade CO2 were injected into the vials, respectively, through a 0·2 μm pore size syringe filter. The vials were shaken until the head-space pressure stabilized indicating that both the partitioning of CO2 between the gas and liquid phases and the dissolution of CO2 in water were at equilibrium. Finally, the head-space was sampled to measure the initial CO2 mole fraction. Each vial was prepared in duplicates. The vials were placed horizontally on an orbital shaker (model ZD-9556 by Madell Technology Group, Orange County, CA, USA) and stirred continuously at 115 rev min−1 throughout the duration of the experiments. Continuous illumination was provided from the top of the orbital shaker. The transparent glass vials could be approximated to a cylindrical tube of diameter 50 mm, of height 80 mm, and of wall thickness 2 mm. The illuminated surface area of each vial was 40 × 10−4 m2. The irradiance, defined as the total radiant flux of visible light from 400 to 700 nm incident on a vial from the hemisphere above it, ranged from 1120 to 16 100 lux. Note that for the lamps used in the experiments 1 lux of irradiance was equivalent to 3 × 10−3 W m−2 and 14 × 10−3μmol m−2 s−1 in the PAR.
Throughout the experiments CO2, H2 and O2 concentrations in the head-space as well as the cyanobacteria concentration and pH in the liquid phase were continually monitored. In addition, the temperature and pressure of the vials were measured to convert the molar fractions of gas species into volumetric mass concentrations. The irradiance incident on individual vials was recorded. Details of the experimental setup and procedures are given in the following sections.
Cyanobacteria culture and concentration measurements
Anabaena variabilis ATCC 29413-UTM was purchased from the American Type Culture Collection (ATCC) and received in freeze dried form. The culture was activated with 10 ml of sterilized milli-Q water. It was cultivated and transferred weekly in ATCC medium 616 with air-CO2 mixture in the head-space with an initial mole fraction of CO2 of 0·05. One litre of ATCC medium 616 contained 1·5 g NaNO3, 0·04 g K2HPO4, 0·075 g MgSO4· 7H2O, 0·036 g CaCl2· 2H2O, 6·0 mg citric acid, 6·0 mg ferric ammonium citrate, 0·02 g Na2CO3, 1·0 mg EDTA and 1·0 ml of trace metal mix A5. One litre of trace metal mix A5 contains 2·86 g H3BO3, 1·81 g MnCl2· 4H2O, 0·222 g ZnSO4· 7H2O, 0·39 g Na2MoO4·2H2O, 0·079 g CuSO4· 5H2O, 49·4 mg Co(NO3)3·6H2O. The pH of the medium was adjusted to be 7·3 by adding 1 mol l−1 HCl and/or 1 mol l−1 NaOH. Then, 20 ml of HEPES buffer solution at pH 7·3 was added to one litre of medium. Finally, the medium was autoclaved at 121°C for 40 min.
The cyanobacteria concentration X was determined by sampling 1 ml of bacteria suspension from the vials and measuring the OD. A calibration curve was created by measuring both the dry cell weight of a cyanobacteria suspension and the corresponding OD. First, the OD of the cyanobacteria was measured in disposable polystyrene cuvettes with light path of 10 mm at 683 nm (Yoon et al. 2002) using a UV-Vis spectrophotometer (Cary-3E; Varian, Palo Alto, CA, USA). Then, the bacteria suspension was filtered through mixed cellulose filter membranes with 0·45 μm pore size (HAWP-04700; Millipore, Billerica, MA, USA) and dried at 85°C over night. The dried filters were weighed immediately after being taken out of the oven on a precision balance (model AT261; Delta Range Factory, USA) with a precision of 0·01 mg. The calibration curve for OD was generated by using 14 different bacteria concentrations ranging from 0·04 to 0·32 kg dry cell m−3. The relation between OD and bacteria concentration is linear for the OD range from 0 to 1·2 and 1 unit of OD corresponds to 0·274 kg dry cell m3.
