A method is provided for the stabilization and control of the two-phase flow of hot fluid containing water issuing from the top of an upwardly rising conduit or riser of a horizontal oil-production well. The fluid enters the bottom of the riser at a temperature higher than the saturation temperature of water at the conditions prevailing at the top of the riser. A first mass rate flow controller is coupled to a mass rate flow detector at the top of the well for controlling mass flow at a substantially constant rate over a short time interval. Signals indicative of the optimal flow rate for the process are input to a second controller. The second controller adjusts the mass flow rate setpoint of the first controller. The second controller has a time constant significantly longer than that of the first controller. Thus, the mass rate of hot fluid is controlled at a substantially constant mass rate over the short term, thereby stabilizing two-phase flow, and is adjusted over the longer term to control the flow of fluid at an optimal rate.