Methods and devices for combusting a carbonaceous fuel in an oxy-combustion fluidized bed reactor involving controlling the local oxygen content within the oxy-combustion reactor to specified levels. The carbonaceous fuel and an oxygen-containing gas are introduced into a fluidized bed reactor and eluted through a fluidized bed of an inert material, dolomite or a combination thereof to combust the fuel and oxygen to produce at least CO2 and steam. The oxygen-containing gas is a mixture of oxygen, recycled CO2 and steam and has sufficient oxygen added to the recycled CO2 and steam that the mixture contains 7-20 mole % oxygen. The carbonaceous fuel and the oxygen-containing gas are introduced into the fluidized bed at a location in sufficiently close proximity to each other to avoid producing a reducing atmosphere at the location. At least a portion of the produced CO2 and steam are recycled to the reactor.