A method and apparatus for upgrading a petroleum feedstock with supercritical water are provided. The method includes the steps of: (1) heating and pressurizing a petroleum feedstock; (2) heating and pressurizing a water feed to above the supercritical point of water; (3) combining the heated and pressurized petroleum feedstock and the heated and pressurized water feed to produce a combined feed; (4) supplying the combined feed to a hydrothermal reactor to produce a first product stream; (5) supplying the first product stream to a post-treatment process unit to produce a second product stream; and (6) separating the second product stream into a treated and upgraded petroleum stream and a water stream.