Productivity Modeling:
Annual ethanol productivity from cyanobacteria has been successfully
modeled by Algenol using a Monod modeling approach (Chance and Roessler,
2019). The Algenol Productivity Model was developed in this manner and
used in conjunction with PI-derived photosynthetic parameters to
estimate expected average outdoor productivities for PBR deployments in
Fort Myers (and elsewhere around the world). The daily biomass
volumetric productivity can be described as:
\(P_{\text{Biomass}}=\alpha E_{k}\text{γln}\left[\frac{E_{k}+E_{s}}{E_{k}+E_{s}e^{-kD}}\right]\frac{t_{1}}{D}-R_{0}C_{0}\gamma t_{2}\)(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), Es is the incident light
intensity (µE m-2 s-1), k is the
absorptivity coefficient of biomass (1/m), D is the effective light path
(m), R0 is the specific respiration rate (µmol C
mgChl.a-1 min-1), C0is 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, Es is constant
at 230 µE m-2 s-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.