The development of a mechanistic model to investigate the impacts of the light dynamics on algal productivity in a Hydraulically Integrated Serial Turbidostat Algal Reactor (HISTAR)

A deterministic model was developed to predict microalgal productivity within the Hydraulically Integrated Serial Turbidostat Algal Reactor (HISTAR). HISTAR consists of two turbidostats, which concomitantly inoculate the first of a series of CFSTRs. The CFSTRs function as a biomass amplifier of the inoculated culture. The model included an analysis of the internal light dynamics within each CFSTR and the effect of the instantaneous average irradiance (Ian(PAR)) on the instantaneous growth rate (μn) within CFSTRn. The latter effect was accomplished using Steele's equation. The instantaneous average irradiance was determined by integrating the Lambert-Beer Law over the depth of the culture within the CFSTRs. Fourier series analysis was used to model the biorhythms of the microalgae. The model was calibrated for biomass using four data sets collected at system dilution rates (Ds) of 0.265 day−1, 0.385 day−1, 0.641 day−1 and 1.127 day−1. The ability of the calibrated model to simulate daily volumetric productivity (Pv) within HISTAR was determined through calculation of the percent standard error of prediction. The overall mean for the four data sets was 24.8%. The average predicted productivity for the data sets was 24.2 g m−3 day−1 (16.2 g m−2 day−1) and the average actual productivity of the data sets were 25.5 g m−3 day−1 (19.9 g m−2 day−1), resulting in only a 5.1% error. Simulations produced by the calibrated model were used to estimate the optimum Ds (between 0.641 day−1 and 0.884 day−1). The model predicted a Pv of 70.2 g m−3 day−1 (Pa = 46.8 g m−2 day−1) at optimum Ds. The maximum Pa observed in the model simulations was 39.9 g m−2 day−1.