### Abstract

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

**Aims: ** The objective of this study is to develop kinetic models based on batch experiments describing the growth, CO_{2} consumption, and H_{2} production of *Anabaena variabilis* ATCC 29413-U^{TM} as functions of irradiance and CO_{2} concentration.

**Methods and Results: ** A parametric experimental study is performed for irradiances from 1120 to 16100 lux and for initial CO_{2} 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 CO_{2} consumption half-time as the time scale.

**Conclusions: ** Monod models predict the growth, CO_{2} consumption and O_{2} production within 30%. Moreover, the CO_{2} consumption half-time is an appropriate time scale for analysing all experimental data. In addition, the optimum initial CO_{2} mole fraction is 0·05 for maximum growth and CO_{2} consumption rates. Finally, the saturation irradiance is determined to be 5170 lux for CO_{2} consumption and growth whereas, the maximum H_{2} production rate occurs around 10 000 lux.

**Significance and Impact of the Study: ** The study presents kinetic models predicting the growth, CO_{2} consumption and H_{2} production of *A. variabilis*. The experimental and scaling analysis methods can be generalized to other micro-organisms.

### Introduction

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

Increased amounts of greenhouse gas emissions as well as the exhaustion of easily accessible fossil fuel resources are calling for effective CO_{2} 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 CO_{2} mitigation. In particular, *Anabaena variabilis* is a cyanobacterium capable of mitigating CO_{2} and producing H_{2}. The objective of this study is to investigate experimentally the CO_{2} mitigation, growth, and H_{2} production of *A. variabilis* ATCC 29413-U^{TM} in BG-11 medium under atmosphere containing argon and CO_{2}. Parameters investigated are the irradiance and the initial CO_{2} mole fraction in the gas phase.

The cyanobacterium *A. variabilis* is a photosynthetic prokaryote listed among the potential candidates for hydrogen production (Pinto *et al.* 2002), whose genome sequence has been completed (Joint Genome Institute 2007). Moreover, *A. variabilis* and its mutants are of great interest in research as hydrogen producers (Hansel and Lindblad 1998; Tsygankov *et al.* 1998; Borodin *et al.* 2000; Happe *et al.* 2000; Pinto *et al.* 2002; Yoon *et al.* 2002). *Anabaena variabilis* utilizes light energy in the spectral range from 400 to 700 nm, known as photosynthetically active radiation (PAR), and consumes CO_{2} to produce biomass, oxygen and hydrogen. The reader is referred to Refs. (Benemann 2000; Madamwar *et al.* 2000; Das and Veziroglu 2001; Pinto *et al.* 2002; Prince and Kheshgi 2005) for detailed reviews of photobiological hydrogen production. In brief, *A. variabilis* utilizes water as its electron donor (Prince and Kheshgi 2005) and produces hydrogen mainly using nitrogenase enzyme (Madamwar *et al*., 2000). The primary role of nitrogenase is to reduce nitrogen to ammonia during nitrogen fixation (Das and Veziroglu 2001). H_{2} is produced as a by product of this reaction (Das and Veziroglu 2001). In the absence of molecular nitrogen, nitrogenase will reduce protons and catalyze the production of H_{2} provided reductants and ATP are present (Das and Veziroglu 2001). Nitrogenase enzyme is located in special cells called heterocysts, which protect nitrogenase from O_{2} inhibition (Tsygankov *et al.* 1998). However, at dissolved O_{2} concentrations higher than 50 *μ*mol l^{−1}, the produced H_{2} is consumed by *A. variabilis* in a reaction catalyzed by the enzyme ‘uptake’ hydrogenase (Tsygankov *et al.* 1998), thus reducing the net H_{2} production rate (Tsygankov *et al.* 1998). Finally, *A. variabilis* also possesses bi-directional hydrogenases located at the cytoplasmic membrane (Madamwar *et al.* 2000). However, unlike nitrogenase, these enzymes are not well protected from oxygen and their functioning is inhibited at relatively low O_{2} concentrations (Benemann 2000).