Temperature, pressure and pH
The temperature of the vials was measured with a thermocouple (Dual Thermometer; Fisher Scientific, Houston, TX, USA). The heat from the high intensity fluorescent bulbs was removed by convective cooling using a fan to maintain a steady-state temperature of 24 ± 1°C throughout the duration of the experiments. The head-space pressure was monitored with a digital gauge pressure sensor (model PX26-005GV; Omega Engineering Inc., Stanford, CT) connected to a digital meter (model DP25B-S by Omega Heater Company). Finally, the pH of the medium was measured with a digital pH probe (model Basic AB Plus; Fisher Scientific).
Lighting and light analysis
The irradiance incident on the vials Gin was provided by fluorescent light bulbs (Ecologic by Sylvania, USA and Fluorex by Lights of America, USA) and varied by changing the number of bulbs. The spectral irradiance of these bulbs was measured with a spectrophotometer (model USB2000, Ocean Optics, Dunedin, FL) connected to a cosine collector over the spectral range from 350 to 750 nm. The spectral irradiance of the light bulbs G, normalized with its maximum value Gmax at 540 nm, along with the reported cyanobacterial absorption coefficient κ (Merzlyak and Naqvi 2000), normalized with its maximum value κmax, are presented in Fig. 1. The irradiance incident on the vials was measured with both a light meter (Fisherbrand Tracable Meter by Fisher Scientific) and a quantum sensor (LI-COR, Model LI-190SL; LI-COR Inc., Lincoln, NE, USA). The total irradiance on each vial was measured individually in the PAR, i.e. within the spectral range from 400 to 700 nm. Due to experimental difficulties in achieving the exact same irradiance for all vials, five different irradiance ranges were explored namely, 1120–1265, 1680–2430, 3950–4600, 7000–8700 and 14 700–16 100 lux.
The gas analysis was carried out every 24 h by sampling 500 μl of head-space volume of the vials. The concentrations of CO2, H2 and O2 in the head-space were measured with a gas chromatographer (HP-5890; Hewlett Packard, Palo Alto, CA) equipped with a packed column (Carboxen-1000; Supelco, Bellefonte, PA, USA) and a thermal conductivity detector (TCD). The gas chromatographer output was processed with an integrator (HP-3395, Hewlett Packard). Throughout the gas analysis, the injector and detector temperatures were maintained at 120°C. During the H2 and O2, analysis argon was used as the carrier gas and the oven temperature was maintained at 35°C. The retention times for H2 and O2 were found to be 2·1 and 7·5 min respectively. On the other hand, during the CO2 analysis, Helium was used as the carrier gas and the oven temperature was maintained at 255°C. The retention time for CO2 was then 4·9 min. Calibration curves for the TCD response were prepared at seven different known gas concentrations from 16 × 10−6 to 3·2 × 10−3 kg m3 for H2, from 25·6 × 10−3 to 1314 × 10−3 kg m3 for O2 and from 3·96 × 10−3 to 352 × 10−3 kg m3 for CO2. All calibration curves were linear within these gas concentration ranges. During the experiments, peak heights were recorded and correlated with the corresponding moles of gas using the respective calibration curves.
The experimental parameters used in the study along with the experimental labels are summarized in Table 2. In brief, the initial CO2 mole fraction in the head-space, xCO2,g,o, varied from 0·03 to 0·20 while the irradiance G varies from 1120 to 16 100 lux. Pressure, temperature and pH were maintained at 1 ± 0·1 atm., 24 ± 1°C and 7·0 ± 0·4, respectively. To develop semi-empirical models for CO2 consumption, growth, H2 and O2 production by A. variabilis ATCC 29413 using the experimental data, the following assumptions are made:
Table 2. Summary of the parameters used in the experiments
YX/CO2 (kg kg−1)
ψCO2 (kg kg−1 h−1)
1The concentration of gases in each phase and the concentration of cyanobacteria in the liquid phase are uniform within a given vial, due to vigorous mixing provided by the orbital shaker.
