NOVELTY - A method for processing and purifying a fluid medium (A) forming two phases with water involves washing out water-soluble components from (A) by forced cocurrent, countercurrent or vortex mixing with steam (optionally mixed with gas), supplied under pressure. Two separate phases are formed, i.e. an aqueous phase containing bonded water-soluble components and a processed (A) phase, which is drawn off.    USE - The medium (A) to be purified is specifically a vegetable oil (e.g. rape, cottonseed, jatropha oil, olive, soya or palm oil), pyrolysis oil or processed fatty acid alkyl ester (obtained by transesterifying animal and/or vegetable oils and/or fats) (all claimed). The process and apparatus are useful in producing biodiesel from these oils and fats.    ADVANTAGE - The purification process can be carried out inexpensively with low energy consumption, using simple, reliable apparatus with no moving parts.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a corresponding plant for treating (A) with steam, comprising a reactor (1) with an inlet tube (3) for (A), an inlet tube (6) for steam (optionally mixed with gas), a tube (5) for drawing off treated (A) and a tube (4) for drawing off aqueous phase. The reactor contains a device (8) for introduction of steam (optionally mixed with gas) at the endpiece (7) of the inlet tube (6), having at least two truncated conical or truncated pyramidal shaped guiding devices (10). A gap is formed between the edge of the upper opening of the guiding device and the introduction device. The end of the (A) inlet tube (3) is in the form of a funnel (13), and is located below the introduction device.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic diagram of a reactor for processing a medium consisting of fatty acid alkyl esters.    Reactor (1)    Reactor wall (2)    Medium Inlet tube (3)    Outlet tube (4)    Treated medium abstraction tube (5)    Steam inlet tube (6)    End-piece (7)    Sintered metal tube, as introduction device (8)    Reactor base support (9)    Guiding device (10)    Supporting frame (11)    Spacer (12)    Funnel (13)    Flange connection (14)    Support for filling state display (15)