Term 3: Photon Energy
The term photon energy, Ephoton , converts PAR as energy
to number of photons. Esolar (1), calculated in term 2, was
used to calculate term 3, the wavelength-weighted average
photon energy, Ephoton.Within the PAR range, photon energy
ranges from most energetic (299 kJ∙mol−1
) at 400 nm (blue)
to least energetic (171 kJ∙mol−1
) at 700 nm (red). These are
calculated using Planck’s law (Ephoton ¼ h c=l, where h is
Planck’s constant (6.63E-34 J∙s), c is the speed of light
(2.998E8 m∙s
−1
), and 1 is wavelength). Ephoton was
calculated to be 225.3 kJ∙mol−1
, or 0.2253 MJ∙mol−1
, also
in good agreement with published values [14, 21]. This
corresponds to a wavelength of 531 nm (green).
Total photon flux density (PFD) over a year can be
calculated from a combination of terms 1, 2, and 3 by Eq. 2.
PFD
mol
m2 year ¼
Efullspectrum
MJ
m2year %PAR
100
Ephoton
MJ
mol ð2Þ
Term 4: Photon Transmission Efficiency
The term photon transmission efficiency accounts for losses
in incident solar energy due to the construction or geometry of
the growth system, either an open-pond or enclosed photobioreactor.
Light reflection or absorption by surfaces and
materials will be minimized in an optimized design, but any
design will have some reduction in the number of incident
photons that reach the cells. For the theoretical case, the
growing system was assumed to preserve total PFD, i.e., no
reduction to 100% photon transmission efficiency. For the
best case, the reduction in PFD due to the growth system was
estimated for an open-pond scenario, where incident solar
energy is lost due to reflection off the open water surface.
Solar geometry equations [10] were used to calculate two
parameters: reflectance off the surface based on angle of
incidence and the predicted magnitude of solar radiation
(assuming no cloud cover) for any given latitude, day of year,
anand time of day. Larger angles of incidence, and thus more
reflection, occur during the early and late hours of the day
when the sun is lower in the sky, but the incident solar energy
during these hours is also lower at these times. The two
parameters were multiplied and summed over a day period to
find an estimate of the total portion of a day’s solar energy lost
due to reflection. Results for the summer and winter solstices
for latitudes 0°, 20°, and 40° are shown in Fig. 4.
Based on the results of this analysis, for the best case,
the reduction in PFD due to growth system geometry was
assumed to be 5%, resulting in a photon transmission
efficiency of 95%.
Term 5: Photon Utilization Efficiency
The term photon utilization efficiency accounts for reductions
in perfect photon absorption due to suboptimal
conditions of the algal culture. A cell under optimal
conditions will absorb and use nearly all incident photons.
However, under suboptimal conditions such as high-light
levels or non-optimal temperatures under which photoinhibition
occurs, some absorbed photons will be re-emitted
as heat or cause damage to the cells. For the theoretical
case, the culture was assumed to be maintained under
perfectly optimal conditions such that all incident photons
would be absorbed and used, i.e., there would be no reduction
in the 100% photon utilization efficiency. For the best case,
reduction in photon utilization due to high-light levels can be
significant for outdoor production, and the magnitude of this
effect varies with species, light, and other ambient conditions
such as temperature. Light utilization efficiency could range
from 50–90% under low-light conditions to 10–30% under
high-light conditions [13]. Therefore, for the best case, a
median value of 50% was chosen, which may be conservatively
high, given that high-light conditions are likely to be
found in outdoor growth systems.
Terms 6 and 7: Quantum Requirement and Carbohydrate
Energy Content
The terms quantum requirement and carbohydrate energy
content together represent the conversion of light energy to
chemical energy via photosynthesis. The basic equation for
photosynthesis is commonly expressed by Eq. 3:
CO2 þ H2O þ 8 photons ! CH2O þ O2 ð3Þ
This equation represents a combination of two reactions:
(1) energy transduction in the two photosystems, which
produces adenosine triphosphate (ATP) and nicotinamide
adenine dinucleotide phosphate (NADPH) via electron
transfer stimulated by photon absorption, and (2) carbon
assimilation in the Calvin cycle, which uses the energy ofthe ATP and NADPH produced in the photosystems to fix
CO2 and produce chemical energy.
Term 6, quantum requirement, represents the energy input
on the left side of Eq. 3 of 8 mol photons per mol of CO2
reduced to CH2O. At perfect efficiency, the quantum
requirement would be 3, because 3 of the least energetic
photons (at 700 nm) have an energy of 3170:9 kJ mol1 ¼
512:7 kJ mol1
. This is slightly higher than the required
energy of 482.5 kJ∙mol−1
. However, extensive debates on this
topic since the middle of the last century have resulted in a
common agreement that the value of 8 mol photons per mol
CO2 reduced to CH2O corresponds to maximally efficient
photosynthesis based on the Z-scheme [6, 11, 15, 23, 25,
34]. While some researches might argue that higher values
may be more realistic, because of our methodology of
conservatism to produce an absolute maximum, 8 was used
because there is not yet consensus on a higher (and thus less
efficient) theoretical quantum requirement.
In Eq. 3, CH2O represents the basic form of chemical
energy captured by photosynthesis. Its actual form is
triosephosphate (C3H5O3P), but the energy content is often
calculated from glucose (C6H12O6). Several reported values
for CH2O include 496, 494, 468.9, and 470 kJ∙mol−1 [6, 13,
29, 34]. The median of the range of cited values,
482.5 kJ∙mol−1
, was used for term 7, carbohydrate energy
content.