2The Damkohler number, defined as the ratio of the reaction rate to the mass transfer rate (Smith et al. 1998), associated with the experimental setup is on the order of 10−4. Therefore, metabolic reactions of the cyanobacteria are not mass transfer limited (Smith et al. 1998).
3The gas species in the liquid and gas phases are at quasi-equilibrium at all times.
4A. variabilis both consumes and produces CO2, O2 and H2. Therefore, the reported gas phase concentration of species correspond to the net consumed or produced quantities.
5The only parameters affecting the bacterial growth and product formation are the CO2 concentration and the irradiance G. The supply of other nutrients such as minerals and nitrate are assumed to be unlimited in the growth medium.
6Given the pH range, the effect of buffer capacity on the growth rate is assumed to be negligible compared with the effects of CO2 concentration and local irradiance.
7The death of micro-organisms is neglected within the time frame of the experiments.
During the growth phase, the time rate of change of micro-organism concentration X can be written as (Dunn et al. 2003),
where μ is the specific growth rate of the cyanobacteria expressed in s−1. In this study, it is assumed to be a function of (i) the average available irradiance denoted by Gav and (ii) the concentration of total dissolved inorganic carbon within the cyanobacterial suspension denoted by CTOT. The specific growth rate has been modelled using the Monod model taking into account (i) light saturation; (ii) CO2 saturation; and (iii) CO2 inhibition as (Asenjo and Merchuk 1995):
where μmax is the maximum specific growth rate, KG is the half-saturation constant for light, KC and KI are the half-saturation and the inhibition constants for dissolved inorganic carbon respectively. First, the spectral and local irradiance G(z) within the suspension is estimated using Beer–Lambert's law as:
where Gλ,in is the spectral irradiance incident on the vials, z is the distance from the top surface of the suspension, X is the micro-organism concentration in kg dry cell m−3, Eext,λ is the spectral extinction cross-section of A. variabilis at wavelength λ. Note that Eext,λ varies by <4% over the PAR and is assumed to be constant and equal to Eext,PAR = 350 m2 kg−1 dry cell (Berberoğlu and Pilon 2007). Then, the available irradiance Gav can be estimated by averaging the local irradiance over the depth of the culture L as:
Experimentally L is equal to 0·02 m.
Finally, CTOT is the total dissolved inorganic carbon concentration in the liquid phase expressed in kmol m−3. It depends on the pH of the medium and on the molar fraction of CO2 in the gas phase xCO2,g and can be written as (Benjamin 2002):
where the three terms on the right hand side correspond to , , and CO concentrations in the liquid phase respectively.
The values of the parameters μmax, KG, KC, and KI in eqn (2) are estimated by minimizing the root mean square error between the experimentally measured cyanobacteria concentrations and the model predictions obtained by integrating eqns (1) and (2). The associated parameters along with those reported by Erickson et al. (1987) for the cyanobacteria Spirulina platensis are summarized in Table 3. Figure 2a compares the cyanobacteria concentrations measured experimentally with the model predictions. It indicates that the model predicts the experimental data for micro-organism concentration within 30%.
Table 3. Summary of the parameters used in kinetic modeling of Anabaena variabilis
Moreover, assuming that the biomass yield based on consumed carbon and denoted by YX/C is constant, as assumed by Erickson et al. (1987), the total dissolved inorganic carbon concentration can be modelled as (Dunn et al. 2003):
The yield YX/C can be expressed in terms of the biomass yield based on consumed CO2 denoted by YX/CO2 as YX/C =MCO2YX/CO2 where MCO2 is the molecular weight of CO2 equal to 44 kg kmol−1. The value of YX/CO2 for each experiment is given in Table 2. The value of YX/C used in this study is the average value obtained across experiments which is equal to 24·96 kg dry cell kmol−1 C. Figure 2b compares CTOT obtained using eqn (5) and the measured pH and xCO2,g with the value predicted by integrating eqn (6). It shows that the model predicts the experimental data within 30%.
