A method and system for processing an input fuel gas and steam to produce separate CO2 and output fuel gas streams. The method comprises the steps of using a decarbonizer segment for reacting at least a solid sorbent with the fuel gas and steam to remove carbon from the input fuel gas and to produce the output fuel gas stream in an exhaust gas from the decarbonizer; using a calciner segment for reacting the solid sorbent from the decarbonizer segment therein to release the CO2 into the CO2 gas stream; wherein CO2 partial pressures and temperatures in the decarbonizer and calciner segments respectively are controlled such that the temperature in the decarbonizer segment is higher than the temperature in the calciner.