A Compendium of Directional Calculations Based on the Minimum-Curvature Method—Part 2: Extension to Steering and Landing Applications

Abstract

Summary The point-to-target calculations contained in Part 1 of the compendium (Sawaryn and Thorogood 2005) were restricted to those cases in which the 3D target coordinates were stated explicitly. However, another class of problems exists where the target's structural position is determined indirectly from other constraints defining the arc's orientation. This new paper builds on the earlier work and contains complete details of twelve explicit algorithms, including the calculation of a target on the basis of the toolface at the start or end of an arc and for the landing of a well path parallel to a formation bedding plane. These cases find practical application in computing trajectories of motor runs and in whipstock operations. The curvature of the trajectory landing on a bedding plane varies with direction and has a distinct minimum and maximum. These values may be used either to minimize the distance to the target or to limit the dogleg severity (DLS) to avoid drillpipe fatigue, a concern in short-radius drilling applications. The algorithms add to the compendium and are useful extensions to the engineer's computational toolkit. The paper shows that the trajectories, computed using the minimum-curvature calculation, are contained within the geometric surfaces defined by a torus or cyclide. These geometries explain why the explicit solutions exist, opening up possibilities for obtaining solutions to the more-complex cases.