Furthermore, assuming that one mole of O2 is evolved per mole of CO2 consumed, the total oxygen concentration in the vial can be computed as,
where YO2/X is the O2 yield based on biomass and equal to 1·28 kg O2 kg−1 dry cell. It is expressed as MO2/YX/C where MO2 is the molecular weight of O2 equal to 32 kg kmol−1. Figure 2c compares the total O2 concentration measured experimentally with that predicted by integrating eqn (7). It indicates that the experimental data for CO2 falls within 30% of model's predictions.
Finally, models similar to eqns (6) and (7) were applied to the H2 concentration in the headspace measured as a function of time. However, yield coefficients could not be obtained to model the experimental data within 30%.
The models described in the previous section depend on quantities such as Gav and CTOT that are not directly measurable. They are typically kept constant by using either a chemostat (Erickson et al. 1987) or a turbidostat (Goldman et al. 1974). However, construction and operation of these devices are relatively expensive and experimentally more challenging than the vial experiments performed in this study. Moreover, a number of assumptions had to be made to estimate the parameters of the kinetic models. Specifically, Gav was estimated using Beer-Lambert's law which does not take into account in-scattering by the micro-organisms and can lead to errors as high as 30% in estimating the local irradiance G(z) (Berberoğlu et al. 2007). Moreover, the growth rates of the micro-organisms were assumed to be independent of pH which varied between 7·0 ± 0·4 during the course of the experiments. Furthermore, the average yields YX/C and YO2/X were assumed to be constant in modeling the CO2 consumption and O2 production. Finally, modeling H2 production with the approach above gave poor results. Therefore, as an alternative to the kinetic models described above, a novel scaling analysis is presented for analysing the data based on the directly measurable initial molar fraction xCO2,g,o and incident irradiance Gin while Gav and CTOT are allowed to vary with time.
Figure 3a shows the evolution of the CO2 molar fraction xCO2,g in the head-space as a function of time t, normalized with the initial CO2 mole fraction xCO2,g,o for different combinations of the total incident irradiance Gin and xCO2,g,o. It indicates that xCO2,g decreases monotonically with increasing time. First, the half-time, denoted by t1/2, is defined as the time required for the CO2 mole fraction in the gas phase to decrease to half of its initial value. Normalizing the time by the half-time and plotting the dimensionless variables xCO2,g/xCO2,g,ovst/t1/2, collapses all the data points to a single line as shown in Fig. 3b. This indicates that the CO2 consumption half time is an appropriate time scale for comparing CO2 consumption under different conditions. Performing a linear regression analysis of the data yields:
with a correlation coefficient R2=0·94. Equation (8) also indicates that xCO2,g vanishes at time t=1·8t1/2.
Moreover, the half-time t1/2 is a function of both the initial CO2 mole fraction and the irradiance Gin. Figure 4a shows t1/2 as a function of xCO2,g,o for different values of Gin. It indicates that t1/2 increases linearly with xCO2,g,o for a given Gin, i.e. t1/2=β(Gin)xCO2,g,o, where the slope β(Gin) is expressed in hours and plotted in Fig. 4b. Two regimes can be identified. In the first regime, β(Gin) decreases linearly with Gin according to β(Gin)=1900−0·3Gin. In the second regime, β(Gin) does not vary appreciably with Gin and has the approximate value of 350 h. Figure 4b indicates that transition between the two regimes occurs around Gin=5170 lux. Therefore, the half-time t1/2 can be expressed as:
Alternatively, the relationship between β and Gin can be approximated with an exponential decay function as .
