An apparatus of hydrocarbon fuel reactors separates and purifies carbon dioxide (CO2). Interconnected fluidized beds are applied in chemical-looping combustion. A multi-stage reduction reaction is processed with iron-based oxygen carriers. Three reduction stages using the iron-based oxygen carriers are accurately and completely controlled. Each of the three stages is separately processed in an individual space. Oxygen in the iron-based oxygen carriers can be fully released. High-purity CO2 is obtained. Hydrogen can be produced as an option. Horizontal connection of three reduction reactors is changed into vertical one. An oxidation reactor is further connected. Thus, the whole structure occupies less area and effectively uses vertical space. Not only small space is effectively used; but also high-volume capacity is obtained. Each of the reactors has better geometry flexibility. The tandem reactor in each layer has less geometric influence and limitation. Therefore, each of the reactors can be resized on its own.