Abstract
Oil well instabilities cause production losses. One of these instabilities, referred to as the “casing-heading” is an oscillatory phenomenon occurring on gas-lift artificially lifted well. This behavior is well represented by a 2D model with a vector field that is not continuously differentiable across several switching curves. These correspond to switches in flow rate functions describing the valves. In order to interpret the observed oscillations as a limit cycle we use the Poincaré-Bendixon theorem with a detailed study of uniqueness of trajectories and the derivation of a positive invariant set. Apart from the general case considered here, an illustrative example is given. The vector field is explicited and a similar limit cycle appears.
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