The Effect Of Hole Curvature On The Trajectory Of A Borehole
Authors: Millheim Keith 
Published: December 2007

Abstract
Hole curvature is the inclination and azimuth variation of a well's trajectory. When analyzing or planning bottom-hole assemblies and monitoring actual planning bottom-hole assemblies and monitoring actual drilling progress, hole curvature effects must be considered. The solution of this complex varying hole trajectory for a given assembly requires high speed computer programs. Analysis of curvature effects using a finite element program will show how significant differences occur in predicting or analyzing bottom-hole assembly responses when compared to the same cases with constant inclination. Analysis of many directional and straight wells show that rates of curvature response can be determined using well data and the finite element or other similar computer programs. From these functions, inclination responses for future wells can be obtained and used for given weight on bits, formation type, and bottom-hole assembly. Hole curvature effects can help explain why certain phenomena occur such as oscillating inclinations, follow through of trajectory after running a different assembly, and slow assembly response.
Wells paths to overcome strong formation effects can be designed using the concepts of hole curvature. Other on-site techniques using the concepts of curvature can be used to control curvature acceleration, overpower strong build and drop trends, and to make decisions when drastic measures are needed to correct the curvature.

Introduction
Trajectory control has long been a topic of concern in the drilling industry. Control of angle variation and buildup in straight holes was recognized as far back as the 1920's. In the 1950's, a major effort was made to understand and analyze the drilling assembly. Many papers were written on the effects of collar and hole size, positioning of a single stabilizer, and effects of formation anisotropy. However, techniques to analyze multistabilizer bottomhole assemblies did not occur until the 1970's. Most of this effort was directed at control of vertical wells with little technology being directed toward directional drilling. Furthermore, when the techniques presented in the technology did not work, it was blamed presented in the technology did not work, it was blamed on the geology, downhole equipment, or the directional driller.
As far back as 1972, Amoco Production Company started accumulating well data on bottom-hole assemblies, directional surveys, bit records, logs, and other related information. Special data forms were sent out and completed on both directional and straight wells in the Gulf of Mexico, Texas, Wyoming, Alaska, North Sea, Trinidad, and Canada. In 1975, an outside company was contracted by Amoco to develop a three-dimensional dynamic finite element program that could analyze any bottom-hole assembly configuration in any type of hole condition. At the same time, all the well data were being processed to determine what major variables seemed to influence the trajectory of the bit.
This paper is the first reporting of the progress in this endeavor. Field analysis, experimental test drilling, and computer analysis of assemblies have shown that hole curvature and its effect are one of the most important variables in controlling the trajectory of the wellbore.
A brief description of the finite element computer program is presented in a companion paper by T. Warren. program is presented in a companion paper by T. Warren. Selected examples of actual well data showing curvature effects and the curvature analysis are cited. Computer analysis of five typical bottom-hole assemblies with two curvatures, slight and moderate, are compared to the same assemblies assuming constant inclination. A method of how to analyze well data and determine curvature response functions are cited. General applications of these and other concepts while planning and/or drilling a well are presented. planning and/or drilling a well are presented. Limited space makes it impossible to relate examples of all the curvature effects, case histories, and additional computer analysis. This paper should be considered as an overview on hole curvature effects; how it can be analyzed, its ramifications in everyday drilling, and how it can be used in the area of trajectory control. Future work in this area undoubtedly will add much to understanding the mechanism plus proving up the applications of trajectory control by proving up the applications of trajectory control by software and hardware developments.