Drill-string dynamics with uncertainty in the bit-rock nonlinear interaction model (original) (raw)
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Non-linear dynamics of a drill-string with uncertain model of the bit–rock interaction
International Journal of Non-linear Mechanics, 2009
The drill-string dynamics is difficult to predict due to the non-linearities and uncertainties involved in the problem. In this paper a stochastic computational model is proposed to model uncertainties in the bit-rock interaction model. To do so, a new strategy that uses the non-parametric probabilistic approach is developed to take into account model uncertainties in the bit-rock non-linear interaction model. The mean model considers the main forces applied to the column such as the bit-rock interaction, the fluid-structure interaction and the impact forces. The non-linear Timoshenko beam theory is used and the non-linear dynamical equations are discretized by means of the finite element method.
Probabilistic model for the bit-rock interaction model of a drill-string system
2021
In this paper a probabilistic model is proposed for the bit-rock interaction model of a drill-string system. A new strategy to take into account uncertainties in a local constitutive nonlinear equation using the nonparametric probabilistic approach is developed. The deterministic model considers the main forces that are applied to the column such as bit-rock interaction, fluid-structure interaction and impact forces. The nonlinear Timoshenko beam theory is applied and the system is discretized by means of the Finite Element Method.
Drill-string with uncertainty in the bit-rock interaction
In this paper a probabilistic model is proposed for the bit-rock interaction model of a drill-string system. A new strategy to take into account uncertainties in a local constitutive nonlinear equation using the nonparametric probabilistic approach is developed. The deterministic model considers the main forces that are applied to the column such as bit-rock interaction, fluid-structure interaction and impact forces. The nonlinear Timoshenko beam theory is applied and the system is discretized by means of the Finite Element Method.
This paper deals with a procedure to perform the identification of the probabilistic model of uncertainties in a bit-rock interaction model for the nonlinear dynamics of a drill-string. The bit-rock interaction model is represented by a nonlinear constitutive equation, whose uncertainties are modeled using the nonparametric probabilistic approach. The identification of the parameter of this probabilistic model is carried out using the maximum likelihood method together with a statistical reduction in the frequency domain using the Principal Component Analysis.
Drill-string dynamics coupled with the drilling fluid dynamics
A drill-string is a slender structure that turns and drills into the rock in search of oil. A numerical model is developed using the Timoshenko beam theory and approximated by means of the Finite Element Method. The aim this work is to investigate the influence of the drilling fluid in the dynamics of the drill-string. So, a model for the fluid-structure interaction that takes into account the drilling fluid that flows downwards the column then goes upwards in the annulus is used. In addition, other efforts that the column is subjected to are considered: rotation at the top; hanging force at the top; bit-rock interaction; shock and rubbing between the column and the borehole; finite strains (what couples axial, torsional, and lateral vibrations); and the own weight of the column.
Stochastic modeling for hysteretic bit–rock interaction of a drill string under torsional vibrations
Journal of Vibration and Control, 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.
Drill-string horizontal dynamics with uncertainty on the frictional force
This paper analyzes the dynamics of a horizontal drill-string. In this dynamics, the frictional forces between the column and the borehole are relevant and uncertain. A stochastic model is proposed for the frictional coefficient: a random field with exponential autocorrelation function. In the numerical analysis, the drill-string is modeled using the bar model (tension/ compression), and is discretized by means of the finite element method. An oscillatory force (due to mud motor) is imposed on the system and there is a bit-rock interaction as the column moves forward. We propose a new way to measure the efficiency of the process: an output/input power ratio. The resultant random ratio is analyzed, and it turns out that it presents a bimodal characteristic, an unexpected result.
Modeling and experimental identification of torsional drill string dynamics under uncertainties
2018
This D.Sc. thesis proposes new perspectives for modeling drill string torsional dynamics under uncertainties. This work develops a novel stochastic hysteretic (nonreversible) bit-rock interaction model. Firstly, a new nominal interaction model, which depends not only on the bit speed, but also on the bit acceleration is developed. Then, a new stochastic model for the bit-rock interaction, taking into account the inherent fluctuations during the drilling, is also proposed. Furthermore, here a new test-rig is proposed to analyze drill string dynamics and bit-rock interaction, which is able to reproduce stick-slip phenomena while drilling a rock sample using standard masonry bits, as well as to validate bit-rock interaction models. An original strategy for modeling uncertainties globally, based on terms of the nonparametric probabilistic approach, considering a simple torsional model for a drill string, is also proposed herein. This strategy allows to control the dispersion level of ea...
Computational modeling of the nonlinear stochastic dynamics of horizontal drillstrings
This work intends to analyze the nonlinear stochastic dynamics of drillstrings in horizontal config- uration. For this purpose, it considers a beam theory, with effects of rotatory inertia and shear deformation, which is capable of reproducing the large displacements that the beam undergoes. The friction and shock effects, due to beam/borehole wall transversal impacts, as well as the force and torque induced by bit-rock interaction, are also considered in the model. Uncertainties of bit- rock interaction model are taken into account using a parametric probabilistic approach. Numerical simula- tions have shown that the mechanical system of inter- est has a very rich nonlinear stochastic dynamics, which generate phenomena such as bit-bounce, stick-slip, and transverse impacts. A study aiming to maximize the drilling process efficiency, varying drillstring velocities of translation and rotation is presented. Also, the work presents the definition and solution of two optimizations problems, one deterministic and one robust, where the objective is to maximize drillstring rate of penetration into the soil respecting its structural limits. A. Cunha Jr (corresponding author) Universidade do Estado do Rio de Janeiro, Instituto de Matem ́atica e Estat ́ıstica, Departamento de Matema ́tica Aplicada, Rua S ̃ao Francisco Xavier, 524, Pav. Jo ̃ao Lyra, Bl. B, Sala 6032, Rio de Janeiro, 20550-900, Brasil E-mail: americo@ime.uerj.br A. Cunha Jr · C. Soize Universit ́e Paris-Est, Laboratoire Mod ́elisation et Simula- tion Multi Echelle, MSME UMR 8208 CNRS, 5, Boulevard Descartes 77454, Marne-la-Vall ́ee, France E-mail: christian.soize@univ-paris-est.fr A. Cunha Jr · R. Sampaio PUC–Rio, Departamento de Engenharia Mecˆanica, Rua M. de S ̃ao Vicente, 225 - Rio de Janeiro, 22451-900, Brasil E-mail: rsampaio@puc-rio.br Keywords nonlinear dynamics · horizontal drill- string · uncertainty quantification · parametric probabilistic approach · robust optimization