# Destruction of Nonholonomic Constraints a Sticking Drill String by the Method of Transverse Vibrations

## Abstract

The proposed discrete-continuum mathematical model for releasing the trapped drill string takes into account the dynamic excitation, the elastic deformation of the free part drilling pipe assembly, and the formation of loads on the grabbed zone, as well as the dynamics of the adhered arrangement drill pipes. The model is designed for the case of the location of the vibration mechanism near the drill rig's grappling area for transverse vibration excitation. The task of releasing the drill string is solved with account of the external force generated by the vibrator and the resistance forces of the captured pipe caused by the pressure on them of the rock. The basis of the proposed method is the equations of longitudinal and bending oscillations of an elastic rod — the differential equations of hyperbolic type in partial derivatives with two independent variables, as well as the molecular-mechanical theory of friction. In the process of solving the system of differential equations was reduced to the Sturm-Lowville problem with boundary conditions of the first and second kind with the subsequent application of the Fourier method. In the paper, formulas were obtained for determining the rock pressure per drill pipe for various types of stuck. Recommendations are formulated to reduce friction due to the use of vibration devices. As a result, dependencies were obtained, which allowed using the results of geophysical research in the well, to evaluate the effectiveness of the use of vibration devices for the elimination of accidents during drilling, without breaking the strength of the pipes. The author conducted an analysis of the influence of low frequency oscillations on the coefficient of friction of drill pipes on the wall of the well when disturbing transverse vibrations. The recommendations on the selection of frequency and amplitude of disturbing force that will free stuck pipe column and prevent their destruction.

## Article Details

Issue
Section
Mathematical and Calculation Physics
Author Biography

### K. G. Levchuk, Івано-Франківський НТУ нафти і газу

доцент, докторант

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