Constant curvature method for planning a 3-D directional well

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 Piecewise-Radius-of-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