Photobioreactors
129
(Eq. 1) to be the best description of the real course for specific growth constant
p [28]:
t.t = t.tmax(l- exp( - ln(2)) ~)
(1)
The light quantity io represents the minimum metabolism maintenance energy.
Grima et al. [34] have modified the hyperbolic model according to Baly [167]
where the empirical exponent N (Eq. 2) takes into account the boundary
conditions of cultivation (AI, I0, pigment content, reactor diameter, etc.) and m,
the specific maintenance rate:
(Pmax " IN'~
p=\~]-m
(2)
The calculation of the light energy value I at a random point within the
cultivation system is rather difficult, because dynamic absorption and scattering
processes on the cells require a complex mathematical approach, such as the
highly numeric Monte Carlo method for three-dimensional space [17]. On the
basis of the hypothesis of Schuster [35], Binouis et al. [36] have developed
a simplified model with the aim of predicting the growth of phototrophic
biomass in a tubular photobioreactor of the MELISSA-project (Eq. 3):
Io
2 coshSz
4I-IJ, = -Z cosh6 + asinh8
1
'!
4FIJ,
dr
(3)
(P) - I-l(rl -- rz) z 2Hr ~max kl + 4IIJ,
The total energy received, 4H J, is defined by the parameters c~ and 6 which
represent pigment absorption and cell dispersion, Z representing the normalized
radius. This approach is suited to rapid on-line calculations, and the error
between real and model values could be reduced to < 10%. The mean volumetric integral (p) could be further integrated over the wave length spectrum
because of the significant influence of the emission of photosynthetically active
radiation (PAR) of the light sources [37]. There are more general considerations
existing, e.g. the model presented by Frohlich et al. [38], who pay attention to
vessel geometry, first limiting inorganic nutrient and light inhibition by defining
a modulus, but they all take complex numerical solutions. As may be seen from
the various approaches, identical radiation conditions are given only if the
geometries of the radiation field and of the radiation spectrum are identical [28].
There are significant variations of the optimum energy and PAR quantum
flux density for the growth of microalgae, from species to species. Richardson
et al. [29] have examined several species as to the genotypical light intensity.
With Dinophyceae Amphidinium carterae living in the depths of the oceans they
established cell division at extremely low light intensity (approximately
1-2 ~tE m- z s- 1) and photoinhibition already at 80 pE m- z s- 1. On the other
hand, the dinoflagellate Gonyaulax polyedra does not grow at light intensities
129
(Eq. 1) to be the best description of the real course for specific growth constant
p [28]:
t.t = t.tmax(l- exp( - ln(2)) ~)
(1)
The light quantity io represents the minimum metabolism maintenance energy.
Grima et al. [34] have modified the hyperbolic model according to Baly [167]
where the empirical exponent N (Eq. 2) takes into account the boundary
conditions of cultivation (AI, I0, pigment content, reactor diameter, etc.) and m,
the specific maintenance rate:
(Pmax " IN'~
p=\~]-m
(2)
The calculation of the light energy value I at a random point within the
cultivation system is rather difficult, because dynamic absorption and scattering
processes on the cells require a complex mathematical approach, such as the
highly numeric Monte Carlo method for three-dimensional space [17]. On the
basis of the hypothesis of Schuster [35], Binouis et al. [36] have developed
a simplified model with the aim of predicting the growth of phototrophic
biomass in a tubular photobioreactor of the MELISSA-project (Eq. 3):
Io
2 coshSz
4I-IJ, = -Z cosh6 + asinh8
1
'!
4FIJ,
dr
(3)
(P) - I-l(rl -- rz) z 2Hr ~max kl + 4IIJ,
The total energy received, 4H J, is defined by the parameters c~ and 6 which
represent pigment absorption and cell dispersion, Z representing the normalized
radius. This approach is suited to rapid on-line calculations, and the error
between real and model values could be reduced to < 10%. The mean volumetric integral (p) could be further integrated over the wave length spectrum
because of the significant influence of the emission of photosynthetically active
radiation (PAR) of the light sources [37]. There are more general considerations
existing, e.g. the model presented by Frohlich et al. [38], who pay attention to
vessel geometry, first limiting inorganic nutrient and light inhibition by defining
a modulus, but they all take complex numerical solutions. As may be seen from
the various approaches, identical radiation conditions are given only if the
geometries of the radiation field and of the radiation spectrum are identical [28].
There are significant variations of the optimum energy and PAR quantum
flux density for the growth of microalgae, from species to species. Richardson
et al. [29] have examined several species as to the genotypical light intensity.
With Dinophyceae Amphidinium carterae living in the depths of the oceans they
established cell division at extremely low light intensity (approximately
1-2 ~tE m- z s- 1) and photoinhibition already at 80 pE m- z s- 1. On the other
hand, the dinoflagellate Gonyaulax polyedra does not grow at light intensities