Borehole trajectory uncertainty and its characterization

To solve the problem of borehole trajectory uncertainty, some methods such as error ellipsoid posture characterization, sectional error ellipse solution and error elliptic cylinder construction were proposed and an application example was given. According to the definition of inclination, azimuth and tool-face angle, a characterization method of error ellipsoid posture of borehole trajectory was presented. By intercepting the error ellipsoid with an arbitrary plane in space, the general concept and algorithm of sectional error ellipse were established to analyze the borehole trajectory errors in horizontal plane, plumb plane, normal plane, etc. Based on the theory of surface tangency and curve projection, a construction method of error elliptic cylinder of borehole trajectory was put forward to evaluate the axial enveloping error of borehole trajectory and its variation along well depth. The research shows that the deeper the well, the greater the borehole trajectory error will be. In deep and ultra-deep wells measured using conventional measurement while drilling (MWD), the borehole trajectory position error reaches tens of meters. The research results provide a complete set of analysis methods for borehole trajectory error, which can evaluate the accuracy and reliability of borehole trajectory monitoring. Key Words: drilling theory, directional drilling, borehole trajectory, measurement-while-drilling, uncertainty analysis, error analysi