Table 1 summarizes previous studies on H_{2} production by *A. variabilis*. It indicates the strain used, the gas phase composition, irradiance and the medium used during growth and H_{2} production stages, as well as the specific growth, CO_{2} consumption, and H_{2} 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) H_{2} production phases for attaining high H_{2} production rates. During the growth phase cyanobacteria fix CO_{2} and nitrogen from the atmosphere to grow and produce photosynthates. In the H_{2} production phase, they utilize the photosynthates to produce H_{2}. 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 H_{2} 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, CO_{2} consumption and H_{2} production rates reported in the literature using various strains of *Anabaena variabilis**A. variabilis strain* | Stage I | Stage II | Maximum reported rates | References |
---|

Gas phase | Medium | Irradiance (lux) | Gas phase | Medium | Irradiance (lux) | *μ* (h^{−1}) | *ψ*_{CO2} (mmol/kg dry cell/h) | *π*_{H2} (mmol/kg dry cell/h) |
---|

Kutzing 1403/4B | 95 vol.% air + 5 vol.% CO_{2} | Allen and Arnon w/o nitrate at 25°C | 1800 | 300 mm Hg vacuum | Same as stage I | 13 000 | N/A | 7000 | 830 | (Markov *et al.* 1995) |

ATCC 29413 | 89 vol.% air + 11 vol.% CO_{2} | BG-11_{o} + 3·5 mmol l^{−1} NaNO_{3} at 30°C | 2500–5500 | Argon | BG-11_{o} w/o nitrate at 30°C | 9000–12 000 | 0·05 | 2700 | 80 | (Yoon *et al.* 2002) |

ATCC 29413 | 98 vol.% air + 2 vol.% CO_{2} | Allen and Arnon w/o nitrate molybdenum replaced w/vanadium at 30°C | 8000 | Argon | Same as stage I | 10 000–14 000 | N/A | N/A | 630 | (Tsygankov *et al.* 1998) |

PK 84 | 98 vol.% air + 2 vol.% CO_{2} | Allen and Arnon w/o nitrate molybdenum replaced w/vanadium at 30°C | 8000 | Argon | Same as stage I | 10 000–14 000 | N/A | N/A | 515 | (Tsygankov *et al.* 1998) |

ATCC 29413 | 73 vol.% Ar + 25 vol.% N_{2} + 2 vol.% CO_{2} | Allen and Arnon w/o nitrate molybdenum replaced w/vanadium at 30°C | 6500 | 93 vol.% Ar + 5 vol.% N_{2} + 2 vol.% CO_{2} | Same as stage I | 6500 | N/A | N/A | 720·37 | (Sveshnikov *et al.* 1997) |

PK 84 | 73 vol.% Ar + 25 vol.% N_{2} + 2 vol.% CO_{2} | Allen and Arnon w/o nitrate molybdenum replaced w/vanadium at 30°C | 6500 | 93 vol.% Ar + 5 vol.% N_{2} + 2 vol.% CO_{2} | Same as stage I | 6500 | N/A | N/A | 2600 | (Sveshnikov *et al.* 1997) |

PK 84 | 98 vol.% air + 2 vol.% CO_{2} | Allen and Arnon w/o nitrate molybdenum replaced w/vanadium at 30°C | outdoor | 98 vol.% Air + 2 vol.% CO_{2} | Same as stage I | Outdoor | 0·03 | N/A | 300 | (Tsygankov *et al.* 2002) |

Most previous studies using *A. variabilis* have used a two stage photobioreactor with relatively limited ranges of CO_{2} concentrations and light irradiance. In addition, to the best of our knowledge, there has been no reported study simultaneously varying irradiance and the initial CO_{2} mole fraction in the gas phase to assess quantitatively the CO_{2} mitigation, growth, and H_{2} 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, CO_{2} consumption and H_{2} production of *A. variabilis* ATCC 29413-U^{TM} as functions of irradiance and CO_{2} concentration and (ii) to provide recommendations on the optimum irradiance and the gas phase CO_{2} mole fraction for achieving rapid growth, high CO_{2} uptake and H_{2} production rates.

