Influence of friction on buckling of a drill string in the circular channel of a bore hole

Valery Gulyayev,Natalya Shlyun

doi:10.1007/s12182-016-0122-5

Valery Gulyayev, Natalya Shlyun

Open Access

https://doi.org/10.1007/s12182-016-0122-5

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Journal: Petroleum Science	Publication Date: Oct 18, 2016
Citations: 13	License type: CC BY 4.0

Affiliation: National Transport University

Abstract

Enhancement of technology and techniques for drilling deep directed oil and gas bore hole is one of the most important problems of the current petroleum industry. Not infrequently, the drilling of these bore holes is attended by occurrence of extraordinary situations associated with technical accidents. Among these is the Eulerian loss of stability of a drill string in the channel of a curvilinear bore hole. Methods of computer simulation should play a dominant role in prediction of these states. In this paper, a new statement of the problem of critical buckling of the drill strings in 3D curvilinear bore holes is proposed. It is based on combined use of the theory of curvilinear elastic rods, Eulerian theory of stability, theory of channel surfaces, and methods of classical mechanics of systems with nonlinear constraints. It is noted that the stated problem is singularly perturbed and its solutions have the shapes of localized harmonic wavelets. The calculation results showed that the friction effects lead to essential redistribution of internal axial forces, as well as changing the eigenmode shapes and sites of their localization. These features make the buckling phenomena less predictable and raise the role of computer simulation of these effects.

Highlights

Not long ago, rather shallow wells with simple outlines were drilled in oil and gas fields
A new statement of the problem of critical buckling of the drill strings in 3D curvilinear bore holes is proposed. It is based on combined use of the theory of curvilinear elastic rods, Eulerian theory of stability, theory of channel surfaces, and methods of classical mechanics of systems with nonlinear constraints
It is noted that the stated problem is singularly perturbed and its solutions have the shapes of localized harmonic wavelets

Summary

Introduction

Rather shallow wells with simple outlines were drilled in oil and gas fields. One of them is unstable bending buckling of a drill string (DS) in the channel of a curvilinear bore hole (Brett et al 1989; Dawson and Paslay 1984; Kyllingstad 1995; Sawaryn et al 2006; Gulyayev et al 2009; Gao and Liu 2013; Huang and Gao 2014; Gao and Huang 2015) This effect is associated with deterioration of conditions of contact interaction between the DS and the bore hole wall, enlargement of friction forces, impossibility of transferring the required axial force to the bit, and the DS lockup situation. The stress–strain state of the moving DS under action of gravity and friction forces is determined; at the second step, the eigenvalue problem for linearized equations is solved It is shown, that the buckling modes have the shapes of harmonic wavelets with localization segments depending on the friction forces

Basic assumptions concerning drill string bending in a curvilinear bore hole

Bifurcational equations of DS equilibrium in a circular bore hole

À a2ðv0Þ2 q þ a cos v þ aðv0Þ2: ð30Þ

À a2ðv0Þ2 : sin v

Critical buckling of a DS moving inside a channel of a circular bore hole