The Effect Of Hole Curvature On Drill Pipe While Drilling Inside Casing Or Open Hole
Authors: Warren Tommy 
Published: December 2007

Abstract
Many problems in a drilling operation can be caused by excessive contact forces between the drill pipe and the casing or hole wall. The contact force pipe and the casing or hole wall. The contact force is mainly controlled by the hole curvature, drill pipe stiffness, and the axial load on the drill pipe. pipe stiffness, and the axial load on the drill pipe. This paper discusses the relationship between the magnitude of the contact forces and the above three variables, as well as several other less significant variables.

Introduction
The lateral force with which the drill string interacts with the casing or open hole wall should be of vital concern in a drilling operation. Large lateral forces can result in excessive casing wear, excessive drill pipe and tool joint wear, and key seats in the hole wall. An understanding of the factors that control the lateral contact forces may allow preventative action to be taken before a problem develops.
The problem of excessive contact force between the drill pipe and the hole wall has been recognized for many years. It was addressed in 1960 by Lubinski, but it has only been during the last few years that detailed computer modeling of the problem has been feasible. This paper presents the results of a finite element computer study of the variables that affect the magnitude of the contact forces under a variety of conditions. The parameters were chosen to represent conditions that may occur in realistic drilling operations.

Finite Element Model
During 1975 a consulting firm was contracted and directed by Amoco to write a dynamic triaxial finite element computer program for the analysis of bottom hole assemblies. This program can be used to analyze any multi-component drill string in a wellbore. The drill string can be divided into a maximum of 51 elements of uniform cross sectional geometry and uniform material. An iterative process of solving for deflections and forces is then performed until the drill string deflections converge within the boundary conditions of the borehole. The required input data is a description of the drill string, wellbore diameter, wellbore survey, drilling fluid density, and axial load (weight on bit). The computed data includes the forces and deflections for each node point. Further discussion of the program is included in the appendix.
Two drill pipe models were investigated before one was chosen for the study. The first model represented a joint of drill pipe with five equal length finite elements and the tool joint as a single element with its length equal to the tool joint length. This model was unstable under certain combinations of axial load and hole curvatures. The second model represented a joint of drill pipe with two finite elements and the tool joint as a zero length element. The zero length element resulted in a single point of contact with the hole wall rather than a point of contact on each end of a short element. Both models gave the same results for the cases in which the first model would converge, thus the second model was used for the study. Figure 1 shows a diagram of the drill pipe configuration that was used for decreasing curvature and Figure 2 shows the increasing curvature configuration.
Table 1 gives the drill pipe and tool joint dimensions that were used in the study. Cases were run for 3-1/2", 4-1/2", 5", 5-1/2", and 6-5/8" drill pipe, with 20", 13-3/8", 9-5/8", and 7" casing sizes. pipe, with 20", 13-3/8", 9-5/8", and 7" casing sizes. The 13-3/8", 9-5/8", and 7" casing sizes will give approximately the same results as 12-1/4", 8-3/4", and 6-1/4" open hole sizes. The effects of hole size, drill pipe size, axial load, hole curvature, length and orientation of the curve, and hole inclination were investigated. Unless otherwise noted, the drill pipe was positioned in the hole so that a tool joint would be at the center of the hole curvature.
All the results presented in this paper were generated from a static (non-rotating) model. The results accurately represent the forces which develop while going in or out of the hole with the drill pipe. pipe.