Drill-Pipe Bending and Fatigue in Rotary Drilling of Horizontal Wells
Authors: Wu Jiang 
Published: December 2007

Abstract
Drilling penetration rate can be increased when drilling a horizontal well by rotating the drill string, which helps to overcome the drag and apply the bit weight. However, drill-pipe fatigue may become a problem for rotating the drill string in the build section of the wellbore especially in drilling medium/short-radius horizontal wells, where the drill pipe experiences a large bending.
This paper presents an analysis of drill-pipe bending and fatigue in rotary drilling horizontal wells. The wellbore curvature, axial compressive load, drill-pipe weight, and drill-pipe tube contact to the wellbore wall are considered. New equations are derived to improve the prediction of the maximum drill-pipe bending stress and drill-pipe fatigue. The results show that drill-pipe tube contact to the wellbore wall, which happens under large axial loads, may help reduce the maximum bending stress, and therefore, benefit the fatigue control. The drill-pipe weight usually increases the bending stress and needs to be considered to accurately predict the fatigue damage.

Introduction
Drill-pipe fatigue was first studied for drill-pipe rotating in a dogleg wellbore section under axial tensile load. The recent application of rotary drilling medium/short-radius horizontal wells involves the situation where drill pipe rotates in the build section of the wellbore under axial compressive load. The drill pipe is first bent along the build section of the wellbore, and then the axial compressive load and drill-pipe weight push further bending or deflection between the tool joints. The maximum bending stress in the drill pipe could be much larger than that calculated by assuming the drill pipe bent with the wellbore curvature.

Maximum Bending Stress
Fig. 1 shows the drill-pipe bending/deflection development in a build section as the axial compressive load increases. Under a small axial compressive load, the maximum bending curvature is located at the midpoint of one joint of drill pipe, and there is no drill-pipe tube contact to the wellbore wall (Fig. 1a). As the axial compressive load increases, the middle of the drill-pipe tube starts to contact the wellbore wall ("point" contact, Fig. 1b). Further increase of axial compressive load increases the contact length in the middle part of the drill-pipe ("arc" contact, Fig. 1c). The maximum bending curvature moves to somewhere in the uncontact portion after the tube contact occurs.
Drill pipe under axial compressive load is considered in this paper for rotating through the build section of the wellbore in drilling a medium/short-radius horizontal well. However, similar equations for axial tensile load condition can be derived by the same approach.
The tubular bending differential equation for the drill pipe in the build section of the wellbore and under axial compressive load is (Fig. 2):
(1)
where
Based on the fact that the tool joints are stiffer than the drillpipe tube and follow the wellbore trajectory, the following boundary conditions exist for drill-pipe bending:
(2)
(3)
The general solution of the above differential equation under these boundary conditions is:
(4)
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