A rotary moving bed and process for separating a carbon dioxide from a gas stream is disclosed. The rotary moving bed can have a rotational assembly rotating on a vertical axis, and a plurality of sorbent cells positioned horizontally to the axis of rotation that fills a vertical space in the moving bed, where the sorbent cells adsorb the carbon dioxide by concentration swing adsorption and adsorptive displacement. The sorbent can be regenerated and the carbon dioxide recaptured by desorbing the carbon dioxide from the sorbent using concentration swing adsorption and desorptive displacement with steam. The gas flows in the system flow in a direction horizontal to the axis of rotation and in a direction opposite the rotational movement of the sorbent cells.