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Purpose <p>To address the issue that current dynamic models of drill strings often simplify the mathematical modeling of the interaction between the drill bit and the rock, thereby failing to accurately reflect the actual behavior of the drill bit, this study aims to explore the dynamic behavior of the horizontal well drill string system equipped with PDC drill bits under different drilling parameters, wellbore curvature, rock properties, and drill bit geometries.</p> Methods <p>In this work, a dynamic mathematical model of the coupled nonlinear system of drillstring-PDC bit-rock under the wellbore trajectory of a three-dimensional curved well is established. The drillstring is spatially discretized into multiple Euler–Bernoulli beam elements using the finite element method. The PDC bit model is established based on projection principles and polygon clipping techniques, which fully accounts for the cutters layout, geometric shapes, state-dependent delay effects, and multiple cutters interactions. A new method for calculating the bit’s depth of cut was proposed. The interaction forces between the bit and the rock were introduced as boundary conditions for the drillstring model, while the displacement of the drillstring’s terminal node is used as an input to the bit model, achieving a nonlinear coupling between the bit and the drillstring. The coupled nonlinear dynamic system is solved using the Newmark method combined with an improved Newton–Raphson iteration scheme.</p> Results <p>The numerical results indicate that increasing the rotational speed and the weight on bit (WOB) will intensify the vibration of the drill string, but it will improve the drilling efficiency. A higher rotational speed helps to suppress the sliding vibration of stuck pipe, while a larger WOB can effectively alleviate the axial stuck pipe sliding phenomenon. An increase in the local curvature of the wellbore trajectory will lead to an increase in the vibration intensity of the drill string at that location. An increase in the strength of the formation rock will cause an increase in the vibration intensity of the drill bit and a greater increase in the axial strength than the torsional strength. In addition, PDC drill bits with more blades and cutting edges help to achieve more stable drilling performance, but too many blades and cutting edges may reduce the drilling speed.</p> Conclusion <p>The conclusions provide a theoretical basis for vibration control of the drillstring, as well as for the selection of appropriate drilling parameters and bottom hole assembly configurations.</p>

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Dynamic Analysis of a Horizontal Well Drillstring System Based on a PDC Bit Model Adaptable to Arbitrary Cutters Configurations

  • 期刊论文

  • 发表日期：

    2026年5月12日

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  • Pan Fang,
  • Ao Shen,
  • Chuan Yang,
  • Yongchun Wu,
  • Caijun Yu,
  • Qing Yu

摘要

Purpose

To address the issue that current dynamic models of drill strings often simplify the mathematical modeling of the interaction between the drill bit and the rock, thereby failing to accurately reflect the actual behavior of the drill bit, this study aims to explore the dynamic behavior of the horizontal well drill string system equipped with PDC drill bits under different drilling parameters, wellbore curvature, rock properties, and drill bit geometries.

Methods

In this work, a dynamic mathematical model of the coupled nonlinear system of drillstring-PDC bit-rock under the wellbore trajectory of a three-dimensional curved well is established. The drillstring is spatially discretized into multiple Euler–Bernoulli beam elements using the finite element method. The PDC bit model is established based on projection principles and polygon clipping techniques, which fully accounts for the cutters layout, geometric shapes, state-dependent delay effects, and multiple cutters interactions. A new method for calculating the bit’s depth of cut was proposed. The interaction forces between the bit and the rock were introduced as boundary conditions for the drillstring model, while the displacement of the drillstring’s terminal node is used as an input to the bit model, achieving a nonlinear coupling between the bit and the drillstring. The coupled nonlinear dynamic system is solved using the Newmark method combined with an improved Newton–Raphson iteration scheme.

Results

The numerical results indicate that increasing the rotational speed and the weight on bit (WOB) will intensify the vibration of the drill string, but it will improve the drilling efficiency. A higher rotational speed helps to suppress the sliding vibration of stuck pipe, while a larger WOB can effectively alleviate the axial stuck pipe sliding phenomenon. An increase in the local curvature of the wellbore trajectory will lead to an increase in the vibration intensity of the drill string at that location. An increase in the strength of the formation rock will cause an increase in the vibration intensity of the drill bit and a greater increase in the axial strength than the torsional strength. In addition, PDC drill bits with more blades and cutting edges help to achieve more stable drilling performance, but too many blades and cutting edges may reduce the drilling speed.

Conclusion

The conclusions provide a theoretical basis for vibration control of the drillstring, as well as for the selection of appropriate drilling parameters and bottom hole assembly configurations.