A stochastic analysis of the coupled lateral-torsional drill string vibration

Drilling operations in the oil and gas industry present a highly complex dynamic. In this paper, the coupled lateral-torsional vibrations of a drill string are investigated in order to define different combinations of vibrations, possible operation regimes, and safe work zones. A three-degrees-of-freedom lumped parameter model is presented, with a constant top speed, fluid-structure interaction, contact with the borehole wall, and a nonlinear bit-rock interaction. Furthermore, a stochastic model is proposed in order to take into account parametric uncertainties. At first, a deterministic model is used to classify different types of dynamic response regime. Subsequently, uncertainties in the borehole wall, in the bottom hole assembly eccentricity, and in the bit-rock interaction are modeled as random variables. Probabilistic maps, which quantify the chance of occurrence of critical phenomena (such as severe torsional vibrations) in different drilling configurations, are constructed and analyzed. In addition, new field data of drill string lateral vibrations are presented.