Furthermore, Fig. 5a compares the values of experimentally determined t1/2 with those predicted by eqn (9). With the exception of one outlier, all the experimentally determined half-times lie within ±20 h of the predictions by eqn (9). The experimental values of t1/2 and td are summarized in Table 2 for each test.
In addition, Fig. 5b shows the medium pH as a function of the dimensionless time t/t1/2 for all runs. It shows that the medium pH increases as the CO2 is consumed by the micro-organisms. It also indicates that the pH changes also scale well with the time scale t1/2.
Figure 6a, b show the normalized concentration of A. variabilis, X/Xo, vs time t for all irradiances and for xCO2, g,o = 0·08 and 0·15 respectively. The initial cyanobacteria concentration Xo is equal to 0·02 kg dry cell m−3 in all cases. Figure 6 establishes that for a given xCO2,g,o, increasing the irradiance increases the growth rate of A. variabilis. Moreover, for a given irradiance Gin within the values tested, decreasing the initial CO2 mole fraction increases the growth rate. Thus, the effects of Gin and xCO2,g,o on cyanobacterial growth seem to be coupled.
Here also, scaling the time with the half-time t1/2 collapses the growth curves for different irradiances onto a single line as shown in Fig. 6c, d for xCO2,g,o = 0·08 and 0·15 respectively. Therefore, the half-time t1/2 correctly captures the time scale of the biological processes for CO2 consumption and bacterial growth. In addition, the cyanobacterial growth is exponential and the cyanobacteria concentration X(t) at time t can be expressed as:
where α is a constant depending on xCO2,g,o and determined experimentally. Figure 7 shows its evolution as a function of xCO2,g,o varying between 0·03 and 0·20. The relationship can be expressed as:
with a correlation coefficient R2 = 0·93. Note that the evolution of X(t) as a function of the irradiance Gin and xCO2,g,o is accounted for through the half-time t1/2 given by eqn (9).
Moreover, the average specific growth rate, denoted by μavg, is the arithmetic mean of the specific growth rates, denoted by μΔt and determined in the time interval Δt during the exponential growth phase of A. variabilis according to (Yoon et al. 2002):
where Xavg,Δt is the arithmetic mean of the cyanobacteria concentration during that time interval Δt. The values of μavg computed for all parameters are summarized in Table 2. Figure 8a presents the variation of the average specific growth rate of A. variabilis denoted by μavg and expressed in h−1, as a function of xCO2,g,o for all irradiances. The error bars indicate the standard error that is the ratio of the standard deviation to the square root of the number of samples.
Furthermore, the average specific CO2 uptake rate, denoted by ψCO2 and expressed in kg kg−1 dry cell h−1, is computed using the same method as that used by Yoon et al. (2002):
where YX/CO2 is the biomass yield based on consumed CO2 expressed in kg dry cell kg−1 of CO2. It is computed as the ratio of the final mass of cyanobacteria produced to the total mass of CO2 injected into the vials. The values of ψCO2 computed for all parameters are also summarized in Table 2. Figure 8b shows the variation of ψCO2 as a function of xCO2,g,o for all irradiances.
Hydrogen and oxygen productions
Figure 9a shows the concentration of hydrogen measured in the head-space as a function of the dimensionless time t/t1/2 for all runs. It indicates that the maximum hydrogen concentration is achieved at high irradiance. Moreover, the concentration of hydrogen accumulated in the head-space normalized with its maximum value CH2,g,max as a function of dimensionless time t/t1/2 for irradiance larger than 7000 lux is shown in Fig. 9b. It establishes that CH2,g/CH2,g,max varies exponentially with t/t1/2 and can be expressed as:
Similarly, Fig. 10a, b show the oxygen concentration and the normalized oxygen concentration with its maximum value, respectively, as functions of the dimensionless time t/t1/2 for all runs. Figure 10(b) indicates that the normalized oxygen concentration varies exponentially with t/t1/2 according to:
To use eqns (14) and (15) to determine the evolution of oxygen and hydrogen concentrations, the maximum concentrations CO2,g,max and CH2,g,max must be expressed in terms of the initial CO2 mole fraction xCO2,g,o and irradiance G. Figure 11 shows that CO2,g,max is independent of irradiance and varies linearly with xCO2,g,o according to:
with a correlation coefficient R2=0·94. This demonstrates that the oxygen yield of A. variabilis, i.e. the mass of O2 produced per mass of CO2 consumed, was constant for the parameters explored.
