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

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.

Simulation of Buckling and Dead Lock States of Drill Strings in Curvilinear Bore Holes

“…Then, it is valid to assume that the rectilinear borehole is horizontal and the infinitely long DS is prestressed by the axial force ) (s F z remaining unchanged throughout its length. In this event, the critical values of force ) (s F z and pitch  are determined by equalities [5,8] 2/ Copyright © Institute of Research Engineers and Doctors, USA .All rights reserved. ISBN: 978-1-63248-132-0 doi: 10.15224/ 978-1-63248-132-0-33 the circular geometry of a bore-hole and invariability of its curvature radius  .…”

“…With its use the technology of industrial drilling the bore-holes 6 km in depth is worked out and the purpose of drilling 7 km bore-holes and deeper is posed [9]. The operating conditions of (dead lock states [1,2,4,6,7] and their driving can be accompanied by the phenomena of bifurcational buckling [3,5,8] of the drill strings as well as self-excitation of vibrations of their bits. However up to now there are not reliable methods of physical and mathematical simulation of the pointed out effects.…”

“…f is gravity, c f is the force of contact interaction between the surfaces of the DS and bore-hole, fr f is the force of friction interaction between these surfaces, in f is the inertia force, fr m is the distributed moment of friction forces.With the aid of correlations (2) -(7) one can transform Eqs (8). to a scalar form and apply it to computer simulation of the DS dragging inside the curvilinear channel of a bore hole.Represent Eqs (8). in the scalar form[6] …”

Solution of the Main Differential Equation of Deformations of the Casing in a Curved Well

“…Як показав аналіз [8,9], система диференціальних рівнянь Кірхгофа, яка описує деформування просторово вигнутого стрижня, є однорідною відносно його жорсткості на згин, тому усі силові чинники можна поділити на EJ (E -модуль пружності матеріалу; J -момент інерції попереччя). Отже, не втрачаючи загальності розв'язку, можна розглядати великі пружні деформації довгого стрижня з одиничною жорсткістю на згин; при цьому згинальний момент чисельно дорівнює кривизні стрижня.…”

Computer simulation of dragging with rotation of a drill string in 3D inclined tortuous bore-hole

“…In their generating, the great role is played by the bending stiffness of a drill string (DS), bore-hole tortuosity and its length, as well as by the type of the technological operation [3,19]. These forces hamper permeability of the force on bit and torque on bit, provoke buckling of the drill string [6,10] and can result in dead lock situations. To predict and eliminate these effects, the mathematic models and software should be elaborated for simulation of the drilling processes in long 3D tortuous bores.…”