You accumulate CO2 via CaO and then release it via heat provided from the thermal system to go back to CaO. The CO2 is then turned into hydrocarbons. Closed loop. The infrastructure is already in place for hydrocarbons at least until we get to a hydrogen infrastructure. Then you can carbon capture till your heart's content.
https://en.m.wikipedia.org/wiki/Circumpolar_deep_water