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

钻井为开采碳氢化合物提供了进入储层的途径。一些水库需要复杂的技术解决方案，例如，允许我们钻超过15公里的长断面几乎是水平的。一个重要的挑战是理解和控制钻柱的复杂非线性动力学，包括导致破坏性冲击和振动的不良影响，如旋转。这些冲击和振动反过来又会导致主要设备故障、效率低下和作业时间损失，每次事故可能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，已经开发了许多数值模型，但是它们不能预测个别情况的行为。为了完善和验证模型，在比例装置上进行了实验测试。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，基于控制的延拓（CBC）是一种将反馈控制与数值分岔分析相结合的基于实验的方法，有可能严谨地研究与钻柱行为相关的非线性物理现象，这是数值模型和当前实验测试方法无法实现的。该项目的总体目标是确定如何将CBC应用于斯伦贝谢剑桥研究实验室现有的实验平台，并随后研究不同的不稳定机制及其非线性动力学。这将需要广泛的建模工作和开发合适的控制方法，这些方法可以处理噪声和不确定性。此外，还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。工作将首先在布里斯托尔现有的实验中积累CBC的经验，并掌握所需的方法。这将需要仔细的实验、数据处理和模型构建。

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.