NOVELTY - The reactor comprises a vessel (1) with a sloping base (3), a feed device (9) for supplying the material to be fermented, discharge device (10) with an outlet in the vessel base, a biogas outlet (41), a vertical draft pipe (6) located inside the reservoir, a pump (5) connected to the pipe, a dam plate (7) located above the top end of the pipe for diverting an upward flow through the pipe towards the vessel peripheral wall (4), and a tubular heat exchanger (15) in the vessel peripheral wall.    USE - Used as a digester for treating sewage sludge, industrial effluent purification process sludge and/or organic waste produced by an industrial process, in order to form biogas (methane).    ADVANTAGE - Sludge with a relatively high water content of 6% or more can be treated with less risk of sedimentation which could otherwise deform the lances used for biogas recirculation. There is also less risk of the formation of a layer of floating debris comprising non or poorly fermentable materials such as wood, plastic and hair. Less foaming occurs, reducing the risk of the gas pipes becoming clogged up with sludge.    DETAILED DESCRIPTION - A fermentation reactor, especially for fermenting sewage sludge, industrial effluent purification process sludge and/or organic waste produced by an industrial process, comprises a vessel with a sloping base wall, a top wall and a peripheral wall; a feed device for supplying the material to be fermented to the vessel; a discharge device with an outlet opening located in or next to the vessel base; a gas outlet for biogas formed inside the vessel; a vertical draft pipe located inside the reservoir, having a first end next to the sloping part of the vessel base and a second end facing the top wall of the vessel; an axial pump located inside or connected to the pipe; a dam plate located above the second end of the pipe for diverting an upward flow through the pipe towards the vessel peripheral wall; and a tubular heat exchanger provided on or in the vessel peripheral wall for heat exchange with the vessel contents. INDEPENDENT CLAIMS are also included for the following:    (A) Second fermentation reactor comprising a vessel with a base wall, a top wall and a peripheral wall; and a support device located inside the vessel, connected to the base and top walls of the vessel in order to support the top wall above the base wall, comprising a vertical draft pipe having a first end facing the base wall and a second end facing the top wall;    (B) Third fermentation reactor comprising a vessel with a base wall, a top wall and a peripheral wall; and a preferably spirally-configured tubular heat exchanger provided on or in the vessel peripheral wall for heat exchange with the vessel contents; and    (C) Method for converting and/or modifying an existing tank into a fermentation reactor, comprising the steps of installing a sloping base wall, a feed device for supplying the material to be fermented to the vessel, a discharge device with an outlet opening located in or next to the vessel base, a vertical draft pipe located inside the reservoir and having a first end next to the sloping part of the vessel base and a second end facing the top wall of the vessel, an axial pump located inside or connected to the pipe, a dam plate located above the second end of the pipe for diverting an upward flow through the pipe towards the vessel peripheral wall, and a tubular heat exchanger provided on or in the vessel peripheral wall for heat exchange with the vessel contents, so long as the reactor is different to the first reactor described above.    DESCRIPTION OF DRAWING(S) - The figure shows a cross-section of the reactor.    cylindrical vessel made from concrete, steel or plastic; (1)    truncated cone-shaped top wall (2)    base wall (3)    peripheral wall (4)    Archimede's screw (5)    draft pipe (6)    dam wall (7)    sludge feed (9)    drainage pipe (10)    heat exchanger (15)    outlet for biogas (41)