Computational Mechanics

, Volume 56, Issue 5, pp 849–878 | Cite as

Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings

  • Americo CunhaJrEmail author
  • Christian Soize
  • Rubens Sampaio
Original Paper


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.


Nonlinear dynamics Horizontal drillstring Uncertainty quantification Parametric probabilistic approach  Robust optimization 



The authors are indebted to Brazilian agencies CNPq, CAPES, and FAPERJ, and French agency COFECUB for the financial support given to this research. The first author is grateful for the institutional support received from PUC-Rio and Université Paris-Est to carry out this work.

Supplementary material

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Supplementary material 1 (avi 2144 KB)
466_2015_1206_MOESM2_ESM.avi (7.3 mb)
Supplementary material 2 (avi 7477 KB)


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Departamento de Matemática Aplicada, Instituto de Matemática e EstatísticaUniversidade do Estado do Rio de JaneiroRio de JaneiroBrasil
  2. 2.Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRSUniversité Paris-EstMarne-la-ValléeFrance
  3. 3.Departamento de Engenharia MecânicaPUC–RioRio de JaneiroBrasil

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