Abstract: An anaerobic waste water purification upflow reactor, includes a vessel (1) containing biomass granules, elements for injecting influent into a lower part of the vessel, a three-phase separator (3) for separating gas, liquid and solid, which is located in an opposite upper part of the vessel, and elements for collecting effluent out of an upper part of the three-phase separator. The three-phase separator (3) includes two solid/liquid settlement zones (12, 13) positioned one above the other in the direction of the upflow (9), above a lower zone provided with gas separation element (10). The reactor includes effluent recirculation elements including element for extracting effluent from the vessel between the two settlement zones and element for re-injecting the extracted effluent into a lower part of the vessel (1).