NOVELTY - The methanation process comprises converting a flue gas (15) of a carbonaceous fuel (3), from a power plant, attached with a water/steam cycle derived, branched off or recovered in the methanation of a carbon dioxide (CO2) gas (8) to methane (21). In the methanation of CO2 to methane, the produced waste heat thermal energy is at least partially coupled into a mass and/or heat energy flow. The mass and/or heat energy flow is subjected to a CO2 gas treatment in a combustion chamber (17) of a steam generator (18) of the power plant and in a power plant flue gas treatment system.    USE - The process is useful for methanation of CO2 gas from an industrial plant such as a metallurgical plant, a chemical plant (all claimed) and a steel plant.    ADVANTAGE - The process ensures economic and energy-efficient methanation of CO2 gas from the industrial plant.    DETAILED DESCRIPTION - The methanation process comprises converting a flue gas (15) of a carbonaceous fuel (3), from a power plant, preferably a carbonaceous gas-fired power plant, attached with a water/steam cycle derived, branched off or recovered in the methanation of a carbon dioxide (CO2) gas (8) to methane (21). In the methanation of CO2 to methane, the produced waste heat thermal energy is at least partially coupled into a mass and/or heat energy flow. The mass and/or heat energy flow is subjected to a CO2 gas treatment or CO2 treatment in a combustion chamber (17) of a steam generator (18) of the power plant and in a power plant flue gas treatment system. One or more gaseous by-products or waste products of an industrial plant, preferably a chemical plant or a metallurgical plant, in the form of a gas mixture containing a blast furnace gas and/or a coke oven gas containing the blast furnace gas, as the carbonaceous fuel is supplied to the combustion chamber of the steam generator. The power plant is formed as an integral part of the industrial plant. A portion of the mass and/or energy flows is integrated in the industrial plant. A portion of by-product or waste from a production process of the industrial plant, preferably gaseous carbonaceous substance or flow is supplied as the carbonaceous fuel into the combustion chamber. A part of the carbonaceous fuel, preferably the carbon-containing substance or flow in the combustion chamber is subject to the methanation after the CO2 gas treatment. In the CO2 gas treatment, the CO2 gas in the power plant flue gas treatment system is deposited by a post-combustion (carbon) capture process by CO2 gas scrubbing with an absorbent. In the methanation and/or CO2 gas treatment, the power plant flue gas treatment system is partially or temporarily operated with surplus power from an electric grid. In the methanation, hydrogen is partially or temporarily generated by an integrated electrolysis in the industrial plant. The electrolysis is partially or temporarily operated with the surplus power from the electric grid. In the methanation, hydrogen from the blast furnace gas is separated by a pressure swing absorption or a membrane separation. A recirculated power plant flue gas as the mass and/or energy flow is supplied into the combustion chamber. The produced methane is fed into a natural gas network and/or stored in a container. An INDEPENDENT CLAIM is included for a power plant or incinerator.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a power plant.    Carbonaceous fuel (3)    CO2 gas (8)    Flue gas (15)    Combustion chamber (17)    Steam generator (18)    Methane. (21)