Stochastic modeling for hysteretic bit–rock interaction of a drill string under torsional vibrations

© The Author(s) 2019. This paper aims at constructing a stochastic model for the hysteretic behavior of the nonlinear bit–rock interaction of a drill string under torsional vibrations. The proposed model takes into account the fluctuations of the stick–slip oscillations observed during the drilling process. These fluctuations are modeled by introducing a stochastic process associated with the variations of the torque on bit, which is a function of the bit speed. The parameters of the stochastic model are calibrated with field data. The response of the proposed stochastic model, considering the random bit–rock interaction, is analyzed, and statistics related to the stability of the drill string are estimated

Hysteretic bit/rock interaction model to analyze the torsional dynamics of a drill string

The present paper proposes a novel hysteretic (non-reversible) bit/rock interaction model for the torsional dynamics of a drill string. Non-reversible means that the torque-on-bit depends not only on the bit speed, but also on the bit acceleration, producing a type of hysteretic cycle. The continuous drill string system is discretized by means of the finite element method and a reduced-order model is constructed using the normal modes of the associated conservative system. The parameters of the proposed hysteretic bit/rock interaction model is fitted with field data. The non-linear torsional vibration and the stability map of the drill string system are analyzed employing the proposed bit/rock interaction model and also a commonly used reversible model (without hysteresis). It turns out that the hysteretic model affects the stability region of the system

A probabilistic model of uncertainties in the substructures and interfaces of a dynamical system: application to the torsional vibration of a drill-string

International audienceIn this paper a new strategy for modeling uncertainties in the substructures and interfaces of a dynamical system is presented. This strategy is based on (1) the reduction of the dynamical model of each substructure using the Craig-Bampton method and (2) the use of the nonparametric probabilistic approach for the global modeling of uncertainties in each substructure. As an improvement with respect to existing nonparametric methods, the methodology proposed here constructs separated models of uncertainties for the inner and interface degrees of freedom, which allows to control separately the levels of fluctuation induced by these two sources of uncertainties. This methodology is applied for the analysis of the random vibration of a drill-string. Three strategies are compared: (1) a full nonparametric probabilistic approach on all the system, (2) the existing nonparametric probabilistic approach together with the Craig-Bampton substructuring method, and (3) the new nonparametric probabilistic approach proposed here with the separation of the inner and interface degrees of freedom uncertainties. It turns out that, for the same level of uncertainty, the three approaches give similar results but the new approach gives more flexibility for the control of the probabilistic model