The Effect of Bottomhole Assembly Dynamics on the Trajectory of a Bit
Authors: Millheim Keith K. , Apostal Michael C. 
Published: December 2007

Summary
This work, which reports on the effect of bottomhole assembly (BHA) dynamics on the trajectory of a bit, is part of an on-going effort to develop a computer model that simulates the three-dimensional (3D) movement of the bit. A theoretical description of the dynamic version of the 3D finite element algorithm is presented. The basic mechanisms associated with pipe rotation are explained by showing the predominant paths of motion of five BHA's as a function of rotary speed, and stabilizer-bit-, and pipe-friction coefficient values.In a parallel test program, five shallow wells were drilled directionally under controlled conditions. Results of these tests are incorporated to demonstrate that dynamic predictions of the bit's tendencies compared well with numerical results predicted by the program.Two other field examples are cited: one from the Gulf of Mexico, and another from Holland. Data from these wells are used to illustrate how the dynamic results can be applied to explain the bit's trajectory behavior.A final section examines the use of the computer-generated results in predicting the tendencies of the bit for the five assemblies.

Introduction
Directional drilling is the science of directing the bit along some predetermined trajectory toward a target. To do this, the bit must be controlled in the vertical (inclination) and horizontal (direction) planes.BHA's, mud motors with deflection subs, whipstocks, and jetting bits all are used as a means of steering the bit along the prescribed trajectory. However, the BHA is the most popular method of controlling a directional, straight, or deviation control well once the initial orientation (kickoff) has been made.Historically, design and operation of BHA's have been based on experience. Certain basic BHA configurations were used to build, hold, and drop angle. The associated direction change (bit turn or bit walk) was considered a byproduct of the process.BHA design evolved from an art to a science when certain computer programs were developed that predicted the static two-dimensional force-displacement behavior of a BHA. Later, Millheim used a 3D static program to explain the responses of BHA's in various geological situations. The main emphasis in all these efforts has been directed toward determining the inclination response of the assemblies.To predict the direction as well as the inclination tendencies of a bit accurately, the rotation of the drillstring must be considered. The 3D static program presented by Millheim has been extended to include a dynamic capability. This paper presents the basic formulation of the algorithm that serves as the basis for the dynamic model.Having a computer code representing a mathematically rigorous solution, however, does not ensure that the code will represent the actual drilling process accurately in the field. In reviewing the computer results, it has been observed that other effects such as geology and hole conditions have to be taken into consideration to predict the inclination tendencies of a BHA successfully. To predict bit direction, rotary speed dynamics have to be included as well.For nearly 3 years, the dynamic 3D model mentioned earlier has been studied and compared against field results. To test the program's predictions further, an experiment was conducted involving five shallow directional wells drilled under controlled conditions in an area where the geology is known accurately.Results of these tests, which are presented in this paper, verify the predicted bit tendencies as generated by me dynamic program.
JPT
P. 2323^