Modeling Biofilm Growth on a CO ₂ -Supplying, Membrane-Based Biofilm Photobioreactor

The membrane-based photo biofilm reactor (MB-PBR) is a novel reactor that uses gas-permeable membranes to deliver carbon dioxide (CO2) directly to the base of phototrophic biofilms. The CO2 supply increases growth rates by reducing carbon limitation and pH increases, but the counter-gradient supply of CO2 and light makes its behavior more complex. We developed a mathematical model to explore its behavior and used a lab-scale MB-PBR to compare growth rates with and without a CO2 supply (control). After 7 days, the MB-PBR biofilm grew to 186 ± 10 μm, compared to 101 ± 10 μm for the control. The biomass productivity was 1.91 ± 0.27 g/(m2 d), compared to 0.49 ± 0.06 g/(m2 d) for the control. Using data fitting, the experimental light attenuation coefficient (ke) and the half-saturation coefficient of light irradiance (KI) were 80,000 1/m and 5 W/m2, respectively. Modeling showed that, for a well-buffered system, increasing the CO2 fraction in the gas supply increased the growth rate but with diminishing returns: adding 5% CO2 doubled the amount of growth, relative to the control, while adding 99% CO2 only quadrupled the growth relative to the control. The beneficial effect of the CO2 supply was smaller for thicker biofilms and lower light intensities. With a weak buffer, the CO2 supply tended to acidify the biofilm interior, slowing growth rates at higher CO2 concentrations. The model showed that, for the same light intensity and biofilm thickness, the maximum growth rate for the MB-PBR was higher, 0.141 g/(m3 s), and it was located closer to the CO2 supply from the membrane. The conventional reactor had a maximum growth rate of 0.086 g/(m3 s), located at the outer biofilm. The model is a practical tool that could be used, for example, to determine, for a given incident light intensity, water buffering, and CO2 in the liquid and membrane supply, the optimal biofilm thickness at which to initiate harvesting. The model provides a fundamental understanding of membrane carbonated algal biofilms as well as a tool to use the MB-PBR most effectively in practice.