Term 3: Photon EnergyThe term photon energy, Ephoton , converts PAR as energyto number of photons. Esolar (1), calculated in term 2, wasused to calculate term 3, the wavelength-weighted averagephoton energy, Ephoton.Within the PAR range, photon energyranges from most energetic (299 kJ∙mol−1) at 400 nm (blue)to least energetic (171 kJ∙mol−1) at 700 nm (red). These arecalculated using Planck’s law (Ephoton ¼ h c=l, where h isPlanck’s constant (6.63E-34 J∙s), c is the speed of light(2.998E8 m∙s−1), and 1 is wavelength). Ephoton wascalculated to be 225.3 kJ∙mol−1, or 0.2253 MJ∙mol−1, alsoin good agreement with published values [14, 21]. Thiscorresponds to a wavelength of 531 nm (green).Total photon flux density (PFD) over a year can becalculated from a combination of terms 1, 2, and 3 by Eq. 2.PFDmolm2 year ¼EfullspectrumMJm2year %PAR100EphotonMJmol ð2ÞTerm 4: Photon Transmission EfficiencyThe term photon transmission efficiency accounts for lossesin incident solar energy due to the construction or geometry ofthe growth system, either an open-pond or enclosed photobioreactor.Light reflection or absorption by surfaces andmaterials will be minimized in an optimized design, but anydesign will have some reduction in the number of incidentphotons that reach the cells. For the theoretical case, thegrowing system was assumed to preserve total PFD, i.e., noreduction to 100% photon transmission efficiency. For thebest case, the reduction in PFD due to the growth system wasestimated for an open-pond scenario, where incident solarenergy is lost due to reflection off the open water surface.Solar geometry equations [10] were used to calculate twoparameters: reflectance off the surface based on angle ofincidence and the predicted magnitude of solar radiation(assuming no cloud cover) for any given latitude, day of year,anand time of day. Larger angles of incidence, and thus morereflection, occur during the early and late hours of the daywhen the sun is lower in the sky, but the incident solar energyduring these hours is also lower at these times. The twoparameters were multiplied and summed over a day period tofind an estimate of the total portion of a day’s solar energy lostdue to reflection. Results for the summer and winter solsticesfor latitudes 0°, 20°, and 40° are shown in Fig. 4.Based on the results of this analysis, for the best case,the reduction in PFD due to growth system geometry wasassumed to be 5%, resulting in a photon transmissionefficiency of 95%.Term 5: Photon Utilization EfficiencyThe term photon utilization efficiency accounts for reductionsin perfect photon absorption due to suboptimalconditions of the algal culture. A cell under optimalconditions will absorb and use nearly all incident photons.However, under suboptimal conditions such as high-lightlevels or non-optimal temperatures under which photoinhibitionoccurs, some absorbed photons will be re-emittedas heat or cause damage to the cells. For the theoreticalcase, the culture was assumed to be maintained underperfectly optimal conditions such that all incident photonswould be absorbed and used, i.e., there would be no reductionin the 100% photon utilization efficiency. For the best case,reduction in photon utilization due to high-light levels can besignificant for outdoor production, and the magnitude of thiseffect varies with species, light, and other ambient conditionssuch as temperature. Light utilization efficiency could rangefrom 50–90% under low-light conditions to 10–30% underhigh-light conditions [13]. Therefore, for the best case, amedian value of 50% was chosen, which may be conservativelyhigh, given that high-light conditions are likely to befound in outdoor growth systems.Terms 6 and 7: Quantum Requirement and CarbohydrateEnergy ContentThe terms quantum requirement and carbohydrate energycontent together represent the conversion of light energy tochemical energy via photosynthesis. The basic equation forphotosynthesis is commonly expressed by Eq. 3:CO2 þ H2O þ 8 photons ! CH2O þ O2 ð3ÞThis equation represents a combination of two reactions:(1) energy transduction in the two photosystems, whichproduces adenosine triphosphate (ATP) and nicotinamideadenine dinucleotide phosphate (NADPH) via electrontransfer stimulated by photon absorption, and (2) carbonassimilation in the Calvin cycle, which uses the energy ofthe ATP and NADPH produced in the photosystems to fixCO2 and produce chemical energy.Term 6, quantum requirement, represents the energy inputon the left side of Eq. 3 of 8 mol photons per mol of CO2reduced to CH2O. At perfect efficiency, the quantumrequirement would be 3, because 3 of the least energeticphotons (at 700 nm) have an energy of 3170:9 kJ mol1 ¼512:7 kJ mol1. This is slightly higher than the requiredenergy of 482.5 kJ∙mol−1. However, extensive debates on thistopic since the middle of the last century have resulted in acommon agreement that the value of 8 mol photons per molCO2 reduced to CH2O corresponds to maximally efficientphotosynthesis based on the Z-scheme [6, 11, 15, 23, 25,34]. While some researches might argue that higher valuesmay be more realistic, because of our methodology ofconservatism to produce an absolute maximum, 8 was usedbecause there is not yet consensus on a higher (and thus lessefficient) theoretical quantum requirement.In Eq. 3, CH2O represents the basic form of chemicalenergy captured by photosynthesis. Its actual form istriosephosphate (C3H5O3P), but the energy content is oftencalculated from glucose (C6H12O6). Several reported valuesfor CH2O include 496, 494, 468.9, and 470 kJ∙mol−1 [6, 13,29, 34]. The median of the range of cited values,482.5 kJ∙mol−1, was used for term 7, carbohydrate energycontent.
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