Mathematical model of the CO2 solubilisation reaction rates developed for the study of photobioreactors

The transfer of CO2 between the gas and liquid phases is one of the most important processes that occur during cultivation of microalgae in photobioreactors. A key factor that influences the rate of mass transfer is the concentration of CO2 in the liquid phase, which, in turn, depends on the rates of the reactions involved in CO2 solubilisation. This work presents a mathematical model for the rate of these solubilisation reactions with correlations that allow the calculation of the model parameters at temperatures from 5 degrees C to 40 degrees C. The model was validated using data of CO2 mass transfer from the literature obtained with two experimental systems: a bubble column for CO2 absorption and a flat-panel photobioreactor. The model was further used to show that the increase in the rate of CO2 absorption that occurs at higher pH values is due to increased consumption of CO2(aq) in the solubilisation reactions and not to an increase in k(L)a. The pH decreases as CO2 is solubilised, therefore, when pH is controlled, the mass transfer rate is higher than it would be without pH control. Our model can be used as a tool to guide the operation, control and scale-up of photobioreactors for the cultivation of microalgae.