Process for the production of a biogas containing methane from an organic matter amenable to anaerobic digestion comprising feeding an anaerobic digester with the organic matter, said anaerobic digester containing a digestion medium comprising microorganisms capable of digesting said organic matter, wherein the total inorganic carbon concentration of the digestion medium is maintained above 9000 mg of equivalent CaCO3/l and the buffering capacity is maintained above 200 mmol/l by the addition of a buffering reagent comprising sodium bicarbonate to the digestion medium.