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Kinetics and energetics of photosynthetic micro-organisms in photobioreactors

Application to Spirulina growth

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Bioprocess and Algae Reactor Technology, Apoptosis

Part of the book series: Advances in Biochemical Engineering Biotechnology ((ABE,volume 59))

Abstract

This paper provides the basis for the description and quantitative analysis of cultures of photosynthetic micro-organisms in batch and in continuous photobioreactors. The methodology generally accepted for modeling submerged aerobic or anaerobic cultures is used and applied to the growth of the blue-green algae Spirulina platensis.

From analysis of the metabolic pathways inside the cell, stoichiometric equations are derived for the main metabolic events which must be considered for Spirulina growth, including exopolysaccharide formation. Together with the description of the reaction kinetics, it forms the basis for modeling.

As the rate of growth is closely related to the light energy available inside the culture medium, special attention is paid to the description of light energy transfer inside a dense liquid medium which absorbs and scatters the light, and the useful concept of working illuminated volume is introduced. The reaction kinetics accounts too for the mineral limitations (nitrogen, sulphur and phosphorus) as well as physical and physiological limitations by the carbon source.

Finally, a so-called biochemically structured model gives a unified vision of yields and rates of growth observed for various light energy inputs and different nutrients limitations. The proposed methodology enables one to define and calculate the thermodynamic efficiency for the light energy conversion process in photobioreactors.

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Abbreviations

A :

Volumetric rate of radiant energy absorbed (W.m−3)

A λ :

Volumetric rate of radiant energy absorbed for radiation of wavelength λ (W.m−4)

Ai :

Chemical affinity for the component i (J.kmole−1)

a:

Extinction coefficient of Lambert (m−1)

C:

State vector (kg.m−3)

Ci :

Mass concentration of component i (kg.m−3)

C′i :

Molar concentration of component i (kmole.m−3)

D:

Dilution rate (h−1)

E:

Acceleration factor by chemical reaction (−)

Ea:

Absorption mass coefficient (m2.kg−1)

Ea(λ):

Absorption mass coefficient for radiation of wavelength λ (m2.kg−1)

Es:

Scattering mass coefficient (m2.kg−1)

Es(λ):

Scattering mass coefficient for radiation of wavelength λ (m2.kg−1)

F:

Volumetric flow rate (m3.h−1)

F:

Radiant energy flux vector (W.m−2)

Fλ :

Radiant energy flux vector for radiation of wavelength λ (W.m−3)

G:

Molar gas flow rate (kmole.h−1)

gi :

Partial molar free enthalpy for the component i (J.kmole−1)

H′:

Henry's constant (Pa.m3.kmole−1)

ΔH:

Enthalpy (J.kmole−1)

Δh* :

Activation enthalpy (J.kmole−1)

Δhd :

Deactivation enthalpy (J.kmole−1)

I:

Specific radiant light intensity (W.m−2)

Iλ :

Specific radiant light intensity for radiation of wavelength λ (W.m−3)

J:

Mean specific intensity (W.m−2)

Jλ :

Mean specific intensity for radiation of wavelength λ (W.m−3)

Jj :

Specific molar conversion rate of reaction j (kmole.kg DM−1.h−1)

K:

Chemical equilibrium constant for a given reaction

Ki :

Partition coefficient between liquid and gas phases (kg.m−3.Pa−1)

Ki :

Monod saturation constant for the component i (kg.m−3)

KJ :

Monod saturation constant for available radiant light energy (W.m−2)

k:

Extinction coefficient for medium only (m−1)

kj, k−j :

Direct and reverse kinetic constants for the reaction i

kJ :

Andrew inhibition constant for available radiant light energy (W.m−2)

kLa:

Volumetric coefficient of gas-liquid transfer (h−1)

L:

Total length or optical thickness of a rectangular reactor (m)

L2 :

Working illuminated length (m)

Lij :

Phenomenological coefficient (kmole2. kg DM−1.J−1.h−1)

Mi :

Molar mass of component i (kg.kmole−1)

m:

