Characterization of CO₂ flux through hollow-fiber membranes using pH modeling

CO₂ must be delivered efficiently during large-scale microalgal cultivation. Bubbleless mass-transfer via diffusion through hollow-fiber membranes (HFM) can achieve much higher CO₂-transfer efficiency than traditional sparging systems. This study developed and used a model to compute accurate values for the CO₂ flux (J_CO2), overall mass-transfer coefficient (K_L), and overall volumetric mass-transfer coefficient (K_La) based on the rate of change of pH in batch experiments. A composite HFM comprised of two macroporous polyethylene layers and a nonporous polyurethane layer was tested for CO₂ transfer to a sodium carbonate solution using a range of total pressures, inlet CO₂ concentrations, and open-end versus closed-end modes of operation. The model accurately computed J_CO2 and K_La for pH values above 8. Key trends are that (i) J_CO2 and K_La increased with increasing average inlet CO₂ partial pressure; (ii) open-end HFMs performed better than closed-end HFMs when the supplied CO₂ was less than 100%; and (iii) the available membrane area used for CO₂ mass-transfer decreased as the inlet CO₂ partial pressure decreased due to depletion of CO₂ inside the membrane, especially for closed-end HFMs, since inert gases could not be vented.