Analysing the nonlinear dynamics of drill strings using control-based continuation

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Drilling provides access to the reservoirs in order to produce hydrocarbons. Some reservoirsrequire complex technical solutions, for example, to allow us to drill over 15km with longsections almost horizontal. A significant challenge is understanding and controlling thecomplex nonlinear dynamics of the drill string including undesirable effects such as whirl,which results in damaging shocks and vibrations. These shocks and vibrations in turn causemajor equipment failure, inefficiencies and lost operational time which can cost millions ofpounds per incident and billions of pounds annually to the industry.To understand the phenomena, numerous numerical models have been developed,however they do not predict the behaviour of individual cases. To refine and validate themodelling, experimental testing on scaled setups are conducted. However due to thecomplexity of the system, these tests are challenging to run as, for example, well-behavedsolutions and whirling solutions can exist under the same test conditions. We believe thatControl-based Continuation (CBC), an experiment-based approach which combinesfeedback control with numerical bifurcation analysis, has potential to rigorously investigatethe nonlinear physical phenomena associated with drill string behaviour in a way thatnumerical models and current experimental testing approaches cannot achieve.The overarching aim of the project is to determine how CBC can be applied to the existingexperimental rigs at Schlumberger's research lab in Cambridge and subsequentlyinvestigate the different mechanisms for instability and their nonlinear dynamics. This willrequire extensive modelling work and development of suitable control methods which areable to deal with noise and uncertainty. Furthermore, it is also likely to require furtheralgorithm development to allow CBC to deal with the noise and, possibly, time varyingeffects. Work will begin by building up experience with CBC on existing experiments atBristol and getting to grips with the methodology required. This will require carefulexperimentation, data processing and model building.