Eventos Anais de eventos
DINAME 2023
XIX International Symposium on Dynamic Problems of Mechanics
A comparison of two drill-string models that include the dynamics of the cutting at the bit
Submission Author:
Hector Eduardo Goicoechea Manuel , RJ
Co-Authors:
Hector Eduardo Goicoechea Manuel, Roberta Lima, Fernando Buezas, Rubens Sampaio
Presenter: Hector Eduardo Goicoechea Manuel
doi://10.26678/ABCM.DINAME2023.DIN2023-0006
Abstract
In this paper, a comparison of the two dynamics predicted by two different models of a drill-string is made. All the simulations consider a structure that is 1200 m long, with the same geometric and material set of parameters. In the first model, an established two degrees-of-freedom (DOF) formulation is used, with 1-DOF for the axial dynamics and 1-DOF for the torsional one. The second model uses the same 1-DOF axial formulation and a wave-equation for the torsional shaft. In both cases, the structural dynamics are coupled with the dynamics of the cutting through the depth-of-cut used in the bit-rock interaction relation. In both models an advection equation is solved along with the equations of motion to calculate the previous depth. The major contributions of the study are: 1) the modelling of the cutting by means of a bit-rock interaction relation, that among other parameters, depends on an instantaneous depth-of-cut, and that does not restrict backward rotation nor bit-bounce; 2) the calculation of the depth-of-cut through the resolution of an advection equation, as an alternative to introducing delays in the system of differential equations; 3) the extension of the advection approach to allow rotation in both directions; 4) the combination of the previous items with a distributed representation to account for the torsional dynamics; 5) the inclusion of the 2-DOF model as a limiting case of the continuous model, for which a strategy introducing an extra parameter α is used. Some application cases considering different operation conditions are simulated. The results show that the dynamics can differ considerably. This suggests that the second model, with a continuous torsional shaft, could be capturing aspects of the dynamics that are neglected in the first model, with the 2-DOF approach. On top of that, some comments regarding the choice of one approach over the other are made.
Keywords
drill-string dynamics, soil cutting, Advection Equation, torsional oscillations, stick-slip
