Self-excitation of deep-well drill string torsional vibrations

Abstract

539.3: 622.24 and O. V. GlushakovaWe address a problem of self-excitation of elastic torsional vibrations of a rotating drill string due to frictional interaction between the drill bit and rock at the deep well bottom. Using the d'Alembert solution to a wave equation, a mathematical model is constructed for a wave torsional pendulum in the form of a nonlinear ordinary differential equation with delayed argument. Special features of generation of self-excited vibrations of drill strings have been determined through computer simulation.Introduction. Rotary drilling is the most widely accepted method for producing oil and gas wells; it involves rock destruction at the well bottom by means of a drill bit attached to the lower end of the drill string (DS) to which rotation is imparted through the torque applied to the DS top end. In the course of drilling, a drill string experiences a number of mechanical actions the most significant of which are the longitudinally nonuniform DS tension force, torque, centrifugal and compound centrifugal forces induced by the drilling fluid flow inside DS, forces of frictional interaction between the DS and the formation, etc. The factors listed above initiate longitudinal, torsional, and bending vibrations in the string and contribute to its flexural buckling. This may cause a stuck DS, wellbore wall falling in, and overall instability of the system [1-5]. One of the dynamic phenomena that may eventually lead to an emergency occurrence in drilling is the self-excitation of torsional vibration of a rotating DS. Since a DS is a torsional pendulum, where an outflow of energy from the drive to environment occurs at the DS bottom part due to energy-dissipative interaction between the drill bit and the formation, the string may pass from the steady equilibrium rotation to torsional self-excited vibration when the conditions of this energy outflow are upset. To study this phenomena we will use here a wave model of a torsional pendulum, which allows for the effects of the finite-velocity propagation of torsional strains along the DS.Special Features of Processes of Self-Excitation of Torsional Vibration in Long Drill Strings. The effects of self-excitation vibration fundamentally differ from other types of vibration processes in dissipative systems in that no periodic external action is needed for their excitation [6,7]. If a mechanical system's transition from some initial state to self-excited vibration conditions occurs without any addition "push," this is a soft self-excitation. If a vibration starts increasing spontaneously only from some limiting amplitude, this is called the hard self-excitation. To periodic self-excited vibration there corresponds a closed loop path in the phase space, which all neighbor paths tend to; this path has been named the stable limit cycle or the attractor [8].With regard to the phenomena that accompany the DS rotation, a study of generation of the DS self-excited torsional vibration enables one to answer three important questions: (i) at what values of the...

Wirl vibrations of the drillstring bottom hole assembly

“…kg/m 3 , r l = × 1 5 10 3 . kg/m 3 ).The components (8) of this moment are directly proportional to flexural rigidity EI and inversely proportional to the drill bit cantilever length e. In this connection, it can be inferred that the increase of EI and decrease of e permit stabilizing the dynamics of the whirl vibrations. However, the total rigidity of the DS lower section and its cantilever is characterized not only by their structural stiffness values but also Ò, Ì z , and w values that determine the Eulerian instability of the system.…”

“…Interestingly, the drill bit circular motions in this case have the opposite orientations. As demonstrated by field data [8][9][10], it is these vibration conditions which are most often accompanied by accident effects. …”

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“…Основні стендові й експериментальні дослідження впливу параметрів режиму буріння та характеристик гірської породи на обертовий момент на долоті вивчали тільки їхній вплив на процес зміни середнього значення моменту [100,101]. Дослідження процесу зміни обертового моменту в часі з фіксацією цієї зміни проводилися низкою дослідників [102][103][104][105]. Внутрішня структура процесу зміни обертового моменту на долоті не досліджувалась і характер зміни його динамічного складника не вивчався.…”

Hopf Bifurcation and Feedback Control of Self-Excited Torsion Vibration in the Drive System

“…The torsion vibration commonly exists in the drive train of various mechanical systems, such as steel rolling mills, vehicles, oil drill strings and machine tools [1,2]. In general, the mechanical drive system consists of motor, gear reducer and working-load.…”