A Geometric Approach to Drill Path Collision Avoidance

Tremendous research activities took place on the proximity analysis of points and straight lines in three-dimensions using Voronoi diagrams. However, less attention has been paid to the proximity of curves in three-dimensions due to the complexity involved in computation. Hence, in this paper, we present a geometric approach to collision detection between curves of restricted topologies in a three-dimensional space. The proximity of petroleum well drilling paths under an oilfield has been chosen as the area of application. Mature oilfields with many existing boreholes, which are exploited by directional drilling, have complex three-dimensional structure underneath. To avoid "blowouts", which may lead to fires and explosions, interference check or collision avoidance calculation is often necessary while planning a new drilling path for such an oilfield. In this paper, we present an efficient volume-sweep approach to collision detection between a newly planned drilling path and the existing drilling paths under such a multiwell oilfield. Upon collision detection, we make use of 2D Voronoi graph topology representation to facilitate further in interactive drill path corrections.