Some naturally flowing oil wells will experience flow instabilities (heading) characterized by regular or irregular cyclic variations in tubing pressure and flow rate. To analyze this phenomena, the unsteady equations of motion for flow are solved by the LaPlace Transform method. This analysis produces a characteristic equation whose coefficients allow one to determine if a particular well is stable or unstable. If the well is unstable it is possible to use a feedback controller which varies the tubing head choke diameter to stabilize the well. By use of the root locus method, various combinations of proportional, derivative and integral controllers are shown to theoretically control some unstable wells.

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