A reactor for conducting a process using supercritical water to upgrade a heavy hydrocarbon feedstock into an upgraded hydrocarbon product or syncrude with highly desirable properties (low sulfur content, low metals content, lower density (higher API), lower viscosity, lower residuum content, etc.) is described. The reactor is operable under continuous) semi-continuous or batch mode and is equipped with means to enable momentum, heat and mass transfer in and out of and within the reactor.