Theoretical and Experimental Evaluation of Drill Pipe Stability Conditions in Slim Holes
Authors: Akgun F. , Gurakin G. , Mitchell B.J. , Eustes A. , Rahman S. 
Published: December 2007

Abstract
Inadequate weight on bit leads to drilling at lower rate of penetration which reflect itself with expensive drilling intervals. Weight on bit is provided by slacking of some of the weights of the tubulars on bit. From the mechanical point of view this means putting bottom section of drill string into compression. The upper limit of the compressional stress that can be imposed on a drill string is bounded by the minimum stress which can lead to the failure of the tubulars. One type of the failure of drill string is called 'drill string buckling'. As the size of tubular decreases, their ability to transmit weight on bit without buckling decreases. Curvature and inclination of drilled hole increase or decrease the amount of compressional load that can be imposed on tubular without buckling. This load is known as Critical Buckling Load. This paper presents a finite element and an experimental approaches to predict the critical buckling load for dropping and building sections of holes.

Introduction
Drilling at minimum cost necessitates optimum weight on bit. This weight is provided by slacking off some of the weights of drill string on bit. As the hook load decreases and slacked off length increases neutral point moves up in the drill string. At the same time, compressional stresses below the neutral point increase. There is a critical value of compressional stresses such that below which pipes are stable. In other word, pipes still have resistance against bending. However, if this value is exceeded then they will shown no resistance against bending. This phenomenon is known as buckling of tubulars and this critical value is known as Critical Buckling Load.
Buckling is not desired in drillstring because of several reasons. One of the reasons is that it may lead to premature failure of the drillstring through fatigue and erosion. It may lead to termination of drilling due to drill string lockup especially in horizontal wells. Lockup occurs when the compression at any location within the drill string is equal to or is greater than the drillstring's resistance to buckling at that location. Therefore, it becomes impossible to provide the necessary weight on bit. Without the weight on the bit, drilling ceases and drilling of the reach is terminated. Therefore, it is essential to determine the maximum load that can be imposed on drillstring.
Critical Buckling Load is not a unique number for a given diameter pipe. There are a number of borehole parameters affecting the magnitude of it. Such as, hole curvature, hole inclination, hole to pipe friction, etc. (Figure 1). Therefore, Critical Buckling Load for a given size pipe can not be determined independent without taking borehole data into consideration.
Compressive load at which pipes buckle can be predicted based on Eigenvalue analyses or based on large Deflection Analysis of Finite Elements Methods. Eigenvalue analysis has the short coming of estimating the upper bound of critical buckling load (bifurcation load). Whereas, the more critical lower bound can be predicted with Large Deflection analysis of Finite Elements Methods (Figure 2).
This study makes use of large deflection analysis of FEM to predict the critical buckling load in dropping holes. This paper also presents an experimental study to predict the critical buckling load in building holes.

FEM modelling of the Drill Pipe and Bore Hole
During a buckling simulation, the drill pipe is released and is allowed to slide down the wall of the borehole and settle into a stable position within the borehole. The pipe may or may not be buckled at the end of the simulation. If the pipe is buckled there will be a length of pipe in contact with the opposite side of the wall of the borehole (high side). The force created by the contact is called the contact force. It's direction is normal to the wall of the borehole.
Whether the pipe buckles or only bends, two forces acting on the drill pipe will be created.
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