A Nonlinear Dynamic Model for Characterizing the Downhole Motions of the Sidetracking Tool in a Multilateral Well

Xiuxing Zhu, Weixia Zhou, Yujian Lei, Peng Jia, Shifeng Xue (), Bo Zhou () and Yuanbo Xia
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Xiuxing Zhu: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Weixia Zhou: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Yujian Lei: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Peng Jia: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Shifeng Xue: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Bo Zhou: College of Pipeline and Civil Engineering, China University of Petroleum (East China), Qingdao 266580, China
Yuanbo Xia: CNPC Tianjin Bo-Xing Engineering Science &Technology Co., Ltd., Tianjin 300451, China

Energies, 2023, vol. 16, issue 2, 1-21

Abstract: It is of practical interest to investigate the mechanical behaviors of a sidetracking tool system and to describe the sidetracking tool’s vibration mechanical response, as this can provide an important basis for evaluating and optimizing the tool structure and effectively controlling the profile of the sidetracking window. In this article, three nonlinear dynamic models with ten, six, and two degrees of freedom, respectively, are established using the Lagrange method to characterize the behavior of the sidetracking tool. It should be noted that in these models, the axial, lateral, and torsional vibration of the tool system are fully coupled. The process of the sidetracking tool mills in the casing-pipe wall is divide into three typical stages, i.e., the window mill, pilot mill, and watermelon mill grinding the casing, respectively. The dynamic response of the three stages is studied to more effectively analyze the influence of the sidetracking tool vibration deformation on the window width. The Runge–Kutta method, which is easy to implement, is applied to solve the supposed nonlinear dynamic model, and some useful findings are as follows. The effects of sidetracking tool vibrations at different stages on window widening size are illustrated quantitatively. The vibration trajectory pattern of the sidetracking tool is different from that of the conventional drilling tool due to the influence of the whipstock, which changes from the general whirling motion pattern to the X reciprocating pattern, and the vibration amplitude decreases. Due to the influence of the tool’s lateral amplitude, the window profile is widened. The widened window size of the window mill and the pilot mill are 3.30 mm and 2.74 mm, respectively, and the extended window size of the watermelon mill is 0.07 mm, while the maximum window width formed by the sidetracking tool is 374.34 mm. This work proposes, for the first time, the coupled vibration model of the sidetracking tool system, which is helpful to better understand the nonlinear dynamic effects of the sidetracking tool, laying the foundation for the optimization of the sidetracking parameters.

Keywords: window milling; sidetracking tool; nonlinear dynamics; vibration; window profile (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2023
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