This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal configuration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit-rock interaction model are taken into account using a parametric probabilistic approach. Numerical simulations have shown that the mechanical system of interest has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits.

中文翻译：

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水平钻柱非线性随机动力学的计算建模

这项工作旨在分析水平配置中钻柱的非线性随机动力学。为此，它考虑了具有转动惯量和剪切变形效应的梁理论，该理论能够再现梁所经历的大位移。模型中还考虑了由于梁/钻孔壁横向冲击引起的摩擦和冲击效应，以及钻头-岩石相互作用引起的力和扭矩。使用参数概率方法考虑了比特-岩石相互作用模型的不确定性。数值模拟表明，感兴趣的机械系统具有非常丰富的非线性随机动力学，会产生钻头反弹、粘滑和横向冲击等现象。一项旨在最大限度提高钻井过程效率的研究，展示了不同的钻柱平移和旋转速度。此外，这项工作提出了两个优化问题的定义和解决方案，一个是确定性的，一个是稳健的，其目标是在尊重其结构限制的情况下最大限度地提高钻柱进入土壤的速度。