Constant Curvature Method for Planning a 3-D Directional Well

Abstract

SPE Members Abstract A new method for planning 3-D directional wellpaths is proposed in this paper. This method, which is referred to as the Constant-Curvature Method, has several advantages over the conventional Radius-of-Curvature Method and Constant-turn-Rate Method. The new method yields constant curvature wellpath sections which are compatible with the directional performance of deflection tools. In addition to this advantage, this method also yields less dogleg severity of well trajectories, and, consequently, less drag and torque on the drill string. As a result, it is expected that the directional drilling operation should be easier, safer, and more economical if the wellpaths are Planned using the proposed method. Mathematically, the formulation of the method involves integrals that do not have closed form solutions and need to be estimated numerically. To avoid the numerical integrations, two alternative approximations to the exact solution, namely Pjecewjs~Radjus~f Curvature Method and Piecewise-Constant-Turn-Rate Method, are presented. Sample computations show that the Piecewise Constant-Turn-Rate Method gives better approximations and the calculations can be carried out using a hand-held calculator. Introduction At present, three methods are available for planning 3-D directional wellpaths, namely, the Radius-of-Curvature, Constant-Turn-Rate, and Turn-in-Plane Methods. A careful comparison and analysis of these methods can be a subject of a separate paper. Here, we just briefly review the basic concepts of these methods. The Radius-of-Curvature Method was originally proposed by Wilson as an improved method for computing directional surveys. Rivero used the equations involved in this method for the purpose of determining the true vertical reservoir thickness. McMillian was the first to utilize the radius of curvature equations for planning directional wellpaths. The second method, the Constant-Turn-Rate Method, was presented by Planeix and Fox to avoid the trial and error procedure associated with the Radius-of-Curvature Method. The third method, the Turn-in-Plane Method, was also presented by McMillian in the form of matrix transformation. Brown employed this method for wellpath planning in the form of coordinates transformation. Sun made a comparison of these three methods and recommended the third method be used for future wellpath design because it gives the shortest simple smooth path between two given points within a plane. The major purpose of this paper is to provide drilling engineers an efficient method of designing 3-D wellpaths with which the number of BHA changes and adjustments are minimized. In the course of wellpath planning for given geological conditions, the designer must consider a number of factors, the most important being the directional performance of the BHA and the strength limitations of the drill string. It is self-evident that the shape of the wellpath should be consistent with the directional tendencies of the BHA during actual drilling operations. Drilling holes without consideration of BHA performance is costly and time consuming due to the numerous tripping operations that are required for BHA changes. Based upon field experiences, it is a rather common belief that a given BHA at a constant weight on bit, has a tendency to drill a hole with a fairly constant curvature. Of course, varying downhole conditions will influence this tendency. P. 619^