Torsional vibrations with bit off bottom: Modeling, characterization and field data validation

A distributed model of a drill string is presented, with Coulomb stiction as a distributed source term, to investigate the effect of borehole inclination and borehole friction on the incidence of torsional vibrations along a drill-string. To isolate the effect of this distributed friction, only cases where the bit is off bottom and with no axial movement are considered, and consequently a purely torsional model is used. The model is used to study the stick slip limit cycle, as caused by distributed Coulomb friction, and the limit-cycle period and amplitude dependence on the friction parameters is derived. This enables the qualitative limit-cycle behavior to be characterized as inertia or stick dominated, and examples of this characterization is validated with the field data. For comparison, high frequency field data from two deviated wells from surface and downhole sensors are considered. Time-series are isolated where angular rotation is restarted after a connection, with the bit off bottom and before axial motion is re-initiated, to make the data consistent with the model assumptions. A close match is obtained between recorded and modeled downhole data, however, in some cases either the initial torsional strain in the drillstring is not known or axial motion is initiated, which violates model assumptions, causing a mismatch.