### Materials and methods

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

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 *μ*m pore size syringe filter, for 10 min with a needle submerged in the liquid phase. The initial CO_{2} mole fraction in the head-space, denoted by *x*_{CO2,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 CO_{2} were injected into the vials, respectively, through a 0·2 *μ*m pore size syringe filter. The vials were shaken until the head-space pressure stabilized indicating that both the partitioning of CO_{2} between the gas and liquid phases and the dissolution of CO_{2} in water were at equilibrium. Finally, the head-space was sampled to measure the initial CO_{2} 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} m^{2}. 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^{−3} *μ*mol m^{−2} s^{−1} in the PAR.

Throughout the experiments CO_{2}, H_{2} and O_{2} 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-U^{TM} 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-CO_{2} mixture in the head-space with an initial mole fraction of CO_{2} of 0·05. One litre of ATCC medium 616 contained 1·5 g NaNO_{3}, 0·04 g K_{2}HPO_{4}, 0·075 g MgSO_{4}· 7H_{2}O, 0·036 g CaCl_{2}· 2H_{2}O, 6·0 mg citric acid, 6·0 mg ferric ammonium citrate, 0·02 g Na_{2}CO_{3}, 1·0 mg EDTA and 1·0 ml of trace metal mix A5. One litre of trace metal mix A5 contains 2·86 g H_{3}BO_{3}, 1·81 g MnCl_{2}· 4H_{2}O, 0·222 g ZnSO_{4}· 7H_{2}O, 0·39 g Na_{2}MoO_{4}·2H_{2}O, 0·079 g CuSO_{4}· 5H_{2}O, 49·4 mg Co(NO_{3})_{3}·6H_{2}O. 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 *μ*m 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 m^{3}.

#### 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 *G*_{in} 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 *G*_{max} at 540 nm, along with the reported cyanobacterial absorption coefficient *κ* (Merzlyak and Naqvi 2000), normalized with its maximum value *κ*_{max}, 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.

#### Gas analysis

The gas analysis was carried out every 24 h by sampling 500 *μ*l of head-space volume of the vials. The concentrations of CO_{2}, H_{2} and O_{2} 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 H_{2} and O_{2}, analysis argon was used as the carrier gas and the oven temperature was maintained at 35°C. The retention times for H_{2} and O_{2} were found to be 2·1 and 7·5 min respectively. On the other hand, during the CO_{2} analysis, Helium was used as the carrier gas and the oven temperature was maintained at 255°C. The retention time for CO_{2} 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 m^{3} for H_{2}, from 25·6 × 10^{−3} to 1314 × 10^{−3} kg m^{3} for O_{2} and from 3·96 × 10^{−3} to 352 × 10^{−3} kg m^{3} for CO_{2}. 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.

### Results

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

The experimental parameters used in the study along with the experimental labels are summarized in Table 2. In brief, the initial CO_{2} mole fraction in the head-space, *x*_{CO2,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 CO_{2} consumption, growth, H_{2} and O_{2} 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 Label | G (lux) | *x*_{CO2,g,o} | *t*_{1/2} (h) | *μ*_{avg} (h^{−1}) | *Y*_{X/CO2} (kg kg^{−1}) | *ψ*_{CO2} (kg kg^{−1} h^{−1}) |
---|

