A new approach for calculating microalgae culture growth based on an inhibitory effect of the surrounding biomass

Ever since the potential of algae in biotechnology was recognized, models describing the growth of algae inside photobioreactors have been proposed. These models are the basis for the optimization of process conditions and reactor designs. Over the last few decades, models became more and more elaborate with the increase of computational capacity. Thus far, these models have been based on light attenuation due to the absorption and scattering effects of the biomass. This manuscript presents a new way of predicting the apparent growth inside photobioreactors using simple models for enzymatic kinetics to describe the reaction between photons and the photosynthetic unit. The proposed model utilizes an inhibition kinetic formula based on the surrounding biomass to describe the average growth rate of a culture, which is determined by the local light intensities inside the reactor. The result is a mixed-inhibition scheme with multiple inhibition sites. The parameters of the new kinetic equation are replaced by empirical regression functions to correlate their dependency on incident light intensity and reactor size. The calibrations of the parameters and the regression functions are based on the numerical solutions of the growth rate computed with a classical Type II model. As a final verification, we apply the new equation in predicting the growth behavior of three phototrophic organisms in reactors of three different sizes.