Critical Buckling of Drill Strings in Cylindrical Cavities of Inclined Bore-Holes

Abstract

Notwithstanding the fact that the problem of drill string buckling (Eulerian instability) inside the cylindrical cavity of an inclined bore-hole attracts attention of many specialists, it is far from completion. This peculiarity can be explained by the complexity of its mathematic model which is described by singularly perturbed equations. Their solutions (eigen modes) have the shapes of boundary effects or buckles (harmonic wavelets) localized in zones of the bore-hole that are not specified in advance. Therefore, the problem should be stated in the domain of entire length of the drill string or in some separated part including an expected zone of its buckling. In the paper, a mathematic model for computer analysis of incipient buckling of a drill string in cylindrical channel of an inclined bore-hole is elaborated. The constitutive equation is deduced with allowance made for action of gravity, contact, and friction forces. Computer simulation of the drill string buckling is performed for different values of the bore-hole inclination angle, its length, friction coefficient, and clearance. The eigen values (critical loads) are found and modes of stability loss are constructed. The numerical results for the case when the inclination angle equals friction angle coincide with ones obtained analytically.

Improving the aluminum drill pipes stability by optimizing the shape of protector thickening

“…Thus, authors [4] examined the loss of stability of drill string of smooth tubes in the sloping well and demonstrated that the numerical results for the case when inclination angle of the well is equal to the angle of friction coincide with those obtained analytically. Researchers [5] studied the impact of rotation speed on the deflection of drill string and the magnitude of reaction in the zone of contact with the well wall.…”

“…That is, research [1,2,[4][5][6][7][8][9][10] is mostly devoted to studying the behavior of drill string, mantled from smooth pipes, under loading.…”

Lateral buckling of drill strings revisited: localised “snaking”

“…This paper offers a new asymptotic treatment for the classical problem of (static) lateral buckling of a long DS that remains in contact with the wall of an inclined straight borehole. The weight of the DS as well as the frictional forces experienced by this configuration are both accounted for, with the mathematical model being formulated as a boundary eigenvalue value problem for an angular displacement [29,36]. Our key results correspond to the non-dimensional three-term asymptotic formulae ( 29), (34), and (37), which capture the dependence of the first two lowest eigenvalues on all the relevant physical parameters.…”

“…A succinct account of the key differential equations and assumptions used in the rest of this paper is presented in this section. The mathematical model we are planning to explore was discussed at length in Gulyayev et al [29] or Musa et al [36], to which interested readers are referred for full details and derivations. Here, we will be content in just highlighting those aspects that are required in order to make the paper reasonably self-contained.…”

“…where ρ st and ρ ℓ represent the densities of the DS material and the drilling fluid, respectively, while e denotes the cross-sectional area of the cylindrical DS pipe. Both Gulyayev et al [29] and Musa et al [36] contain some confusing information about R ; in the former reference, this is incorrectly identified as F ax ( 0 ) (page 428), while in the latter, it is stated (page 29) that F ax ( 0 ) = f g ( cos β − η sin β ) S 0 —if taken at face value, this statement in conjunction with equations ( 19 ) and ( 21 ) in the same reference would render R ≡ 0 .…”