| A three-dimensional numerical model has been developed to predict wellbore trajectory in both the vertical and horizontal plane. The finite element method is utilized to determine the transient dynamic behavior of a bottom hole assembly during drilling. The effects of rock-bit interaction have also been incorporated.; The equation of motion of the bottom hole assembly is solved using the Wilson-(THETA) numerical integration algorithm. An iterative procedure, utilizing the Newton-Raphson method, has been incorporated to insure that the assembly remains confined within the wellbore. The degree of non-elastic behavior of the formation during impact of the bottom hole assembly with the hole wall is represented by a restitution coefficient. Contact forces are used to include the effect of sliding friction through a Coulomb friction coefficient. To provide the correct boundary condition at the bit-rock interface, rock-bit interaction models have been developed for a roller cone bit and a Polycrystalline Diamond Compact Bit. These rock-bit interaction models yield a force input at the lowest node of the bottom hole assembly model.; Statistical analyses have been performed to determine the relative importance of the following: friction effects at the bit, at the stabilizers, and at the drill collars; radial clearance at the bit and at the stabilizers; damping; and restitution coefficient. Bottom hole assemblies for building, holding and dropping hole angles, each using both a roller cone bit and a Polycrystalline Diamond Compact bit have been used in the study. For these assemblies the effects of hole curvature (in both vertical and horizontal plane), hole inclination, bit/stabilizer clearance, weight on bit, rotary speed, rock strength, friction coefficient, restitution coefficient, and cone offset (for roller cone bit only) have been determined. Comparisons between model predictions and field performance for 26 different bottom hole assemblies, all with a roller cone bit, have been made. The computational and field results compare favorably. |
