Numerical calculation for the distance to target center in directional and horizontal wells

The calculation of the distance to target center is important in the trajectory quality inspection, and its core is to solve the coordinate of the entry point to targets. The entry point is a cross point of trajectory and a spatial plane: in directional wells, this plane is the horizontal plane; in horizontal wells, it is the vertical plane of the target axis. A scanning algorithm for target-entry interval is given according to the concept of directed distance from point to plane. This method can fast determine the target-entry interval. This article studies the numerical iterative method-bisection and its convergence performance, which is used to solve the key-parameter equation of target-entry point, and provides detailed formulas for three interval curve types of spatial arc, cylindrical helical, and natural curve. Theoretical and practical cases show that the bisection method is very effective in obtaining the numerical solution of target-entering point.