Carbon dioxide (CO2) levels in the atmosphere have reached unprecedented levels due to increasing anthropogenic emissions and increasing energy demand. CO2 capture and utilization can aid in stabilizing atmospheric CO2 levels and producing carbon-neutral fuels. Utilizing hollow fiber membranes (HFMs) for microalgal cultivation accomplishes that via bubbleless gas-transfer, preventing CO2 loss to the atmosphere. Various lengths and geometries of HFMs were used to deliver CO2 to a sodium carbonate solution. A model was developed to calculate CO2 flux, mass-transfer coefficient (KL), and volumetric mass-transfer coefficient (KLa) based on carbonate equilibrium and the alkalinity of the solution. The model was also applied to a sparging system, whose performance was compared with that of the HFMs. Typically, HFMs are operated in closed-end mode or open-end mode. The former is characterized by a high transfer efficiency, while the latter provides the advantage of a high transfer rate. HFMs were evaluated for both modes of operation and a varying inlet CO2 concentration to determine the effect of inert gas and water vapor accumulation on transfer rates. For pure CO2, a closed-end module operated as efficiently as an open-end module. Closed-end modules perform significantly worse when CO2-enriched air was supplied. This was shown by the KLa values calculated using the model. Finally, a mass-balance model was constructed for the lumen of the membranes in order to provide insight into the gas-concentration profiles inside the fiber lumen. For dilute CO2 inlet streams, accumulation of inert gases -- nitrogen (N2), oxygen (O2), and water vapor (H2O) -- significantly affected module performance by reducing the average CO2 partial pressure in the membrane and diminishing the amount of interfacial mass-transfer area available for CO2 transfer.