command to gradually open the choke 9 to a predetermined value so that the hydrocarbons transported achieve the minimum flowrate qm the controller 18 waits for a length of time that has been predetermined by calculating the time required for a sweep through the pipe 6 to ensure that the minimum flowrate qm for transported hydrocarbons becomes established the start up phase then comprises a step of ramping up to transport speed during which step the controller 18 determines an instability factor f for the pressure pf in the lower section 7 of the pipe 6 using the following formula pfmax represents the maximum value of the pressure pf over a sliding 5 minute period pfmin represents the minimum value of the pressure pf over a sliding 5 minute period pfmean represents the temporal mean value of the pressure pf over a sliding 5 minute period the controller 18 compares f with two thresholds f1 and f2 which have been predetermined by calculating characteristic fluctuations of an acceptably stable flow f2 being higher than f1 if f is lower than f1 which is equal for example to 50 and if the flowrate of transported hydrocarbons estimated from the aperture of the choke 9 and from the difference in pressures measured by the sensors 14 and 21 is lower than a target production flowrate set by an operator the controller 18 increases the aperture of the outlet choke 9 by a predetermined amount for example 2 of the maximum aperture if f is lower than f1 and.