Directional deflection equations for steerable drilling tools and the control mechanism of wellbore trajectory

To meet the wellbore trajectory control requirements for all kinds of steering drilling modes, the directional deflection equations for steerable drilling tools and the process control method for wellbore trajectory were proposed and an application example was given. By proving that the orientation direction of steerable drilling tool was consistent with the principal normal direction of borehole trajectory, directional deflection equations for steerable drilling tools were established. By establishing the relation curves between the build-up rate and tool face angle, and the relationship between built-up rate and orientation azimuth angle of steerable drilling tool, a process control technique for wellbore trajectory was presented. The research shows that the build-up rate of steerable drilling tool determines the curvature of wellbore trajectory, the orientation direction of steerable drilling tool determines the principal normal direction of wellbore trajectory; the orientation azimuth angle and the tool face angle both have the orientation function, and they can calculate and complement each other. These research results reveal the interaction mechanism and control mechanism between steerable drilling tools and wellbore trajectory, so the control scheme of wellbore trajectory can be formed based on the planned wellbore trajectory, and operating characteristics of steerable drilling tool can be controlled and monitored while drilling.