TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The biomethanation reactor comprises packed column, bubble column with hole intermediate shelves, bubble tray column, packed bed column, multistage fin column, gas lift cascade, gas-lift loop reactor with perforated plates, jet loop reactor with perforated plates or spinning cone column, preferably packed column, bubble column with hole intermediate shelves, bubble tray column or packed bed column. In the biomethanation reactor porous carrier body, preferably packages made of porous plastic material or porous ceramic are used as a material transfer surface, preferably packings, random packings, pellets or beads, whose pores serve as settling areas for methane bacteria for their immobilization. A segment mounting is used as the biomethanation reactor in a biogas fermenter or a fermentation residue storage, which supplies biogas or carbon dioxide-containing exhaust gas of biogas treatment and hydrogen, where biomethane is discharged from the methane-enriched gas.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: The method further comprises adding precipitating chemicals for precipitating harmful gases comprising ammonia and hydrogen sulfide present in the biogas, to the bacterial suspension from the main fermenter or the secondary fermenter or the fermentation residue before their introduction into the biomethanation reactor. The method comprises supplying the gas mixture to the packed column for intermediate compression, supplying the exhaust gas of the packed column to the bubble column for intermediate compression, and supplying the exhaust gas of the bubble column to the bubble tray column. The reactor columns are designed such that the material transfer rate for hydrogen in each column is adapted to reaction rate of the biocatalysts. The bacterial suspension outflowing from the biomethanation reactor is recycled for increasing trickling density in the reactor. The bacterial suspension outflowing from the biomethanation reactor is separated in a microfiltration step into a solids-free liquid partial stream and a bacteria-containing suspension concentrate stream, where the concentrate stream is recycled to the input of the biomethanation reactor, which increases bacterial density in the biomethanation reactor. The method comprises superstoichiometrically supplying hydrogen to the biomethanation reactor for increasing material transfer rate of hydrogen with respect to carbon dioxide, where unreacted hydrogen is separated from the product gas by membrane separation, mixed with the biogas and regeneratively generated hydrogen, and is recycled to the biomethanation reactor. The bacterial suspension is supplied as a biocatalyst to the biomethanation reactor, which is produced by separating the coarser solid phase from the digestate. In the method valuable metabolic products of the methane bacteria, preferably cobalamin (vitamin B12) are obtained from the suspension discharging from the biomethanation reactor. EXAMPLE - No suitable example given.