0GH | 7000 | 0·20 | 74·4 | 0·024 | 0·373 | 0·065 |

0IJ | 14 700 | 0·20 | 65·3 | 0·028 | 0·352 | 0·081 |

1AB | 1120 | 0·15 | 232·8 | 0·009 | 0·451 | 0·020 |

1CD | 1680 | 0·15 | 189·3 | 0·013 | 0·589 | 0·023 |

1EF | 3950 | 0·15 | 82·3 | 0·024 | 0·465 | 0·051 |

1GH | 8700 | 0·15 | 49·5 | 0·033 | 0·398 | 0·082 |

1IJ | 16 100 | 0·15 | 46·8 | 0·036 | 0·381 | 0·094 |

2AB | 1175 | 0·08 | 120·6 | 0·013 | 0·555 | 0·024 |

2CD | 1820 | 0·08 | 98·4 | 0·016 | 0·626 | 0·026 |

2EF | 4300 | 0·08 | 53·2 | 0·027 | 0·489 | 0·055 |

2GH | 8000 | 0·08 | 37·1 | 0·038 | 0·440 | 0·086 |

2IJ | 16 100 | 0·08 | 39·1 | 0·041 | 0·433 | 0·094 |

3AB | 1195 | 0·04 | 71·4 | 0·018 | 0·685 | 0·026 |

3CD | 1815 | 0·04 | 57·3 | 0·022 | 0·755 | 0·030 |

3EF | 4190 | 0·04 | 32·0 | 0·037 | 0·629 | 0·059 |

4AB | 1265 | 0·03 | 64·9 | 0·017 | 0·840 | 0·020 |

4CD | 2430 | 0·03 | 73·8 | 0·023 | 0·859 | 0·026 |

4EF | 4600 | 0·03 | 27·3 | 0·029 | 0·748 | 0·038 |

- 1
The 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.

- 2
The 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).

- 3
The gas species in the liquid and gas phases are at quasi-equilibrium at all times.

- 4
*A. variabilis* both consumes and produces CO_{2}, O_{2} and H_{2}. Therefore, the reported gas phase concentration of species correspond to the net consumed or produced quantities.

- 5
The only parameters affecting the bacterial growth and product formation are the CO_{2} concentration and the irradiance *G*. The supply of other nutrients such as minerals and nitrate are assumed to be unlimited in the growth medium.

- 6
Given the pH range, the effect of buffer capacity on the growth rate is assumed to be negligible compared with the effects of CO_{2} concentration and local irradiance.

- 7
The death of micro-organisms is neglected within the time frame of the experiments.

#### Kinetic modelling

During the growth phase, the time rate of change of micro-organism concentration *X* can be written as (Dunn *et al.* 2003),

- (1)

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 *G*_{av} and (ii) the concentration of total dissolved inorganic carbon within the cyanobacterial suspension denoted by *C*_{TOT}. The specific growth rate has been modelled using the Monod model taking into account (i) light saturation; (ii) CO_{2} saturation; and (iii) CO_{2} inhibition as (Asenjo and Merchuk 1995):

- (2)

where *μ*_{max} is the maximum specific growth rate, *K*_{G} is the half-saturation constant for light, *K*_{C} and *K*_{I} 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:

- (3)

where *G*_{λ,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}, *E*_{ext,λ} is the spectral extinction cross-section of *A. variabilis* at wavelength *λ*. Note that *E*_{ext,λ} varies by <4% over the PAR and is assumed to be constant and equal to *E*_{ext,PAR} = 350 m^{2} kg^{−1} dry cell (Berberoğlu and Pilon 2007). Then, the available irradiance *G*_{av} can be estimated by averaging the local irradiance over the depth of the culture *L* as:

- (4)

Experimentally *L* is equal to 0·02 m.

The values of the parameters *μ*_{max}, *K*_{G}, *K*_{C}, and *K*_{I} 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*Parameter | Present study | Erickson *et al.* (1987) | Equation |
---|

*μ*_{max} (1 h^{−1}) | 0·10 | 0·12 | Eqn (2) |

*K*_{G} (lux) | 4440 | 4351 | Eqn (2) |

*K*_{C} (kmol C m^{−3}) | 0·0002 | 0·0002 | Eqn (2) |

*K*_{I} (kmol C m^{−3}) | 0·0182 | N/A | Eqn (2) |

*Y*_{X/C} (kg dry cell kmol^{−1} C) | 24·96 | 25·18 | Eqn (6) |

*Y*_{O2/X} (kg O_{2} kg^{−1} dry cell) | 1·28 | N/A | Eqn (7) |

Moreover, assuming that the biomass yield based on consumed carbon and denoted by *Y*_{X/C} is constant, as assumed by Erickson *et al.* (1987), the total dissolved inorganic carbon concentration can be modelled as (Dunn *et al.* 2003):

