An Innovative Method for Designing Smooth Catenary Well Trajectories in Extended-Reach Drilling

A catenary well trajectory is known for its reduced drag and torque during drilling. Modern deflection tools have made it possible to drill catenary well trajectories efficiently, thanks to tool’s capacity of dynamic build rate that creates wellbore profile of varying curvature. However a method to design well trajectory with smooth transition from the kick-out point to the catenary section to reduce “dog-leg” and thus friction is still lacking. This paper presents a 2D mathematical solution to fill the gap. The solution uses equations of closed-form rather than numerical computations. The complete well trajectory profile involves a vertical section, a transitional arc section, a catenary section, and a horizontal/slant section. A case study is presented to compare the friction forces on the drill string in a catenary trajectory profile and a conventional trajectory profile of arc type. The calculation procedure of catenary trajectory design was realized in an MS Excel spreadsheet with direct inputs, which provides an excellent flexibility to meet well trajectory design requirement. The presented mathematical model is an easy-to-use and reliable tool for designing catenary well trajectories in extended-reach wells to minimize wellbore friction and thus increase well depth.