A system and method is provided for upgrading a continuously flowing process stream including heavy crude oil (HCO). A reactor receives the process stream in combination with water, at an inlet temperature within a range of about 60° C. to about 200° C. The reactor includes one or more process flow tubes having a combined length of about 30 times their aggregated transverse cross-sectional dimension, and progressively heats the process stream to an outlet temperature T(max)1 within a range of between about 260° C. to about 400° C. The reactor maintains the process stream at a pressure sufficient to ensure that it remains a single phase at T(max)1. A controller selectively adjusts the rate of flow of the process stream through the reactor to maintain a total residence time of greater than about 1 minute and less than about 25 minutes.