Global analysis of drill string buckling in the channel of a curvilinear bore-hole

Abstract

Currently, with advent of new techniques of drilling deep and curvilinear bore-holes, the conditions of their drivage become more drastic and severe. In these cases, redistribution of gravity, contact and friction forces acting on a drill string can give rise to emergency situations, one of which is the loss of its equilibrium stability and buckling. This phenomenon has been studied comprehensively as applied to the inclined rectilinear holes, but it is still understood incompletely if the drill string buckles in the channel of a curvilinear hole. In this paper, a new formulation of the problem on critical buckling of drill strings in inclined holes with variable geometry is devised through the use of the theory of curvilinear flexible rods. The stated eigen value problem is demonstrated to be singularly perturbed, that is the reason why its solutions have the shapes of localized harmonic wavelets. The computation results testify that the buckling phenomenon manifestation is determined by the relation between the influences of gravity and friction forces dictated by the angle of the bore-hole inclination. The peculiarities of the drill string behavior associated with the values of critical loads, pitches of the buckling wavelets, their widths and places of their localization in the rectilinear and curvilinear inclined bore-holes are discussed.