The present application focuses on systems and methods that utilize one or more carbon dioxide (CO2) sorbent substrates and a swing cycle, e.g., a moisture swing cycle, to increase the partial pressure of the CO2 in a gaseous feedstock, which is delivered through a membrane to a bioreactor, such as a membrane carbonation photobioreactor. Such systems and processes offer an effective means for concentrating and capturing CO2 obtained from air and delivering the concentrated CO2 to a photobioreactor through a membrane.