Computer Simulation of the Least Energy Consuming and Emergency-Free Regimes of Drilling of Hyper Deep Curvilinear Bore-Holes

Abstract

The problem of computer simulation of mechanical behavior of drill strings in hyper deep vertical, inclined and horizontal bore-holes is stated with the aim of forecasting the possible initiation of emergency situations during carrying out drilling operations. The question of stability and post-critical non-linear deforming and dynamics of the drill strings are considered. It is shown that all of them are singularly perturbed from the mathematical point of view and because of this, they are poorly amenable to theoretical (computational) analysis. The algorithms allowing surmounting these difficulties are proposed.The software for study of these phenomena is elaborated.In the stages of design of an elongated curvilinear bore-hole with complicated 3D geometry and technological regimes of their drivage, the elaborated software permits one to construct its trajectory securing the smallest values of resistance forces and to choose the least energy-consuming and safe regimes of drilling. It ensures also the possibility to determine the requirements for the necessary accuracy of the bore-hole drivage and for the acceptable geometrical distortions and imperfections.In the stage of the bore-hole drivage, the created software permits to calculate forces and moments of resistance forces with allowance made for the real geometry of the bore-hole and admitted distortion of its axial line. It is possible to prognosticate possible emergency situations and design the measures for their exclusion. At the stage of the emergency situation liquidation, this software allows to simulate the mechanical behavior of the system and its responses to the methods used for elimination of the failure consequences.

Lateral buckling of drill strings revisited: localised “snaking”

“…A summary of several key direct numerical simulations of this non-dimensional bifurcation problem is included in §3. We also take this opportunity to rectify some of the innaccurate statements made in [29]; in particular, we show that the critical eigenmodes are localised near either the right or the left ends of the DS, depending on the value of the borehole inclination angle relative to a critical value (which is defined in the next section). The information gleaned from these numerical results is later exploited in §4 to flesh out the asymptotic structure of the eigenvalue problem that governs the buckling of the DS.…”

“…A succinct account of the key differential equations and assumptions used in the rest of the paper is presented in this section. The mathematical model we are planning to explore was discussed at length in references [29] (pp. 407-437) or [36], to which interested readers are referred for full details and derivations.…”

“…Broadly speaking, the motivation for the present study is partly related to the recent monograph [29], in which Gulyayev et al have collected in one place a broad spectrum of topics related to drillstring mechanics. This is a welcome addition to the literature, not least because the authors follow an applied mathematics approach and do not rely excessively on purely numerical solutions.…”

“…Another notable features include the systematic introduction of frictional forces in many of the mechanical models proposed, as well as the careful formulation of the corresponding boundary-value problems studied. Although reference [29] emphasises the singularly-perturbed character of many of the situtions encountered in drillstring mechanics, no serious attempts were made to capitalise on this observation. It is the purpose of this paper to discuss in some detail the asymptotic behaviour of one of the buckling models included in Chapter 7 of [29].…”

“…Although reference [29] emphasises the singularly-perturbed character of many of the situtions encountered in drillstring mechanics, no serious attempts were made to capitalise on this observation. It is the purpose of this paper to discuss in some detail the asymptotic behaviour of one of the buckling models included in Chapter 7 of [29]. This model is an extension of that proposed earlier by Paslay and Bogy [24], in the sense that it incorporates (albeit in a simplified form) the neglected frictional effect of the contact interaction between the DS and the inner surface of the borehole.…”