Bottom-Hole Assembly Analysis Using the Finite-Element Method
Authors: Millheim Keith , Jordan Steven , Ritter C.J. 
Published: December 2007

The complex behavior of most bottom-hole assemblies can be analyzed using the finite-element method. If the wellbore trajectory, hole diameter, fluid density, and assembly dimensions are known, various properties can be determined. The tendency of a bit either to build or to drop angle can be assessed.

Introduction
Predicting the actual trajectory of a drilling bit is very Predicting the actual trajectory of a drilling bit is very complex. Many variables interact causing the bit to follow a certain trajectory. Assembly configuration and dimensions, lithology, dip, bit, type, hole curvature, magnitude of inclination, bit weight, and rotary speed are some of the more important parameters that control inclination and azimuth of the bit.
The drilling industry has been aware of directional problems and the need to understand these problems for problems and the need to understand these problems for many years. The first major approach was presented by Woods and Lubinski, who emphasized the importance of the bottom-hole assembly makeup. First, the "slick assembly" was analyzed to show the importance of the point of tangency, collar diameter, etc. Further research point of tangency, collar diameter, etc. Further research introduced the concept of single stabilizer placement to increase the point of tangency so that the negative or pendulum forces could be increased. Early research pendulum forces could be increased. Early research recommended multispaced stabilizers to increase the bottom-hole assembly stiffness. This commonly was referred to as the "packed-hole assembly."
Currently, most assembly designs are based on the slick, single, or multistabilizer configurations. Exceptions are the use of square collars, mud motors, and special directional tools. Field experience is an important aspect of this technology.
Actual assemblies and drilling situations are too complex to rely on the simpler idealizations that do not account for varying collar dimensions, material properties, and multistabilizer arrangements. Recognizing this, properties, and multistabilizer arrangements. Recognizing this, new technology is being developed using numerical solution methods and high-speed digital computers. These techniques have been presented in the literature. Fischer and Bradley et al. analyzed various assemblies that had negative side force tendencies, using a finite-difference approximation. They also investigated square collars, hole inclination, and other important effects. Similar computer programs exist.
This paper presents a numerical approach that has gained popularity in other engineering applications. This technique, known as the finite-element method, is used to solve four bottom-hole assemblies. One is a moderate building assembly, the others range from a holding assembly with a slight dropping tendency to a stronger dropping assembly.
The basic finite-element technique used for analyzing these four assemblies is presented. The method of solution using a general-purpose, finite-element system is described, along with the mathematical idealizations that achieve tangency of the collars with the wellbore. The nonlinear solution for one assembly demonstrates how the collars react as the load is applied to the system. The solutions for each assembly show various reaction forces and displacements. From the side force at the bit, the general inclination tendency can be determined. The effects of large displacement and boundary contact also are discussed.
Technical Approach
The Finite-Element Method
JPT
P. 265