- (6)

The yield *Y*_{X/C} can be expressed in terms of the biomass yield based on consumed CO_{2} denoted by *Y*_{X/CO2} as *Y*_{X/C} =*M*_{CO2}*Y*_{X/CO2} where *M*_{CO2} is the molecular weight of CO_{2} equal to 44 kg kmol^{−1}. The value of *Y*_{X/CO2} for each experiment is given in Table 2. The value of *Y*_{X/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 *C*_{TOT} obtained using eqn (5) and the measured pH and *x*_{CO2,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 O_{2} is evolved per mole of CO_{2} consumed, the total oxygen concentration in the vial can be computed as,

- (7)

where *Y*_{O2/X} is the O_{2} yield based on biomass and equal to 1·28 kg O_{2} kg^{−1} dry cell. It is expressed as *M*_{O2}/*Y*_{X/C} where *M*_{O2} is the molecular weight of O_{2} equal to 32 kg kmol^{−1}. Figure 2c compares the total O_{2} concentration measured experimentally with that predicted by integrating eqn (7). It indicates that the experimental data for *C*_{O2} falls within 30% of model's predictions.

Finally, models similar to eqns (6) and (7) were applied to the H_{2} concentration in the headspace measured as a function of time. However, yield coefficients could not be obtained to model the experimental data within 30%.

#### Scaling analysis

The models described in the previous section depend on quantities such as *G*_{av} and *C*_{TOT} 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, *G*_{av} 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 *Y*_{X/C} and *Y*_{O2/X} were assumed to be constant in modeling the CO_{2} consumption and O_{2} production. Finally, modeling H_{2} 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 *x*_{CO2,g,o} and incident irradiance *G*_{in} while *G*_{av} and *C*_{TOT} are allowed to vary with time.

##### CO_{2} consumption

Figure 3a shows the evolution of the CO_{2} molar fraction *x*_{CO2,g} in the head-space as a function of time *t*, normalized with the initial CO_{2} mole fraction *x*_{CO2,g,o} for different combinations of the total incident irradiance *G*_{in} and *x*_{CO2,g,o}. It indicates that *x*_{CO2,g} decreases monotonically with increasing time. First, the half-time, denoted by *t*_{1/2}, is defined as the time required for the CO_{2} 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 *x*_{CO2,g}/*x*_{CO2,g,o}*vs**t*/*t*_{1/2}, collapses all the data points to a single line as shown in Fig. 3b. This indicates that the CO_{2} consumption half time is an appropriate time scale for comparing CO_{2} consumption under different conditions. Performing a linear regression analysis of the data yields:

- (8)

with a correlation coefficient *R*^{2}=0·94. Equation (8) also indicates that *x*_{CO2,g} vanishes at time *t*=1·8*t*_{1/2}.

Moreover, the half-time *t*_{1/2} is a function of both the initial CO_{2} mole fraction and the irradiance *G*_{in}. Figure 4a shows *t*_{1/2} as a function of *x*_{CO2,g,o} for different values of *G*_{in}. It indicates that *t*_{1/2} increases linearly with *x*_{CO2,g,o} for a given *G*_{in}, i.e. *t*_{1/2}=*β*(*G*_{in})x_{CO2,g,o}, where the slope *β*(*G*_{in}) is expressed in hours and plotted in Fig. 4b. Two regimes can be identified. In the first regime, *β*(*G*_{in}) decreases linearly with *G*_{in} according to *β*(*G*_{in})=1900−0·3*G*_{in}. In the second regime, *β*(*G*_{in}) does not vary appreciably with *G*_{in} and has the approximate value of 350 h. Figure 4b indicates that transition between the two regimes occurs around *G*_{in}=5170 lux. Therefore, the half-time *t*_{1/2} can be expressed as:

- (9)

Alternatively, the relationship between *β* and *G*_{in} can be approximated with an exponential decay function as .

