Kinetics and Energetics of Photosynthetic Micro-Organisms in Photobioreactors
171
The total Spirulina biomass produced requires a fifth equation for the
exopolysaccharide synthesis, which is established from the exopolysaccharide
composition [9] and from the data of Oura [29]:
CO2 + 2.220H20 + 0.015H2SO4 + 3.330ATP + 1.920(NADPH, H +)
( JEP8 )
' CH1.65000.95080.015 + 3.330Pi + 3.330ADP + 1.920NADP +
(26)
In the general case, the respective rates of exopolysaccharide (Eq. 26) and
active biomass (Eq. 25) synthesis remain undetermined. The classical unstructured approach may be used by weighting the two equations with fractions only
valid for a restricted range of operating conditions. Taking as an example
a limitation by light energy transfer with an incident radiant energy flux lower
than 20 W.m- 2, one can assume a molar fraction of 0.9 for active biomass and
0.1 for exopolysaccharide [7]. The combination of the synthesis equations (Eqs.
25 and 26) then gives, for the total biomass produced:
CO2 + 1.463H20 + 0.173HNO3 + 0.006H2SO4 + 3.544ATP
+ 2.779(NADPH, H +)
(27)
The consumptions of ATP and reduced cofactors NADPH, H + can be further
eliminated; the two stoichiometric equations for photosynthesis are
(Jcov)
2.779NADP + + 2.779H20
, 2.779(NADPH, H +) + 1.38902
(28)
3.544(ADP + Pi)(JAT,)3.544ATP + 3.544H20
(29)
which gives, by addition of Eqs. (27-29):
CO2 + 0.698H20 + 0.173HNO3 + 0.006H2SO4 + 0.006Pi
(Jx'r)
' CH1.57500.459No.173So.oo6Po.oo 6 + 1.38902
(30)
This equation corresponds to the single stoichiometric equation for Spirulina
growth, only valid for low radiant light energy inputs (< 20 W.m-2). It always
holds for photosynthesis, since as discussed in Sect. 2.3.2, respiration of
S. platensis is inhibited by light. Unlike the case of respiration, the elemental mass
balance of this equation does not require experimentally determined conversion
yields and it is fully predictive, since the six stoichiometric coefficients are calculated
from the six conservation balances of the C, H, O, N, S and P elements.
Considering the ionic forms of the salts and taking into account the
H + balance, Eq. (30) is rewritten as
HCO3 + 0.698H20 + 0.173NO3 + 0.006SO 2- + 0.006HPO 2+ 0.197H + CH1.57500.459No.17380.006P0.006
+ 1.38902 + OH(31)
171
The total Spirulina biomass produced requires a fifth equation for the
exopolysaccharide synthesis, which is established from the exopolysaccharide
composition [9] and from the data of Oura [29]:
CO2 + 2.220H20 + 0.015H2SO4 + 3.330ATP + 1.920(NADPH, H +)
( JEP8 )
' CH1.65000.95080.015 + 3.330Pi + 3.330ADP + 1.920NADP +
(26)
In the general case, the respective rates of exopolysaccharide (Eq. 26) and
active biomass (Eq. 25) synthesis remain undetermined. The classical unstructured approach may be used by weighting the two equations with fractions only
valid for a restricted range of operating conditions. Taking as an example
a limitation by light energy transfer with an incident radiant energy flux lower
than 20 W.m- 2, one can assume a molar fraction of 0.9 for active biomass and
0.1 for exopolysaccharide [7]. The combination of the synthesis equations (Eqs.
25 and 26) then gives, for the total biomass produced:
CO2 + 1.463H20 + 0.173HNO3 + 0.006H2SO4 + 3.544ATP
+ 2.779(NADPH, H +)
(27)
The consumptions of ATP and reduced cofactors NADPH, H + can be further
eliminated; the two stoichiometric equations for photosynthesis are
(Jcov)
2.779NADP + + 2.779H20
, 2.779(NADPH, H +) + 1.38902
(28)
3.544(ADP + Pi)(JAT,)3.544ATP + 3.544H20
(29)
which gives, by addition of Eqs. (27-29):
CO2 + 0.698H20 + 0.173HNO3 + 0.006H2SO4 + 0.006Pi
(Jx'r)
' CH1.57500.459No.173So.oo6Po.oo 6 + 1.38902
(30)
This equation corresponds to the single stoichiometric equation for Spirulina
growth, only valid for low radiant light energy inputs (< 20 W.m-2). It always
holds for photosynthesis, since as discussed in Sect. 2.3.2, respiration of
S. platensis is inhibited by light. Unlike the case of respiration, the elemental mass
balance of this equation does not require experimentally determined conversion
yields and it is fully predictive, since the six stoichiometric coefficients are calculated
from the six conservation balances of the C, H, O, N, S and P elements.
Considering the ionic forms of the salts and taking into account the
H + balance, Eq. (30) is rewritten as
HCO3 + 0.698H20 + 0.173NO3 + 0.006SO 2- + 0.006HPO 2+ 0.197H +
+ 1.38902 + OH(31)