Carbon dioxide (CO₂) availability strongly affects the productivity of algal photobioreactors, where it is dynamically exchanged between different compartments, phases, and chemical forms. To understand the underlying processes, we constructed a nonequilibrium mathematical model of CO₂ dynamics in a flat-panel algal photobioreactor. The model includes mass transfer to the algal suspension from a stream of bubbles of CO₂-enriched air and from the photobioreactor headspace. Also included are the hydration of dissolved CO₂ to bicarbonate ion (HCO₃⁻) as well as uptake and/or cycling of these two chemical forms by the cells. The model was validated in experiments using a laboratory-scale flat-panel photobioreactor that controls light, temperature, and pH and where the concentration of dissolved CO₂, and partial pressure of CO₂ in the photobioreactor exhaust are measured. First, the model prediction was compared with measured CO₂ dynamics that occurred in response to a stepwise change in the CO₂ partial pressure in the gas sparger. Furthermore, the model was used to predict CO₂ dynamics in photobioreactors with unicellular, nitrogen-fixing cyanobacterium Cyanothece sp. The metabolism changes dramatically during a day, and the distribution of CO₂ is expected to exhibit a pronounced diurnal modulation that significantly deviates from chemical equilibrium.
