Analysis of Stick-Slip Oscillations of Drill-String via Cosserat Rod Model

An integrated model for the study of the complex dynamical and geometrical behaviour of a drill-string is developed based on the modified Cosserat rod element method. The model includes general deformation of the rod with flexure, extension, torsion and shear, and allows analysis of the main vibration modes, torsional, axial and lateral, and also their couplings. Shape functions are obtained from the solution of nonlinear partial differential equations of motion in quasi-static sense, containing up to third order nonlinear terms, and the final ordinary differential equations of motion for the elements are derived from Lagrange’s approach. Boundary conditions are taken as applied to a drill-string to account for the motor and the drill-bit. The model offers significant performance advantage over a standard Finite Element approach, which facilitates numerical analysis. Such model is capable of simulating stick-slip oscillations in the drill-bit–rock interface and contact of the drill-string with borehole wall along its length.