A method for upgrading a petroleum feedstock using a supercritical water petroleum upgrading system, the method comprising the steps of: introducing the petroleum feedstock into the supercritical water petroleum upgrading system; introducing a water into the supercritical water petroleum upgrading system; introducing an auxiliary feedstock into the supercritical water petroleum upgrading system; operating the supercritical water petroleum upgrading system such that the petroleum feedstock and the water combine to form a mixed petroleum feedstock; operating the supercritical water petroleum upgrading system such that the mixed petroleum feedstock and the auxiliary feedstock are introduced separately and simultaneously into a lower portion of an upflowing supercritical water reactor, where the auxiliary feedstock is introduced into the upflowing reactor such that a portion of a fluid contained within the upflowing reactor located proximate to the bottom of the upflowing reactor does not lack fluid momentum; operating the upflowing supercritical water reactor such that the fluid contained within the upflowing reactor is maintained at a temperature equal to or greater than the critical temperature of water, at a pressure equal to or greater than the critical pressure of water, and is moving in an upwards direction, such that supercritical water forms from the introduced water in the fluid contained within the upflowing reactor; operating the upflowing supercritical water reactor such that the upgraded and desulfurized petroleum product forms as the reaction product between the introduced petroleum feedstock and the supercritical water in the fluid contained within the upflowing reactor; operating the supercritical water petroleum upgrading system such that an upflowing reactor product fluid passes from an upper portion of the upflowing reactor, where the product fluid comprises the upgraded and desulfurized petroleum product, and where the amount of passing upflowing reactor product fluid is equivalent to the combined amount of the introduced mixed petroleum feedstock and the auxiliary feedstock; and operating the supercritical water petroleum upgrading system such that a gas-phase hydrocarbon product, the upgraded and desulfurized petroleum product and an aqueous-phase product are separately selectively separated from the upflowing reactor product fluid. introducing the petroleum feedstock into the supercritical water petroleum upgrading system; introducing a water into the supercritical water petroleum upgrading system; introducing an auxiliary feedstock into the supercritical water petroleum upgrading system; operating the supercritical water petroleum upgrading system such that the petroleum feedstock and the water combine to form a mixed petroleum feedstock; operating the supercritical water petroleum upgrading system such that the mixed petroleum feedstock and the auxiliary feedstock are introduced separately and simultaneously into a lower portion of an upflowing supercritical water reactor, where the auxiliary feedstock is introduced into the upflowing reactor such that a portion of a fluid contained within the upflowing reactor located proximate to the bottom of the upflowing reactor does not lack fluid momentum; operating the upflowing supercritical water reactor such that the fluid contained within the upflowing reactor is maintained at a temperature equal to or greater than the critical temperature of water, at a pressure equal to or greater than the critical pressure of water, and is moving in an upwards direction, such that supercritical water forms from the introduced water in the fluid contained within the upflowing reactor; operating the upflowing supercritical water reactor such that the upgraded and desulfurized petroleum product forms as the reaction product between the introduced petroleum feedstock and the supercritical water in the fluid contained within the upflowing reactor; operating the supercritical water petroleum upgrading system such that an upflowing reactor product fluid passes from an upper portion of the upflowing reactor, where the product fluid comprises the upgraded and desulfurized petroleum product, and where the amount of passing upflowing reactor product fluid is equivalent to the combined amount of the introduced mixed petroleum feedstock and the auxiliary feedstock; and operating the supercritical water petroleum upgrading system such that a gas-phase hydrocarbon product, the upgraded and desulfurized petroleum product and an aqueous-phase product are separately selectively separated from the upflowing reactor product fluid.