Planning the Directional Well - A Calculation Method

Abstract

Summary This paper describes a radius-of-curvature calculation of the three-dimensional (3D) path of a directionally drilled well from kickoff point to target. Slant-well, S-shape, and maximum turn well paths can be computed. Equations are developed for calculating critical points along the well path in terms of cartesian coordinates and directional survey parameters. The effect of right-hand walk (drift) and a technique for calculating the appropriate lead to compensate for drift is presented. Introduction In contrast to the many references on methods for calculating directional surveys, there is a notable absence of articles discussing the related problem of well planning. Wilson derived the concept of compounded wellbore curvature in discussing the curvature method to calculate directional surveys. However, no 3D method has been published to handle the calculation of well paths that have both changes of azimuth and changes of inclination. This is a common type of well path, especially in sidetracked holes and for drilling around salt domes. The intent of this paper is to describe a procedure that will accommodate the 3D geometry of practical well trajectories. The general solution assumes that all curvatures between two points are constant. The only other limitations imposed are a maximum curvature and a maximum inclination. Radius-of-Curvature Equations The radius-of-curvature method used in this procedure is a preferred approach to well-path calculation because of its relative simplicity and general use in the industry for interpreting directional surveys. It also appears to conform to the geometry of directional drilling since the objective of turning a well with, for example, a bent sub and downhole mud motor is to drill a well path with constant radius of curvature. Rivero has generalized the radius-of-curvature equations to the following form. Cases 1 and 2. (1) Case 1. . (2) (3) This case represents a constant curvature in azimuth as well as inclination. JPT P. 952^