Low dimensional model of multi-impact jarring

Downhole stuck tools are a significant source of downtime during drilling, and jarring tools can remedy such problems. In a typical jarring operation, axial impact releases a stuck tool during drilling. Innovative jarring tool designs generate multiple, high-frequency impacts, but existing models of jarring operations focus on conventional jarring with a single impact. In this work, we developed two low-dimensional models to describe a multi-impact jarring system to investigate nonlinear behaviour during multi-impact jarring. A simplified strongly nonlinear one degree-of-freedom model with a realistic dynamic loading scenario was selected for investigation through a direct numerical simulation. Typical nonlinear dynamics characteristics, such as time–history evolutions, phase portraits, and bifurcation diagrams, are presented. In addition, novel steady-state force equilibrium diagrams are constructed. Results of the numerical simulations indicate the system behaviour is sensitive to operational parameters, namely the excitation frequency. We present examples of the system dynamic responses ranging from periodic to chaotic solutions, strongly affecting the transmitted force onto a stuck pipe. Our analysis shows that the external excitation frequency has a major effect on system operation and can be used to improve tool performance.