Prediction of maximum algal productivity in membrane bioreactors with a light-dependent growth model

Algal productivity in steady-state cultivation systems depends on important factors such as biomass concentration, solids retention time (SRT), and light intensity. Current modeling of algal growth often ignores light distribution in algal cultivation systems and does not consider all these factors simultaneously. We developed a new algal growth model using a first principles approach to incorporate the effect of light intensity on algal growth while simultaneously considering biomass concentration and SRT. We first measured light attenuation (decay) with depth in an indoor algal membrane bioreactor (A-MBR) cultivating Chlorella sp. We then simulated the light decay using a multi-layer approach and correlated the decay with biomass concentration and SRT in model development. The model was calibrated by delineating specific light absorptivity and half-saturation constant to match the algal biomass concentration in the A-MBR operated at a target SRT. We finally applied the model to predict the maximum algal productivity in both indoor and outdoor A-MBRs. The predicted maximum algal productivities in indoor and outdoor A-MBRs were 6.7 g·m^-2·d^-1 (incident light intensity 5732 lx, SRT approximately 8 d) and 28 g·m^-2·d^-1 (sunlight intensity 28,660 lx, SRT approximately 4 d), respectively. The model can be extended to include other factors (e.g., water temperature and carbon dioxide bubbling) and such a modeling framework can be applied to full-scale, continuous flow outdoor systems to improve algal productivity.