Abstract
The present paper studies the effect of an axial elastic tool (known as a shock sub), mounted downhole in the drill-string, on the occurrence of axial and torsional self-excited vibrations. In particular, we evaluate the feasibility of stabilizing the axial dynamics, dominated by a bilateral (feedback) coupling between the bit-rock interaction and the drill-string wave-equations, through the insertion of a passive down-hole tool. We consider the problem of unwanted drill-string vibrations and explain how these vibrations relate to the so-called axial instability using a distributed parameter (infinite dimensional) model. The equations describing the feedback system causing this instability are derived and then extended to accommodate for the inclusion of the effect of the shock sub. Conditions for the design parameters of the shock sub needed to avoid axial instability are then derived and their practical feasibility are considered.
Original language | English |
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Article number | 106217 |
Number of pages | 14 |
Journal | Journal of Petroleum Science and Engineering |
Volume | 181 |
DOIs | |
Publication status | Published - 1 Oct 2019 |
Funding
This research was financially supported by ConocoPhillips, AkerBP, Statoil, Wintershall and the RCN grant ( 203525/O30 ) DrillWell, by European Union's Seventh Framework Programme for research, technological development and demonstration under Marie Curie grant agreement no [ 608695 ], and the FRIPRO Mobility Grant Fellowship Programme (FRICON). Appendix A
Keywords
- Distributed parameter systems
- Drill-string vibrations
- Hyperbolic systems
- Infinite dimensional systems
- Stability
- Stick-slip