Evolution pattern and control mode of well deviation for spatial-arc trajectories

Abstract

The well deviation equation of spatial-arc trajectory was established, the solution methods to determine the posture of the inclined plane that the spatial-arc trajectory lies on and the extreme value of inclination angle of the spatial-arc trajectory were presented, and the evolution pattern and control mode of well deviation for spatial-arc trajectories was revealed. Some parameters can be calculated by the forward model and inverse model respectively, including the inclination angle and azimuth angle at any point along a spatial-arc trajectory, the inclined angle and inclined azimuth angle of the inclined plane that the spatial-arc trajectory lies on and the various parameters at the point with extreme inclination angle, and the calculated results from the forward model are the same as those from the inverse model. There are two points with extreme inclination angles along a spatial-arc trajectory or its trendline, and the tangent lines of wellbore trajectory at the points with minimum and maximum inclination angles point to downdip and updip directions of the inclined plane respectively, the bending angle and azimuth angle differences between the two points are both 180°. The posture of inclined plane and parameters at extreme inclination points relate to the inclination angle and tool face angle at the beginning point of well interval, but have nothing to do with the interval length. The inclined angle mode for controlling a spatial-arc trajectory is ambiguous, so the tool-face angle or directional azimuth angle modes should be used. Key words: drilling theory, directional drilling, wellbore trajectory, spatial-arc model, well deviation evolution