Productivity Modeling
Ethanol productivity from genetically modified cyanobacteria has been
successfully modeled by Algenol using a Monod modeling approach (Legere
2017). The Algenol Productivity Model has been adapted for biomass-only
production and used in conjunction with PE-derived photosynthetic
parameters to estimate expected outdoor productivities for PBR
deployments in Fort Myers (and elsewhere around the world). The daily
biomass volumetric productivity can be described as:
\(P_{\text{Biomass}}=\alpha E_{k}\text{γln}\left[\frac{E_{k}+E_{0}}{E_{k}+E_{0}e^{-kD}}\right]\frac{t_{1}}{D}-R_{0}C_{c}\gamma t_{2}\)(3)
where \(\alpha\) is the quantum yield in the low light limit (mol C /mol
photons), Ek is the photosaturation parameter (µE
m-2 s-1), \(\gamma\) is the
conversion between fixed C to dry weight biomass (gDW mol
C-1), E0 is the incident light
intensity (µE m-2 s-1) at the
culture surface (corrected approximately for reflection losses), k is
the absorptivity coefficient of biomass (m-1), D is
the effective light path (m), R0 is the specific
respiration rate (µmol C mgChl.a-1min-1), Cc is the Chl.a concentration
(mgChl.a m-3), t1 is the time for
light-on (sec), and t2 is the time for respiration load
(min). Light-on time (t1) is about half of the
respiration load time (t2) for outdoor cultivation. For
the indoor PBR experiment, 12 hr light/12 hr dark cycle,
E0 is constant at 230 µE m-2s-1, and the average light path (D) is approximately
the radius of the reactor tubes with illumination from one side. The
productivity data are quoted as the mean values ± SD (n = 2) for
the two independent replicate cultures. The derivation of Equation (3)
is included in Supplementary Material along with application of model to
a large scale outdoor PBR cultivation of Arthrospira (Chance and
Roessler 2019). The model applies to a static system, in that none of
the mixing rates involved in these cultivations involve significant
movement of culture components on the time scale of the photosynthetic
reactions. (See Supplemental Material.)