A circulating moving bed and process for separating a carbon dioxide from a gas stream is disclosed. The circulating moving bed can include an adsorption reactor and a desorption reactor, and a sorbent that moves through the two reactors. The sorbent can enter the adsorptive reactor and one end and move to an exit point distal to its entry point, while a CO₂ feed stream can enter near the distal point and move countercurrently through the sorbent to exit at a position near the entry point of the sorbent. The sorbent can adsorb the CO₂ by concentration swing adsorption and adsorptive displacement. The sorbent can then transfer to a regeneration reactor and can move countercurrently against a flow of steam through the regeneration reactor. The sorbent can be regenerated and the carbon dioxide recaptured by desorbing the carbon dioxide from the sorbent using concentration swing desorption and desorptive displacement with steam.

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