NOVELTY - Treating (m1) organic material by digestion involves (A) digesting the organic material to produce volatile organic acids ; (B) creating conditions such that at least some of the volatile organic acids enter a gaseous state; and (C) extracting at least some of the volatile organic acids from the gaseous state.    USE - For treating organic material for producing organic acid (particularly acetic acid) useful in e.g. methanogenesis (claimed), as feed stock for reacting the acetic acid with an alcohol to form an ester useful as liquid biofuel, dehydrated to acetic anhydride, as a liquid fuel carrier being catalytically converted to gaseous components immediately before combustion in a combustion engine or fuel cell, as a commodity chemical (glacial acetic acid); and for treating organic biomass or waste material such as sewage or algae.    ADVANTAGE - The method provides acetic acid which is a purer substrate than organic material slurry. Using acetic acid as a substrate limits, and prevents the requirement for large volumes of biomass (organic material) slurry to be transferred between digester vessels when two-phase anaerobic digestion is undertaken, therefore simplifies the equipment required, as a gaseous substrate (and possibly smaller volumes of slurry) is the only components which need to be transferred between the first and second digester vessels. The process allows methanogenesis to occur without the requirement for slurry, or to utilize a smaller volume of slurry which is optimized for methanogenesis, which allows conditions for methanogenesis to be optimized, and maintained optimizing methane production, thus allow retrofitting of the anaerobic digesters to incorporate the method, and to increase the efficiency of methane production, which significantly, increase their efficiency, while being a cheap and easy modification. In the method, no additional chemicals are involved, and the gas used to purge the digester contents of volatile acids is the reactor gas itself which is recycled after the volatile acids have been stripped or condensed out. Other gaseous reactor constituents remains in the gas phase and is recycled to the reactor. In the reactor, once the condition is optimized, the reaction occurs at a steady state and does not require chemical adjustment, because the volatile acid is removed from the reactor as fast as it is formed, and the gas purging avoids the need to stir the reactor to compensate for the energy requirement of purging. The method can be retrofitted to two stage anaerobic rectors or digesters allowing the complete separation of the methanogenic stage from the hydrolysis and acetogenic stages of anaerobic digestion, which allow better optimization of both stages. Gas phase separation is inherently simpler and cleaner than solid, liquid or salt separation or extraction. Gas phase extraction does not require the multistage reactors and clarifiers, and centrifuges and filters. In the gas phase extraction, the desired products do not mix with other reactor liquors as is the case for counter current liquid extraction.    DETAILED DESCRIPTION - INDEPENDENT CLAIMS are included for the following:    (1) a digester configured to operate according to the method (m1); and    (2) methanogenesis (m2) involving introducing acetic acid as a substrate into a digestive vessel for the second phase of anaerobic digestion.