Modelling and controlling of drill string stick slip vibrations in an oil well drilling rig

Mitigating of drill string vibrations, plays a distinctive role in increase of rate of penetration and consequently decrease of the operation costs, prevent of severe damages to drill string and bit, increase of drilling operation quality and safety, and enhance the performances of the controllers. This study deals with modelling and controlling of drill string vibrations with focus on stick slip vibrations in vertical wells. The approach taken to subdivide the drill string into smaller torsional sections and model the complete system dynamically and employ the extracted torsional model to model the stick slip vibrations mathematically. To mitigate and or active control of stick slip vibrations, three architectures are developed and proposed, manipulation of the rotational speed, manipulation of the weight on bit, and increasing of the damping in the bottom of the drill string. The performance of each strategy is analysed individually as well as relative to each other, using a mathematical measure when the drill string length is divided into smaller torsional sections. By the aid of the simulations and mathematical measures, it is shown that manipulation of rotational speeds at the surface may not be an effective solution to reduce the stick slip vibrations, however manipulation of weight on bit and increasing of damping at the bottom of string can be two effective solutions to mitigate these kinds of vibrations. As a general conclusion, it is proved that the manipulation of bottom side drilling parameters is more effective than the manipulation of surface drilling parameters.