Furthermore, Fig. 5a compares the values of experimentally determined *t*_{1/2} 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 *t*_{1/2} and *t*_{d} are summarized in Table 2 for each test.

In addition, Fig. 5b shows the medium pH as a function of the dimensionless time *t*/*t*_{1/2} for all runs. It shows that the medium pH increases as the CO_{2} is consumed by the micro-organisms. It also indicates that the pH changes also scale well with the time scale *t*_{1/2}.

##### Cyanobacterial growth

Figure 6a, b show the normalized concentration of *A. variabilis*, *X*/*X*_{o}, *vs* time *t* for all irradiances and for *x*_{CO2, g,o} = 0·08 and 0·15 respectively. The initial cyanobacteria concentration *X*_{o} is equal to 0·02 kg dry cell m^{−3} in all cases. Figure 6 establishes that for a given *x*_{CO2,g,o}, increasing the irradiance increases the growth rate of *A. variabilis*. Moreover, for a given irradiance *G*_{in} within the values tested, decreasing the initial CO_{2} mole fraction increases the growth rate. Thus, the effects of *G*_{in} and *x*_{CO2,g,o} on cyanobacterial growth seem to be coupled.

Here also, scaling the time with the half-time *t*_{1/2} collapses the growth curves for different irradiances onto a single line as shown in Fig. 6c, d for *x*_{CO2,g,o} = 0·08 and 0·15 respectively. Therefore, the half-time *t*_{1/2} correctly captures the time scale of the biological processes for CO_{2} consumption and bacterial growth. In addition, the cyanobacterial growth is exponential and the cyanobacteria concentration *X*(*t*) at time *t* can be expressed as:

- (10)

where *α* is a constant depending on *x*_{CO2,g,o} and determined experimentally. Figure 7 shows its evolution as a function of *x*_{CO2,g,o} varying between 0·03 and 0·20. The relationship can be expressed as:

- (11)

with a correlation coefficient *R*^{2} = 0·93. Note that the evolution of *X*(*t*) as a function of the irradiance *G*_{in} and *x*_{CO2,g,o} is accounted for through the half-time *t*_{1/2} given by eqn (9).

Moreover, the average specific growth rate, denoted by *μ*_{avg}, is the arithmetic mean of the specific growth rates, denoted by *μ*_{Δt} and determined in the time interval Δ*t* during the exponential growth phase of *A. variabilis* according to (Yoon *et al.* 2002):

- (12)

where *X*_{avg,Δt} is the arithmetic mean of the cyanobacteria concentration during that time interval Δ*t*. The values of *μ*_{avg} 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 *μ*_{avg} and expressed in h^{−1}, as a function of *x*_{CO2,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 CO_{2} uptake rate, denoted by *ψ*_{CO2} and expressed in kg kg^{−1} dry cell h^{−1}, is computed using the same method as that used by Yoon *et al.* (2002):

- (13)

where *Y*_{X/CO2} is the biomass yield based on consumed CO_{2} expressed in kg dry cell kg^{−1} of CO_{2}. It is computed as the ratio of the final mass of cyanobacteria produced to the total mass of CO_{2} injected into the vials. The values of *ψ*_{CO2} computed for all parameters are also summarized in Table 2. Figure 8b shows the variation of *ψ*_{CO2} as a function of *x*_{CO2,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*/*t*_{1/2} 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 *C*_{H2,g,max} as a function of dimensionless time *t*/*t*_{1/2} for irradiance larger than 7000 lux is shown in Fig. 9b. It establishes that *C*_{H2,g}/*C*_{H2,g,max} varies exponentially with *t*/*t*_{1/2} and can be expressed as:

- (14)

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*/*t*_{1/2} for all runs. Figure 10(b) indicates that the normalized oxygen concentration varies exponentially with *t*/*t*_{1/2} according to:

