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

Abstract

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.

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

“…This macroscopic phenomenon is related to a frictional memory due a friction force's delay, where the bandwidth of the loop increases according to the drill string acceleration Hess DP and Soom A (1990); Olsson KJ et al (1998); Wojewoda J et al (2008). The deterministic hysteretic bit-rock interaction model considered in the present paper Real FF et al (2018) reads…”

“…In Real FF et al (2018), the authors have highlighted large fluctuations of the nonlinear bit-rock interaction law during the drilling. These fluctuations which are mainly due to the random soil mechanical properties during the drilling, and have to be taken into account in order to study the stability of the drill string with a good robustness.…”

“…As proposed in Real FF et al (2018), the rotational displacements about a rotating frame is considered. Let θ rel (x, t) be the relative torsional degree of freedom in the rotating frame associated to the top sectional area (at x = 0).…”

“…A window average smoothing was used to filter measurements noise and obtain these stickslip cycles. A deterministic bit-rock interaction model that takes into account the observed hysteresis (non-reversibility) effect was proposed in Real FF et al (2018). Hysteretic (non-reversible) behaviour is more evident when the drill bit is slipping (high torsional oscillations).…”

“…In Real FF et al (2018), the parameters of this bitrock interaction model have been calibrated such that it fits with the mean field data cycle. The optimal parameters are b 0 = −3478, b 1 = 938, b 2 = 2.56, b 3 = 0.38, b 4 = 0.78, and b 5 = 1.1, β 1 = 14%, β 2 = 10.6. .…”