Robust Approach Estimates Effective Length for Lateral Vibrations
Authors: Carpenter Chris 
Published: December 2024

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This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 217755, “To What Extent Can the Notion of an Effective Length Be Reliable To Assess the BHA Lateral Behavior?” by Mohamed Mahjoub, SPE, Ngoc-Ha Dao, SPE, and Khac-Long Nguyen, Helmerich & Payne, et al. The paper has not been peer reviewed.

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Many models in the industry use the notion of an effective length to make predictions about the bottomhole assembly (BHA). A criterion is chosen to cut the drillstring at a certain distance from the bit and use only that part for the computations. Though this method is computationally efficient, no consensus exists regarding what criteria should be chosen or a perfect method regarding the computation of that length. This study aims to compensate for the lack of in-depth analysis on this important subject. It shows the importance of understanding the strengths and limits of frequency-based models compared with more-complex time-domain modeling.

Introduction
The notion of effective length is widely used in the industry for various types of drillstring mechanical models, whether for directional purposes, survey corrections, or assessment of vibration behavior of the BHA. The drillstring is cut at a given distance from the bit, known as the effective length (see example in Fig. 1, where an approximately 45-m effective length is used for a computation to predict the BHA build and turn rates). Ideally, the choice of this length should reflect the independence of what is happening close to the bit from the rest of the drillstring. This approach has the obvious advantage of reducing computation time significantly but has the shortcoming of being insufficiently well defined.
The study of BHA lateral dynamics is more challenging because of the transient nature of the external forces that act on the drillstring. In the complete paper, different computations are conducted on several types of BHAs in order to examine when the notion of an effective length is valid and reliable and to determine the primary factors that make it challenging to isolate BHA behavior from the rest of the drillstring.

Models and Data
The BHA model used in this paper was used in the literature to study the microtortuosity of well trajectories. The model combines bit directional characteristics with the BHA design, namely stabilizer placement, in order to predict BHA preferential or equilibrium 3D curvature. The effective length can affect the results of this type of computation by changing the distribution and intensity of contact forces, thereby changing the overall preferential curvature.
For BHA dynamics, the simplest type of modeling is frequency-based and consists of predicting the natural frequencies of the system, which can be translated into critical or forbidden rotation speeds that should be avoided to prevent resonance. An intermediary approach, also based on frequency domain, is the use of forced vibration computations. Both frequency-based models are considered linear models and, thus, cannot account for the nonlinearities related to the contact and friction forces.
The most complex type of dynamics study is carried out in time domain. In this case, the nonlinearities related to the contact and friction forces are taken into consideration in addition to other transient external excitations.