- (15)

To use eqns (14) and (15) to determine the evolution of oxygen and hydrogen concentrations, the maximum concentrations *C*_{O2,g,max} and *C*_{H2,g,max} must be expressed in terms of the initial CO_{2} mole fraction *x*_{CO2,g,o} and irradiance *G*. Figure 11 shows that *C*_{O2,g,max} is independent of irradiance and varies linearly with *x*_{CO2,g,o} according to:

- (16)

with a correlation coefficient *R*^{2}=0·94. This demonstrates that the oxygen yield of *A. variabilis*, i.e. the mass of O_{2} produced per mass of CO_{2} consumed, was constant for the parameters explored.

Figure 12a shows *C*_{H2,g,max} as a function of both irradiance and of the initial CO_{2} mole fraction. It indicates that within the parameter ranges explored, the optimum irradiance for maximum H_{2} production was around 10 000 lux. Figure 12b shows *C*_{H2,g,max} as a function of *x*_{CO2,g,o} for irradiances larger than 7000 lux for which H_{2} production is the largest. It indicates that *C*_{H2,g,max} increases with increasing *x*_{CO2,g,o}. As a first order approximation, the relationship between *C*_{H2,g,max} and *x*_{CO2,g,o} can be written as:

- (17)

with a correlation coefficient *R*^{2} of 0·75.

### Discussion

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

Kinetic models describing the cyanobacterial growth, carbon uptake, and O_{2} production depend on the specific growth rate *μ* which is a function of the instantaneous available irradiance *G*_{av} and total dissolved inorganic carbon concentration *C*_{TOT}. In an earlier study, Badger and Andrews (1982) suggested that both H_{2}CO and HCO can act as substrate for cyanobacteria. Furthermore, Goldman *et al.* (1974) used *C*_{TOT} 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 *C*_{TOT}. However, it is equivalent to using *C*_{TOT} 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, *C*_{TOT} 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 *C*_{TOT} to be used in eqn (2). Furthermore, the aforementioned studies did not account for the inhibitory effect of dissolved inorganic carbon (i.e. *K*_{I} = ∞) as the concentration of inorganic carbon was low, *C*_{TOT} <0·67 × 10^{−3} kmol C m^{−3}. However, in the present study, the inorganic carbon concentration reached up to *C*_{TOT} < 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 *μ*_{max}, *K*_{G}, and *K*_{C} 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 *K*_{I}.

Moreover, due to the fact that CO_{2} consumption and O_{2} production are mainly growth related processes, their evolution has been successfully modelled using the specific growth rates. On the other hand, H_{2} evolution is a much more complex process. It depends on the active enzyme concentration, the O_{2} 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 CO_{2} consumption, cyanobacterial growth, as well as hydrogen and oxygen productions as functions of *t*_{1/2} has been developed. Experimental data indicates that *t*_{1/2} is a relevant time scale for CO_{2} consumption, growth, H_{2} and O_{2} 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 *x*_{CO2,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 *x*_{CO2,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 CO_{2} mole fraction of 0·11, *μ*_{avg} 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 CO_{2} uptake rate exhibits similar trends to those of the average specific growth rate with an optimum *x*_{CO2,g,o} around 0·05 for maximum *ψ*_{CO2}. Yoon *et al.* (2002) reported an average specific CO_{2} uptake rate *ψ*_{CO2} of about 0·130 kg CO_{2} kg^{−1} dry cell h^{−1} for *x*_{CO2,g,o} around 0·05 and irradiance around 4000 lux, whereas, in the present study, it was only 0·060 kg CO_{2} kg^{−1} dry cell h^{−1} under the same irradiance and *x*_{CO2,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 CO_{2} uptake metabolism of *A. variabilis* as confirmed by Tsygankov *et al.* (1999). Note that due to experimental difficulties in capturing fast CO_{2} consumption rate with the available equipment and procedure, no experiments were conducted for initial CO_{2} mole fraction less than 0·08 at irradiances higher than 5000 lux.

