NOVELTY - The process comprises supplying an electrical energy in a first mode to a source of hydrogen to produce hydrogen, and supplying thermal energy to a carbon dioxide source (2) to produce carbon dioxide. In the first mode, a part of the supplied thermal energy is produced by partial conversion of a part of the supplied electric energy. A further part of the thermal energy is provided by heat generated in a catalytic methanation and/or a production of hydrogen process. The thermal energy is supplied to different collectors with different temperature levels.    USE - The process is useful for the catalytic methanation of hydrogen from a source of hydrogen and a carbon dioxide-containing feed gas from a carbon dioxide source to produce a methane-rich product gas (claimed).    ADVANTAGE - The process allows the catalytic methanation of hydrogen in a simple and energy efficient manner.    DETAILED DESCRIPTION - The process comprises supplying an electrical energy in a first mode to a source of hydrogen to produce hydrogen, and supplying thermal energy to a carbon dioxide source (2) to produce carbon dioxide. In the first mode, a part of the supplied thermal energy is produced by partial conversion of part of the supplied electric energy. A further part of the thermal energy is provided by heat generated in a catalytic methanation and/or a production of hydrogen process. The thermal energy is supplied to different collectors with different temperature levels. The further part of the thermal energy is provided to a first temperature level, and the electrical energy is provided to a second temperature level higher than the first temperature level. The further part of the thermal energy is provided to a third temperature level, and the electrical energy is provided to a fourth temperature level higher than the third temperature level. The fourth temperature level is equal to the first temperature level. A change between the first and second modes is carried out for one day. The carbon dioxide source comprises a raw biogas separator for separating the carbon dioxide, an amine scrubber, and a biogas plant (15). The thermal energy is supplied, to the collector, from the separator, the amine scrubber, primary fermenters, secondary fermenter and/or sanitization of the biogas plant. A methane-rich product gas is generated as a signal by the separator, and is fed into an existing gas network (20). The thermal energy is supplied in the second mode by combustion of a fuel gas, production of the raw biogas from the biogas plant and/or bio-methane from a biogas processing plant. An INDEPENDENT CLAIM is included for a methanation system.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic view of a process for catalytic methanation of hydrogen.    Electrolyzer (1)    Carbon dioxide source (2)    Biogas plant (15)    Existing gas network (20)    Control unit. (30)