A method for the purification of waste water by the use of a heat-exchanger type reaction vessel composed of a plurality of inner tubes and a shell defining jointly with the outer peripheries of the inner tubes a passage for the flow of a heat transfer medium, which method comprises passing said waste water through said inner tubes and, at the same time, feeding a molecular oxygen-containing gas to the flow of said waste water thereby establishing contact between said waste water and said feed gas and consequently effecting wet oxidation of the impurities present in said waste water.
