Evaluation of inclined arc trajectory parameters for design and control of 3D directional well

Abstract

The circular-arc trajectory on inclined the plane is one of the models for the orbit design of directional drilling. The key issue of the design and control for the circular-arc trajectory is how to judge the theoretical calculated values of the target-hitting azimuth and tool face angle, because the target-hitting azimuth and tool face angle toward targets of 3D directional well may exist in four quadrants of 0 ${}^{\circ}$ $\sim$ 360 ${}^{\circ}$ . Based on the spatial geometric model of the circular-arc trajectory on the inclined plane, a new evaluation method of target azimuth change is proposed according to coordinates of the target relative to the horizontal projection of two lines’ intersection. These two lines are tangents at the starting and ending points of the complete build-up curve section respectively. Therefore, the analytic expression of a criterion for target azimuth change in the deflecting section is obtained. For control of circular-arc trajectory, a judgmental method of the tool face angle is also discussed in the paper, and its criterion is worked out using quadrant overlap of the value calculated by two formulas of tool face angle. The practical engineering cases have demonstrated that the new evaluation methods of the target azimuth and the tool face angle are effective. And the trajectory data of back calculation shows high accuracy to hit the target. Compared with traditional evaluation modes, the methods proposed in this paper avoid the ambiguity of 0 ${}^{\circ}$ azimuth and the partial increase of tool face angle. Simultaneously they can be applied directly in practical project as well as algorithm of directional drilling software.

Keywords

Directional drilling well trajectory inclined arc target azimuth tool face angle evaluation model

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