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

钻井提供了进入储层的通道，以生产碳氢化合物。一些钻探需要复杂的技术解决方案，例如，允许我们在长段几乎水平的情况下钻探超过15公里。一个重大的挑战是理解和控制复杂的非线性动力学的钻柱，包括不希望的影响，如涡动，这会导致破坏性的冲击和振动。这些冲击和振动反过来又会导致主要设备故障、效率低下和运营时间损失，每次事故造成数百万英镑的损失，每年给行业带来数十亿英镑的损失。为了理解这些现象，人们开发了许多数值模型，但它们无法预测个别情况的行为。为了完善和验证themodelling，实验测试规模设置进行。然而，由于系统的复杂性，这些测试具有挑战性，例如，在相同的测试条件下可能存在良好的解决方案和旋转解决方案。我们认为，基于控制的连续（CBC），一个基于实验的方法相结合的反馈控制与数值分岔分析，CBC具有严格研究与钻柱行为相关的非线性物理现象的潜力，这是数值模型和当前实验测试方法无法实现的。该项目的首要目标是确定CBC如何应用于斯伦贝谢研究的现有实验钻机实验室在剑桥，并不断研究不同的机制不稳定和他们的非线性动力学。这将需要大量的建模工作和开发合适的控制方法，能够处理噪声和不确定性。此外，它也可能需要进一步的算法开发，以允许CBC处理噪声和可能的时变效应。工作将开始通过建立经验与CBC现有的实验在布里斯托尔和获得掌握所需的方法。这需要仔细的实验、数据处理和模型建立。

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.