A method for upgrading a continuously flowing process stream including heavy crude oil (HCO), comprising: conveying the process stream continuously through a fluid flow path in a downstream direction, the flow path including a reactor; the reactor receiving the process stream in combination with water, at an inlet temperature within a range of about 60 °C to about 200 °C; the reactor including one or more process flow tubes defining an aggregated interior cross-sectional dimension in a plane extending transversely to the downstream direction therethrough, the one or more flow tubes having a combined length of at least about 30 times the aggregated interior cross-sectional dimension; the reactor applying heat to the process stream flowing therethrough, to progressively heat the process stream from the inlet temperature at an upstream portion of the reactor, to an outlet temperature T(max)1 within a range of between about 260 °C to about 400 °C at a downstream portion of the reactor; the reactor maintaining the process stream at a pressure within a range of about 103 to about 207 bar (about 1500 to about 3000 psia), sufficient to ensure that the process stream remains a single phase at T(max) 1; selectively adjusting by means of a controller a rate of flow of the process stream through the reactor to maintain a total residence time of the process stream in the reactor of greater than about 1 minute and less than about 25 minutes; wherein said rate of flow, said flow tube lengths, and said application of heat, minimize or prevent coke formation; and separating water, light hydrocarbons (LHC) and any other volatile components having boiling points at atmospheric pressure below a BP(LHC1) value of about 280 °C, by means of a recovery unit disposed downstream of the reactor in the fluid flow path and including one or more separators, wherein the process stream retains heavy hydrocarbons (HHC) components having boiling points higher than BP(LHC1) to form an HHC process stream. conveying the process stream continuously through a fluid flow path in a downstream direction, the flow path including a reactor; the reactor receiving the process stream in combination with water, at an inlet temperature within a range of about 60 °C to about 200 °C; the reactor including one or more process flow tubes defining an aggregated interior cross-sectional dimension in a plane extending transversely to the downstream direction therethrough, the one or more flow tubes having a combined length of at least about 30 times the aggregated interior cross-sectional dimension; the reactor applying heat to the process stream flowing therethrough, to progressively heat the process stream from the inlet temperature at an upstream portion of the reactor, to an outlet temperature T(max)1 within a range of between about 260 °C to about 400 °C at a downstream portion of the reactor; the reactor maintaining the process stream at a pressure within a range of about 103 to about 207 bar (about 1500 to about 3000 psia), sufficient to ensure that the process stream remains a single phase at T(max) 1; selectively adjusting by means of a controller a rate of flow of the process stream through the reactor to maintain a total residence time of the process stream in the reactor of greater than about 1 minute and less than about 25 minutes; wherein said rate of flow, said flow tube lengths, and said application of heat, minimize or prevent coke formation; and separating water, light hydrocarbons (LHC) and any other volatile components having boiling points at atmospheric pressure below a BP(LHC1) value of about 280 °C, by means of a recovery unit disposed downstream of the reactor in the fluid flow path and including one or more separators, wherein the process stream retains heavy hydrocarbons (HHC) components having boiling points higher than BP(LHC1) to form an HHC process stream. <EOS>