NOVELTY - Processing a feed material comprises: forming and maintaining a brine phase with water and at least one soluble inorganic compound; creating a pressure on the brine phase of less than 500 bar; heating the brine phase to greater than 374 degrees C, with an established density for the brine phase of greater than 700 kg/m; and introducing the feed material into the brine phase for reaction with it to produce an effluence.    USE - The method is useful for processing a feed material (claimed) for converting waste materials (biomass, municipal sludge and biosolids, coal, and waste plastic) into innocuous mineral byproducts.    ADVANTAGE - The method: allows high reaction rates to be attained in a dense medium at supercritical water temperatures without the need for excessively high pressures; enables homogeneous catalysis at supercritical temperatures since catalytic salts can be solubilized along with the reactants; avoids the use of precious metal catalysts; utilizes soluble or insoluble additives to protect catalysts from poisoning; utilizes a dense phase yielding high heat transfer rates, facilitating rapid heatup of feed materials and reducing the opportunity for tar and char formation; utilizes high levels of soluble salts to prevent deposition of low solubility salts, thus reduces the capital and operating costs associated with a high-pressure process; and provides combination of high reaction rates and high density reaction phase which allows small size reactors to be used.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is also included for an apparatus for processing a feed material, comprising: a source of the feed material; a reactor vessel formed with a chamber for holding a brine phase therein, where the brine phase is maintained at a temperature of greater than 374 degrees C, under a pressure of less than 500 bar, with an established density of greater than 700 kg/m; a level controller to maintain the brine level at a point corresponding to at least half of the reactor vessel volume; a means for introducing the feed material into the brine phase, for reaction with it to produce an effluence; and an exit pipe connected in fluid communication with the chamber for removing the effluence from it.