The trajectory of a wellpath is a tortuous space curve with permanent changes in directions and curvatures. A usage of steerable directional drilling tools in nowadays drilling practices even more forces the bit apart from its natural tendencies of running a smooth course - enforcing a highly curved shape of the well. Although this is well known all to the author's knowledge existing wellpath computation methods are based on piecewise approximating the wellpath with constant curvature linear, circular and helical curves and arcs.

A new proposed trajectory computation method gives up these old paradigms and introduces a new approach to accurately calculate the spatial course of a wellpath while maintaining its realistic shape from standard wellbore survey measured depth, inclination and azimuth data. In detail the discussed algorithm is founded on fundamental differential geometry practices in synergy with piecewise spline-curve approximation techniques. This limits the common problems of spline-curve approximations. The result is a highly accurate wellpath description with proven curvature continuity in any position along its course.

The proposed new method is a further step in more accurate wellbore trajectory and dogleg severity computation- especially for complex shaped and extended reach wells. The proposed model's accuracy and reliability is proven and verified with a complex shaped, 11.3 km synthetic wellbore example (with known results) followed by extended-reach and complex shaped field case studies.

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