Figure 12a shows CH2,g,max as a function of both irradiance and of the initial CO2 mole fraction. It indicates that within the parameter ranges explored, the optimum irradiance for maximum H2 production was around 10 000 lux. Figure 12b shows CH2,g,max as a function of xCO2,g,o for irradiances larger than 7000 lux for which H2 production is the largest. It indicates that CH2,g,max increases with increasing xCO2,g,o. As a first order approximation, the relationship between CH2,g,max and xCO2,g,o can be written as:
with a correlation coefficient R2 of 0·75.
Kinetic models describing the cyanobacterial growth, carbon uptake, and O2 production depend on the specific growth rate μ which is a function of the instantaneous available irradiance Gav and total dissolved inorganic carbon concentration CTOT. In an earlier study, Badger and Andrews (1982) suggested that both H2CO and HCO can act as substrate for cyanobacteria. Furthermore, Goldman et al. (1974) used CTOT given by eqn (5) in the Monod model to successfully predict algal growth in carbon limited conditions for pH between 7·05 and 7·61. More recently, Erickson et al. (1987) modelled the growth rate of the cyanobacteria S. platensis under light and inorganic carbon limited conditions using the Monod model. Table 3 indicates that the parameters they reported for S. platensis agree well with those obtained in the present study for A. variabilis. Note that Erickson et al. (1987) expressed the Monod model only in terms of HCO concentration as opposed to CTOT. However, it is equivalent to using CTOT as the pH was kept constant and equal to 9·2. Then, the ratio of HCO to H concentrations is about 800 while CO concentration is negligibly small. In other words, at pH 9·2, CTOT is approximately equal to the HCO concentration. In the present study, the pH varies from 6·6 to 7·4 and the ratio of HCO to H concentration varies between 2 and 12. Therefore, both species need to be accounted for in computing CTOT to be used in eqn (2). Furthermore, the aforementioned studies did not account for the inhibitory effect of dissolved inorganic carbon (i.e. KI = ∞) as the concentration of inorganic carbon was low, CTOT <0·67 × 10−3 kmol C m−3. However, in the present study, the inorganic carbon concentration reached up to CTOT < 20 × 10−3 kmol C m−3 and ignoring the carbon inhibition effects in eqn (2) resulted in poor model predictions. The values of the retrieved parameters μmax, KG, and KC agree with those reported by Erickson et al. (1987) and are valid for low carbon concentrations. In addition, the inhibitory effect of large inorganic carbon concentration is successfully accounted for by the modified Monod model through the parameter KI.
Moreover, due to the fact that CO2 consumption and O2 production are mainly growth related processes, their evolution has been successfully modelled using the specific growth rates. On the other hand, H2 evolution is a much more complex process. It depends on the active enzyme concentration, the O2 concentration in the medium, the irradiance, as well as the growth rate. Therefore, simple models similar to eqns (6) or (7) could not model all data within ±30%.
Furthermore, these models assume that the irradiance within the culture and the concentration of the dissolved inorganic carbon are known while they cannot be measured directly. Consequently, in the second part of this paper a new analysis for CO2 consumption, cyanobacterial growth, as well as hydrogen and oxygen productions as functions of t1/2 has been developed. Experimental data indicates that t1/2 is a relevant time scale for CO2 consumption, growth, H2 and O2 production. The simplicity of this analysis resides in the fact that it depends on directly measurable and controllable quantities. Furthermore, it can be used to determine the light saturation of photosynthesis as shown in Fig. 4. However, the applicability of this scaling analysis is limited to systems having (i) the same initial cyanobacteria concentration and (ii) similar pH.
