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Experimental validation of a nonequilibrium model of CO2 fluxes between gas, liquid medium, and algae in a flat-panel photobioreactor

  • Original Paper
  • Published:
Journal of Industrial Microbiology & Biotechnology

Abstract

Carbon dioxide (CO2) availability strongly affects the productivity of algal photobioreactors, where it is dynamically exchanged between different compartments, phases, and chemical forms. To understand the underlying processes, we constructed a nonequilibrium mathematical model of CO2 dynamics in a flat-panel algal photobioreactor. The model includes mass transfer to the algal suspension from a stream of bubbles of CO2-enriched air and from the photobioreactor headspace. Also included are the hydration of dissolved CO2 to bicarbonate ion (HCO −3 ) as well as uptake and/or cycling of these two chemical forms by the cells. The model was validated in experiments using a laboratory-scale flat-panel photobioreactor that controls light, temperature, and pH and where the concentration of dissolved CO2, and partial pressure of CO2 in the photobioreactor exhaust are measured. First, the model prediction was compared with measured CO2 dynamics that occurred in response to a stepwise change in the CO2 partial pressure in the gas sparger. Furthermore, the model was used to predict CO2 dynamics in photobioreactors with unicellular, nitrogen-fixing cyanobacterium Cyanothece sp. The metabolism changes dramatically during a day, and the distribution of CO2 is expected to exhibit a pronounced diurnal modulation that significantly deviates from chemical equilibrium.

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Abbreviations

a B :

Specific gas–liquid interfacial bubble area (m−1)

h :

Henry constant (m3 Pa mol−1)

k :

Rate of CO2 hydration (s−1)

k L :

Liquid-phase mass transfer coefficient (m s−1)

l :

Rate of HCO −3 dehydration (s−1)

\( n_{{{\text{CO}}_{2} }} \) :

Number of CO2 molecules (mol)

r B :

Bubble radius (m)

J :

Aeration rate (m3 s−1)

N B :

Number of bubbles

\( P_{{{\text{CO}}_{2} }}^{\text{bubble}} \) :

Partial CO2 pressure inside bubble (Pa)

\( P_{{{\text{CO}}_{2} }}^{\text{IN}} \) :

Partial CO2 pressure of gas entering bioreactor (Pa)

\( P_{{{\text{CO}}_{2} }}^{\text{OUT}} \) :

Partial CO2 pressure of gas leaving bioreactor headspace (Pa)

\( P_{{{\text{CO}}_{2} }}^{\text{X}} \) :

Partial CO2 pressure of bubble entering bioreactor headspace (Pa)

R :

Universal gas constant (m3 Pa K−1 mol−1)

S B :

Bubble surface (m2)

S H :

Liquid to headspace surface (m2)

T :

Temperature of the photobioreactor (K)

V B :

Volume of bubble (m3)

V H :

Volume of headspace (m3)

V L :

Volume of liquid (m3)

\( \alpha_{{{\text{CO}}_{2} }} \) :

Mass transfer rate from bubble to liquid phase (mol s−1)

\( \beta_{{{\text{CO}}_{2} }} \) :

Mass transfer rate from headspace to liquid phase (mol s−1)

\( \gamma_{{{\text{dCO}}_{2} }} \) :

Rate of dissolved carbon dioxide uptake by algae (mol s−1)

\( \gamma_{{{\text{HCO}}_{3}^{ - } }} \) :

Rate of bicarbonate uptake by algae (mol s−1)

τ :

Bubble lifetime (s)

A :

Flux of CO2 into bioreactor (mol s−1)

B :

Flux of CO2 into headspace (mol s−1)

Γ:

Flux of CO2 out of bioreactor (mol s−1)

[dCO2]:

Concentration of CO2 dissolved in liquid phase (mol m−3)

[HCO −3 ]:

Concentration of bicarbonate ions in liquid phase (mol m−3)

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Acknowledgments

L.N. and J.Č. were supported by grants AV0Z60870520 (Czech Academy of Sciences), and by GAČR 206/09/1284 (Czech Science Foundation) as well as by Photon Systems Instruments, Ltd. N.K. and A.K. were supported by grants from the Israel Science Foundation (Bikura program) and the Hebrew University. The authors are grateful to Rainer Machne of Universität Wien for critically checking the model equations and reading of the manuscript.

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Authors and Affiliations

  1. Institute of Systems Biology and Ecology ASCR, Zámek 136, 37333, Nové Hrady, Czech Republic

    Ladislav Nedbal & Jan Červený

  2. Photon Systems Instruments, Ltd., Koláčkova 39, 62100, Brno, Czech Republic

    Ladislav Nedbal & Jan Červený

  3. Department of Plants and Environmental Sciences, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel

    Nir Keren & Aaron Kaplan

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  1. Ladislav Nedbal
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  2. Jan Červený
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Correspondence to Ladislav Nedbal.

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Nedbal, L., Červený, J., Keren, N. et al. Experimental validation of a nonequilibrium model of CO2 fluxes between gas, liquid medium, and algae in a flat-panel photobioreactor. J Ind Microbiol Biotechnol 37, 1319–1326 (2010). https://doi.org/10.1007/s10295-010-0876-5

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  • DOI: https://doi.org/10.1007/s10295-010-0876-5

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