Figures 9 and 10 show that H_{2} and O_{2} 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, H_{2} production using the nitrogenase enzyme is not expected to stop when the growth stops or slows down such as during two stage H_{2} production (Yoon *et al.* 2002). However, increased concentration of evolved O_{2} could have inhibited H_{2} production. In addition, the initial anaerobic conditions promotes the bidirectional hydrogenase activity. Therefore, the observed H_{2} production during the experiments is expected to be due to the bidirectional hydrogenase activity. Furthermore, the decrease in the H_{2} concentration for *t*/*t*_{1/2} > 1·5 can be attributed to consumption of the produced H_{2} 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, *C*_{H2,g} and *C*_{O2,g} reach their maximum at dimensionless time *t*/*t*_{1/2} equal to 1·37 and 1·55, respectively, and shortly before the CO_{2} concentration vanishes at *t*/*t*_{1/2} equal to 1·8. Note that the reported values of CO_{2}, O_{2}, and H_{2} values correspond to the net produced or consumed quantities as it is difficult to experimentally distinguish the contribution of each phenomenon. In particular, CO_{2} is being consumed during photosynthesis and being produced during respiration and possibly during H_{2} production, provided H_{2} production is catalyzed by nitrogenase (Das and Veziroglu 2001). Similarly, O_{2} is being produced during photosynthesis and consumed during respiration.

Figures 11 and 12 show the maximum O_{2} and H_{2} concentrations attained in the headspace as functions of *x*_{CO2,g,o} for different irradiances. Unlike for *C*_{O2,g,max}, it is difficult to establish a simple and reliable relationship between *C*_{H2,g,max} and the parameters *G* and *x*_{CO2,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 CO_{2} 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 CO_{2} in the atmosphere. In contrast, the present study indicates that hydrogen production by the wild strain is possible under argon and CO_{2} 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) CO_{2} fixation and H_{2} 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 H_{2} by the wild strain *A. variabilis* at high dissolved O_{2} concentrations (Tsygankov *et al.* 1998).

### Conclusions

- Top of page
- Abstract
- Introduction
- Materials and methods
- Results
- Discussion
- Conclusions
- Acknowledgements
- References

A parametric experimental study has been performed to assess the CO_{2} consumption, growth, H_{2} and O_{2} productions of the cyanobacteria *A. variabilis* ATCC 29413-U^{TM} in batch experiment. The main parameters are the irradiance and the initial CO_{2} mole fraction in the head-space. The micro-organisms were grown in atmosphere containing argon and CO_{2}, at a pH of 7·0 ± 0·4 with nitrate in the medium. A new scaling analysis for CO_{2} consumption, growth, and H_{2} and O_{2} production is presented. Under the conditions presented in this study, the following conclusions can be drawn for *A. variabilis*,

- 1
Kinetic equations based on the Monod model are used to model the growth, carbon uptake, and O

_{2} production by

*A. variabilis* taking into account (i) light saturation; (ii) CO

_{2} saturation; and (iii) CO

_{2} 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 H

_{2} production rate.

- 2
The CO_{2} consumption half-time, defined as the time when the CO_{2} mole fraction in the gas phase decreases to half of its initial value, is a relevant time scale for CO_{2} consumption, growth, H_{2} and O_{2} production. It depends on the total irradiance incident on the vials and the initial CO_{2} mole fraction.

- 3
The scaling analysis facilitates the determination of the saturation irradiance which is found to be 5170 lux.

- 4
For maximum specific CO_{2} consumption and specific growth rates, the optimum initial CO_{2} mole fraction in the gas phase is about 0·05 for any irradiance between 1000 and 16 000 lux.

- 5
Optimum irradiance for maximum H_{2} production has been found to be around 10 000 lux despite the low overall H_{2} production rates.

- 6
Neither the CO_{2} 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 CO_{2} mitigation. Moreover, it is expected that the above experimental and scaling analysis method can be used for analyzing other CO_{2} mitigating and H_{2} producing micro-organisms.