Moreover, Fig. 8a establishes that an optimum xCO2,g,o around 0·05 exists for maximum average specific growth rate for all irradiances. Moreover, it shows that the average specific growth rate increases with increasing irradiance. Yoon et al. (2002) reported that for experiments conducted at 30°C with xCO2,g,o around 0·11 the average specific growth rate decreased from 0·054 to 0·046 h−1 for A. variabilis as the irradiance increased from 3500 to 7000 lux. In the present study at 24°C with initial CO2 mole fraction of 0·11, μavg increased from 0·028 to 0·038 h−1 for the same increase in irradiance. The observed discrepancy between the results reported in this study and those reported by Yoon et al. (2002) can be attributed to the combination of the differences in pH and in temperature.
Furthermore, Fig. 8b shows that the average specific CO2 uptake rate exhibits similar trends to those of the average specific growth rate with an optimum xCO2,g,o around 0·05 for maximum ψCO2. Yoon et al. (2002) reported an average specific CO2 uptake rate ψCO2 of about 0·130 kg CO2 kg−1 dry cell h−1 for xCO2,g,o around 0·05 and irradiance around 4000 lux, whereas, in the present study, it was only 0·060 kg CO2 kg−1 dry cell h−1 under the same irradiance and xCO2,g,o. The difference can be attributed to the fact that the experiments of the present study were conducted at 24°C instead of 30°C (Yoon et al. 2002). It is apparent that increasing the temperature enhances the CO2 uptake metabolism of A. variabilis as confirmed by Tsygankov et al. (1999). Note that due to experimental difficulties in capturing fast CO2 consumption rate with the available equipment and procedure, no experiments were conducted for initial CO2 mole fraction less than 0·08 at irradiances higher than 5000 lux.
Figures 9 and 10 show that H2 and O2 concentrations in the headspace increases exponentially during the growth phase. Due to the presence of nitrate in the medium (initially about 20 mmol l−1), the nitrogenase activity is expected to be low (Madamwar et al. 2000). Moreover, H2 production using the nitrogenase enzyme is not expected to stop when the growth stops or slows down such as during two stage H2 production (Yoon et al. 2002). However, increased concentration of evolved O2 could have inhibited H2 production. In addition, the initial anaerobic conditions promotes the bidirectional hydrogenase activity. Therefore, the observed H2 production during the experiments is expected to be due to the bidirectional hydrogenase activity. Furthermore, the decrease in the H2 concentration for t/t1/2 > 1·5 can be attributed to consumption of the produced H2 due to the presence of uptake hydrogenase (Tsygankov et al. 1998). However, unlike hydrogen, the oxygen concentration does not decrease appreciably beyond the exponential growth phase. Finally, CH2,g and CO2,g reach their maximum at dimensionless time t/t1/2 equal to 1·37 and 1·55, respectively, and shortly before the CO2 concentration vanishes at t/t1/2 equal to 1·8. Note that the reported values of CO2, O2, and H2 values correspond to the net produced or consumed quantities as it is difficult to experimentally distinguish the contribution of each phenomenon. In particular, CO2 is being consumed during photosynthesis and being produced during respiration and possibly during H2 production, provided H2 production is catalyzed by nitrogenase (Das and Veziroglu 2001). Similarly, O2 is being produced during photosynthesis and consumed during respiration.
