An oblique circular arc representation for wellbore trajecories, a geometric analysis termed the sectional method, is presented. This approach permits projected line segments to be functions of the dogleg angle and to be related to usually measured displacements between survey stations. The advantages of this analysis are: a solution for the dogleg angle and a method of survey interpretation, the sectional method; a procedure for exact interpolation of true vertical depth, azimuth, and inclination between survey stations; a basis of solution for a computer program which provides course correction information during a turn to a target. The program provides a solution summary for a course correction from various survey stations in a well to any planned target. As a result, an optimum course correction or “minimum plugback depth” can be quickly determined. Once the desired kickoff point is selected, the program provides an exact solution of true vertical depth, azimuth, inclination, and toolface angle for every 100 of correction course length. The latter result provides a dramatic improvement in existing technology because all measurements used to control the correction run are now based on a center of turn rather than the arbitrary reference used in the typical ouija board solution; and because the solution is exact, such variables as effective toolface angle can better be evaluated and precisely corrected resulting in the smoothest possible turn with minimum doglegs.

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