Extinction coefficient of Lambert-Beer (m2.kg−1)

ni :

Number of moles of component i inside the bioreactor (kmole)

P:

Pressure (Pa)

Pi :

Partial pressure for the component i (Pa)

p(θ, θ′, φ, φ′ or p(u, u′ or p(cosΘ):

Phase function (−)

q:

Coupling coefficient (−)

qi :

Specific mass conversion rate of component i (kg.kg DM−1.h−1)

R:

Reflexion (−)

R:

Total radius or optical thickness of a cylindrical reactor (m)

R:

Ideal gas constant (R=8.3143 J. mole−1.K−1)

R2 :

Working illuminated radius (m)

Ri:

Mass volumetric conversion rate of component i in reference to light limitation only (kg.m−3.h−1)

r:

Radius (m)

ri :

Mass volumetric conversion rate of component i (kg.m−3.h−1)

r′i :

Molar volumetric conversion rate of component i (kmole.m−3.h−1)

S:

Cross section (m2)

T:

Transmission (−)

T:

Temperature (K)

t:

Time (h)

u, u′:

Unit vector (−)

V:

Volume (m3)

V2 :

Working illuminated volume (m3)

v:

Specific photosynthesis or respiration rate (kmole.kg DM−1.h−1)

X:

Biotic state vector (kg.m−3)

x:

Generalized force ratio (−)

Y:

Abiotic state vector (kg.m−3)

Yi/j :

Global mass conversion yield of substrate i into product j (−)

yi :

molar gas fraction of component i (−)

Z:

Dimensionless length or radius (−)

Z2 :

Dimensionless working illuminated length or radius (−)

z:

Length (m)

zi :

Mass fraction of the component i (−)

〈〉=1/V∭vdV:

Mean volumetric integral (−)

γ:

Illuminated fraction volume (−)

η, ηth :

Thermodynamic efficiency (−)

θ, θ′, Θ:

Angle (rd)

ζ:

Proportionality coefficient (−)

ε:

Gas hold-up (−)

λ:

Wavelength (m)

μ:

Specific growth rate (h−1)

μM :

Maximum specific growth rate (h−1)

Vij :

Stoichiometric coefficient for the component i in reaction j (−)

σ:

Dissipation function of entropy (J.kgDM−1.h−1)

φ, φ′:

Angle (rd)

η:

Phenomenological stoichiometric coefficient (−)

ω, ω′, Ω, Ω′:

Solid angle (−)

\(\bar \omega _0 \) :

Albedo of single scattering=Es/(Ea+Es) (−)

ATP:

Adenosine tri-phosphate

C:

Carbohydrates or bicarbonate

CH:

Chlorophyll a

COF:

Cofactor

EPS:

Exopolysaccharide

G:

Glycogen or gas

L:

Lipids or liquid

N:

Nitrate

NA:

Nucleic acids

Pr:

Protein

PC:

Phycocyanin

P:

Phosphate

R:

Respiration

r:

r-direction

S:

Sulfate

T:

Total volume

X:

Biomass

XA:

Active biomass

XT:

Total biomass

z:

z-direction

ΦS:

Photosynthesis

E:

For the incoming flow in the reactor

′:

For molar concentration

*:

For gas-liquid equlibrium

+:

Positive direction

−:

Negative direction

PFTR:

Plug flow tubular reactor

WTR:

Well-mixed tank reactor

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Authors and Affiliations

  1. Laboratoire de Génie Chimique Biologique, Université Blaise-Pascal, 24, Avenue des Landais, 63177, Aubière Cedex, France

    J.-F. Cornet, C. G. Dussap & J.-B. Gros

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  1. J.-F. Cornet
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  2. C. G. Dussap
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  3. J.-B. Gros
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Cornet, JF., Dussap, C.G., Gros, JB. (1998). Kinetics and energetics of photosynthetic micro-organisms in photobioreactors. In: Bioprocess and Algae Reactor Technology, Apoptosis. Advances in Biochemical Engineering Biotechnology, vol 59. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102299

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  • DOI: https://doi.org/10.1007/BFb0102299

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