Bayesian approach to identify the bit–rock interaction parameters of a drill-string dynamical model

Abstract

A drill string is a slender structure used to search for oil and gas. Many works have tackled the problem of modeling the drill-string dynamics in a vertical well. One important aspect in this dynamics is the bit-rock interaction, and, therefore, an identification of the parameters of the bit-rock interaction model becomes crucial. Few works related to this identification problem have been published. The present paper applies the Bayesian approach to identify the parameters of the bit-rock interaction model considering a simplified drill-string dynamical model which takes into account only torsional vibrations. It is assumed an additive Gaussian noise model, and the Metropolis-Hasting algorithm is used to approximate the posterior distribution of the variables analyzed.

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

“…This type of torque-on-bit and bit speed 2 relation (weakening effect) has been observed experimentally before [9,19]. Some authors consider a non-linear function for the torque-on-bit versus bit speed to represent the bit rock/interaction model [4,17], while others apply a switching mechanism [6]. One can find coupled axial-torsional bit/rock interaction models, such as [12,22].…”

“…There are several papers available in the literature concerned with the drill string torsional dynamics and stick-slip oscillations [4,8,5,17,18,7,23]. A pure torsional model is sometimes enough to represent this kind of system.…”

“…Field data of a five kilometer drill string is analyzed in [18], where again a pure torsional model presented satisfactory results reproducing field data, where torsional vibration was the dominant phenomenon observed. More generally, a coupled axial-lateral-torsional model should be applied [21,17]. A full description model, including all dynamics, although possible, presents many difficulties due to lack of downhole data.…”

Stick–slip vibrations in oil well drillstring: A review

“…For such bit-rock interaction model, the stochastic friction forces and the parameters selection are sources of uncertainties. In a latest work by Ritto, 42 identification of factors of the bit-rock contact model was investigated. In order to control stick-slip vibration through startup trajectory design, Aarsnes et al 43 presented a distributed model of drillstring to replicate the stick-slip vibration caused by transition of static and dynamic frictions.…”

Bayesian inference applied to journal bearing parameter identification

“…The methodology of model updating using Bayesian inference was used by Zhang et al [17], where modeling errors were considered. Marwala [18] used Bayesian inference to updating a finite element model, and Ritto [19] applied it to parameter identification in drill bits.…”