Figures 11 and 12 show the maximum O2 and H2 concentrations attained in the headspace as functions of xCO2,g,o for different irradiances. Unlike for CO2,g,max, it is difficult to establish a simple and reliable relationship between CH2,g,max and the parameters G and xCO2,g,o due to the complexity of the hydrogen metabolism of A. variabilis. This complexity arises because (i) the hydrogen production is a strong function of both the irradiance G and the initial CO2 concentration (Markov et al. 1997a) and (ii) the produced hydrogen is being consumed back by the micro-organisms at a rate comparable to the production rate of hydrogen (Tsygankov et al. 1998). Tsygankov et al. (1998) reported that the wild strain A. variabilis ATCC 29413 did not produce any hydrogen in the presence of CO2 in the atmosphere. In contrast, the present study indicates that hydrogen production by the wild strain is possible under argon and CO2 atmosphere albeit at a lower production rate. Indeed, the maximum hydrogen production observed in our experiments was 0·3 mmol kg−1 dry cell h−1 whereas reported rates for wild A. variabilis strains range from 5·58 mmol kg−1 dry cell h−1 in dark fermentation (Shah et al. 2001), 165 mmol kg−1 dry cell h−1 in a multi stage photobioreactor (Yoon et al. 2006), and to 720 mmol kg−1 dry cell h−1 under nutritional stress (Sveshnikov et al. 1997). The low hydrogen production rates observed in the present study are attributed to (i) CO2 fixation and H2 production processes competing for the reductants generated from water splitting (Prince and Kheshgi 2005); (ii) the presence of nitrate in the medium (Shah et al. 2001); and (iii) the consumption of the produced H2 by the wild strain A. variabilis at high dissolved O2 concentrations (Tsygankov et al. 1998).
A parametric experimental study has been performed to assess the CO2 consumption, growth, H2 and O2 productions of the cyanobacteria A. variabilis ATCC 29413-UTM in batch experiment. The main parameters are the irradiance and the initial CO2 mole fraction in the head-space. The micro-organisms were grown in atmosphere containing argon and CO2, at a pH of 7·0 ± 0·4 with nitrate in the medium. A new scaling analysis for CO2 consumption, growth, and H2 and O2 production is presented. Under the conditions presented in this study, the following conclusions can be drawn for A. variabilis,
1Kinetic equations based on the Monod model are used to model the growth, carbon uptake, and O2 production by A. variabilis taking into account (i) light saturation; (ii) CO2 saturation; and (iii) CO2 inhibition. The parameters obtained agree well with values reported for other cyanobacteria (Erickson et al. 1987) at low inorganic carbon concentrations and expands the model to large concentrations when growth inhibition occurs. The experimental data falls within 30% of the model predictions. However, similar approach could not predict experimental data for H2 production rate.
2The CO2 consumption half-time, defined as the time when the CO2 mole fraction in the gas phase decreases to half of its initial value, is a relevant time scale for CO2 consumption, growth, H2 and O2 production. It depends on the total irradiance incident on the vials and the initial CO2 mole fraction.
3The scaling analysis facilitates the determination of the saturation irradiance which is found to be 5170 lux.
4For maximum specific CO2 consumption and specific growth rates, the optimum initial CO2 mole fraction in the gas phase is about 0·05 for any irradiance between 1000 and 16 000 lux.
5Optimum irradiance for maximum H2 production has been found to be around 10 000 lux despite the low overall H2 production rates.
6Neither the CO2 consumption nor the growth rate was inhibited by irradiance up to about 16 000 lux.
Finally, the kinetic equations can be used in simulations for optimizing the operating conditions of a photobioreactor for rapid growth and maximum CO2 mitigation. Moreover, it is expected that the above experimental and scaling analysis method can be used for analyzing other CO2 mitigating and H2 producing micro-organisms.
The authors gratefully acknowledge the support of the California Energy Commission through the Energy Innovation Small Grant (EISG 53723A/03-29; Project Manager: Michelle McGraw). They are indebted to Chu Ching Lin, Edward Ruth, Jong Hyun Yoon, and Dr James C. Liao for their helpful discussions and exchanges of information.
volumetric mass concentration, kg m−3
molar concentration of total dissolved inorganic carbon, kmol m−3