TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: The feeding rate of the anaerobic digester with the organic matter is at least 4, preferably at least 5 kg of dry organic matter/cubic meter of digestion medium and per day. The volatile organic acids content of the aqueous liquid of the digestion medium is maintained to less than 3000, preferably less than 1500 mg HAc/l by the addition of a buffering reagent comprising sodium bicarbonate to the digestion medium. The addition of a buffering reagent comprising sodium bicarbonate is limited so that the sodium concentration of the aqueous liquid of the digestion medium is less than 60 g/l, preferably less than 6 g/l. The pH-value of the digestion medium falls below 6.5, a buffering reagent comprising calcium carbonate, and/or magnesium carbonate, and/or sodium carbonate, is introduced into the digestion medium to increase the pH-value up to at least 6.5, and then a buffering reagent comprising sodium bicarbonate is introduced into the digestion medium to increase the pH-value up to at least 6.90, preferably up to at least 7.35. In the process, a nutrient additive, preferably comprising bone char, is introduced into the digestion medium; and several anaerobic digesters are operated in series or in parallel. The organic matter amenable to anaerobic digestion feeding the anaerobic digester is withdrawn from a hydrolyser-reactor. The process further comprises: collecting the biogas containing methane; burning the biogas with a gas containing oxygen into an exhaust gas containing acidic gas matter, injecting sodium bicarbonate solid particles in the exhaust gas and carrying out a neutralization of part of the acidic gas matter of the exhaust gas into corresponding sodium salts and a partially purified exhaust gas; and collecting the sodium salts from the partially purified exhaust gas, where the part of the collected sodium salts is further used as a buffering reagent comprising sodium bicarbonate or used as a buffering reagent comprising calcium carbonate, and/or magnesium carbonate, and/or sodium carbonate added to the digestion medium. Preferred Components: The buffering capacity of the digestion medium is at most 500, preferably at most 400 mmole/l. The sodium concentration of the digestion medium is at least 0.6, preferably at least 2 g/l. The pH of the digestion medium is maintained at 6.90-7.90, preferably 7.35-7.75. The sodium bicarbonate of the buffering reagent comprising sodium bicarbonate is a powder in which the sodium bicarbonate powder has a particle size distribution such that at least 10%, preferably 50% of the particles have a diameter of more than 100 mu m. EXAMPLE - Three digesters were fed on a starting period of 28 days. The three digesters were filled initially with digestion medium coming from a biogas production unit using maize silage, grass silage, and pig and/or cow manure. The same amount and same composition of organic matter were used for feeding the three digesters, fed in once time on a daily basis. The daily feeding rate was remained constant on a week basis, i.e. same amount each day on a 7 days period. After the starting period of 28 days (4 weeks), the organic content feeding rate was progressively increased from 1 gram of organic content per liter of digestion medium and per day (equivalent to kg/m3/day) to reach 3.5 gram of organic content per liter and day (kg/m3/day) for each anaerobic digester of working volume of 10.5 L. Then the three digesters were fed above 4 g of organic content per liter and day (equivalent to kg/m3/day): 4.09 up to 6.01 kg/m3/day during 5 weeks (35 days). In a third period the feeding rate was decreased to 2.54 kg/m3/day and reincreased rapidly to 5.52 kg/m3/day to simulate variations of the feeding rates. Sodium bicarbonate was used as a buffering reagent to maintain a total inorganic carbon concentration of the aqueous liquid of the digestion medium during the anaerobic digestion above 9000 equivalent calcium carbonate mg/l and a buffering capacity of the digestion medium above 200 mmole/l. The quantities of sodium bicarbonate added to digesters, where the amount of sodium bicarbonate was 0.5 w.%, up to 1 w.% and down to 0.125 wt.% of the dry matter of the digestion medium and worked up to give biogas.