A method for transforming selected renewable oils and fats, and optionally polyester waste plastic materials, into a plurality of reaction products via supercritical water is disclosed. The method comprises: conveying the selected oils and fats material through an extruder, wherein the extruder is configured to continuously convey the selected oils and fats material to a supercritical fluid reaction zone; injecting hot compressed water into the supercritical fluid reaction zone, while the extruder is conveying the selected oil and fats material into the supercritical fluid reaction zone so as to yield a mixture; retaining the mixture within the reaction zone for a period of time sufficient to yield the plurality of reaction products. The reaction zone may be characterized by a tubular reactor having an adjustably positionable inner tubular spear, wherein the tubular reactor and the inner tubular spear further define an annular space within the reaction zone, and wherein the mixture flows through the annular space and into a reaction products chamber.