A system and method for separating and/or purification of CO2 gas from a CO2 feed stream is described. The system and method include a plurality of fixed sorbent beds, adsorption zones and desorption zones, where the sorbent beds are connected via valve and lines to create a simulated moving bed system, where the sorbent beds move from one adsorption position to another adsorption position, and then into one regeneration position to another regeneration position, and optionally back to an adsorption position. The system and method operate by concentration swing adsorption/desorption and by adsorptive/desorptive displacement.