Longitudinal vibration of a heterogeneous drill string during directional drilling
In most cases, when drilling directional wells, a drill string «lies» on the bottom wall of a well. In this case, during the flow of wave processes, the role of the dissipative forces acting along the length of the drill string should sharply increase. Dissipative forces acting along the length of the drill string in an inclined well, are a combination of friction, obeying the Amonton -Coulon’s law, and the forces beyond the direct control of the normal pressure. The article studies the problem of wave perturbations propagation along a heterogeneous drill string with account of the dry friction forces during directional drilling. Investigated the case when a drill string is composed of two different segments, equivalent to the sectors of drill pipes and drill collars is studied. A mathematical model of the wave propagation in a drill string, consisting of two different segments, with account of Coulomb friction force, when drilling directional wells is developed. To solve the nonlinear problem related to the occurrence of wave processes along the length of the drill string with account the dry friction force, the method of averaging and the method of mechanical analogue, that allowed to linearize the task are applied. The conducted analysis of the mathematical model of the wave propagation processes along a drill string in an inclined well has allowed to establish the relationship between the parameters (amplitude and frequency) of harmonic disturbance and mechanical parameters of a drill string under which the bottom-hole perturbation propagates through the drill string. The conditions of the longitudinal resonance development and the ratio to determine the boundaries of the total attenuation of downhole perturbations during its propagation through the drill string, consisting of two different segments, are obtained.