Hole Deviation and Drill String Behavior
Authors: Murphey C.E. , Cheatham J.B. 
Published: December 2007

Abstract
Presently, complete control of borehole direction cannot be obtained during drilling, and most straight-hole drilling methods attempt to resist hole deviation rather than control direction. Many of the theories advanced as possible explanations of the cause of hole deviation are summarized herein. A new correlation of physical variables is introduced to indicate how factors such as drill collar stiffness, clearance and bit weight influence borehole deviation Method is proposed for predicting the rate of change of hole angle when drilling conditions are changed.
Introduction
Control of borehole direction-during drilling can be difficult and costly. Unintentional crooked holes are often trilled in dipping formations and many times directional drilling is required when the surface location is not directly above the target area - for example, at offshore and mountainous locations. Drilling progress can be greatly hindered in either air or liquid drilling when it becomes necessary to use low bit weight to prevent excessive hole angle build-up. If hole inclination becomes too great, drill pipe drag becomes excessive and fishing risks are increased, logging is more difficult and problems of differential sticking, key seating and fatigue failures may be encountered. Dog-legs and key seats are more serious problems than steep inclination angles; therefore, reducing rate of direction change is preferred to attempting to maintain absolutely vertical holes. Consequently, a straight inclined hole is preferable to a nearly vertical crooked hole containing numerous dog-legs. In this paper, theories of the cause of hole deviation and analyses of drill string behavior under down-hole conditions are summarized. Methods for computing hole deviation are presented and systems for resisting deviation as well as means for providing control of hole direction are discussed. A new correlation of physical variables is introduced to indicate how factors such as drill collar stiffness, clearance and bit weight influence borehole deviation. A method is proposed for predicting the rate of change of hole angle when drilling conditions are changed.
REVIEW OF PREVIOUS WORK ON HOLE DEVIATION
Significant progress in the theoretical analysis of hole deviation problems has been made in the past 15 years. The pioneering work has been primarily a result of the efforts of Lubinski and Woods. In 1950, Lubinski considered the buckling of a drill string in a straight vertical hole, a problem also considered by Willers in 1941. It was concluded that very low bit weights must be used to prevent hole deviation resulting from drill collar buckling. The use of conventional stabilizers was proposed in 1951 by MacDonald and Lubinski as a method for permitting greater bit weights to be carried without drill collar buckling. These authors pointed out that 2 degrees nearly vertical spiral hole can cause severe key seating and drill pipe wear, whereas a 3 degrees straight inclined hole with deviation all in one direction, while not vertical, will not result in serious drilling or producing problems. Studies were continued with an investigation of straight inclined holes by Lubinski and Woods in 1953. In this paper they concluded that perfectly vertical holes cannot be drilled even in isoscopic formations unless extremely low bit weights are used. They postulated that constant drilling conditions produce holes of constant inclination angle and varying conditions cause the hole to drill at a new equilibrium angle. This analysis was not concerned with drill string buckling since it was based on an equilibrium solution in which the drill string was presumed to lie along the lower side of the hole above the point of tangency. Weight of the drill collars below the point of tangency tends to force the hole toward the vertical, whereas the weight on bit tends to force the hole away from the vertical.
SPEJ
P. 44ˆ