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 (CO 2 ) directly to the base of phototrophic biofilms. The CO 2 supply increases growth rates by reducing carbon limitation and pH increases, but the counter-gradient supply of CO 2 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 CO 2 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/(m 2 d), compared to 0.49 ± 0.06 g/(m 2 d) for the control. Using data fitting, the experimental light attenuation coefficient ( k e ) and the half-saturation coefficient of light irradiance ( K I ) were 80,000 1/m and 5 W/m 2, respectively. Modeling showed that, for a well-buffered system, increasing the CO 2 fraction in the gas supply increased the growth rate but with diminishing returns: adding 5% CO 2 doubled the amount of growth, relative to the control, while adding 99% CO 2 only quadrupled the growth relative to the control. The beneficial effect of the CO 2 supply was smaller for thicker biofilms and lower light intensities. With a weak buffer, the CO 2 supply tended to acidify the biofilm interior, slowing growth rates at higher CO 2 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/(m 3 s), and it was located closer to the CO 2 supply from the membrane. The conventional reactor had a maximum growth rate of 0.086 g/(m 3 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 CO 2 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.