Mathematical Model and Experimental Investigation of Bit-Bounce in Horizontal Oil Well Drillstring

  • Baojin Wang
  • Fushen RenEmail author
  • Zhigang Yao
  • Tiancheng Fang
Research Article - Mechanical Engineering


The bit-bounce is detrimental to the service life of drillstring and bit. This study highlights the influence of axial excitation and torsional excitation on the bit-bounce in horizontal well. Because of the complicated surroundings of downhole, Hamilton principle, a kind of energy method, is employed in this paper to derive the motion equation of the drillstring, which is discreted through finite element method. The impact–friction between the drillstring and borehole wall, and bit–rock and fluid–structure interaction are also modeled in this paper. The research results show that both axial excitation and torsional excitation greatly affect the dynamic behavior of the drillstring. Both the amplitude and the intensity of bit-bounce reduce with the development of the axial excitation and torsional excitation. And the test results are in agreement with the numerical simulation. The results of both have been mutually verified.


Coupled vibrations Hamilton principle Drillstring Qualitative analysis Horizontal well 

List of Symbols


Angular displacement along x direction


Angular displacement along y direction


Angular displacement along z direction


Displacement along x direction


Displacement along y direction


Displacement along z direction


Strain energy


Kinetic energy


Work done by the external forces


Work done by gravity


Work done by impact–friction


Work done by fluid–structure interaction


Work done by bit–rock interaction


Number of elements


Length of element


Local coordinate


Displacement vector of element


The first derivative with time

\({\mathbf{N}}_{{\mathbf{u}}}^{\prime }\)

The first derivation of shape function with ξ


Variation of the displacement ue


Radial displacement of drillstring


Gap between the drillstring and borehole wall


External radius of drillstring


Radius of borehole wall


Impact factor

\(\varPsi_{\text{im}} \left( r \right)\)

Determination coefficient of the drillstring


Coefficient of kinetic friction between drillstring and borehole wall


Contact force in normal direction


Coordinate at node n


Cutting torque


Cutting weight


Radius of bit


Intrinsic specific energy


A number characterizing the orientation of the cutting force


Maximum contact load


Instantaneous cutting depth


Number of blades of bit


Shape function of u

\({\mathbf{N}}_{{\theta_{x} }}\)

Shape function of θx


Normal component of hydrodynamic forces


Tangential component of hydrodynamic forces


Lateral non-viscous hydrodynamic force


Frictional viscous hydrodynamic force


Mass per unit length


Pressure of internal flow


Pressure of external flow


Flow speed of internal flow


Flow speed of external flow


Density of drilling mud


Viscous force


Viscous force


Viscosity damping coefficient


Hydraulic diameter


Output pressure of pump


Angular velocity vector


Cross-sectional moment of inertia matrix


Polar moment of inertia


Cross-sectional moment of inertia


Volume of drillstring


Strain tensor


Stress tensor


Vector of linear force


Vector of nonlinear force


Additional damping factor


Additional damping factor


Driving angular speed


Initial axial speed


Time step


Integral coefficient


Integral coefficient



The authors would like to acknowledge financial support by Natural Science Foundation of China, Project 11372071, Natural Science Foundation of Heilongjiang Province, Project LH2019A003, and Fundamental Research Funds for Provincial Undergraduate Universities of Heilongjiang Province, Project 2019QNL-13.


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Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Department Mechanical Science and EngineeringNortheast Petroleum UniversityDaqingChina
  2. 2.Department of Petroleum EngineeringMissouri University of Science and TechnologyRollaUSA
  3. 3.Beijing Industrial Technician CollegeBeijingChina
  4. 4.School of Civil Engineering and ArchitectureNortheast Petroleum UniversityDaqingChina

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