Abstract
Comparative analysis whether considering the lateral inertia or not, aiming at the longitudinal vibration of the drill string in drilling progress, is proposed. In the light of the actual condition, the mechanical model of the drill string about vibration is established on the basis of the theoretical analysis. Longitudinal vibration equation of the drill string is derived from the Rayleigh-Love model and one-dimensional viscoelastic model. According to the Laplace transform method and the relationships among parameters of the model, the solutions to complex impedance at the bottom of the drill string are obtained, and then the comparison results are analyzed, which is the lateral inertia effect on longitudinal vibration characteristics. The researches show that the smaller the length of the drill string, the greater the cross-sectional area of the drill string, the greater the damping coefficient of bottom hole on the bottom of the drill string, and the more evident the effect on the dynamic stiffness of the drill string with lateral inertia effect. The Poisson ratio of the drill string only has some effects on it taking account of the lateral inertia effect, and the influence is relatively small compared with the former three conditions.
Highlights
In oil and gas drilling engineering, the drill string is a slender structure connecting downhole tools and drilling rig
The drill string vibration can be divided into three forms such as longitudinal, lateral, and torsional vibration, in which the longitudinal vibration is the main factor of drilling efficiency and safety
For obtaining the results of the equation, similar to the method which is used for the solution of model without considering the influence of lateral inertia effect on drill string vibration, considering the initial and continuity conditions, the vibration equation of the drill string is solved by Laplace transform, and the displacement expression of the drill string, with considering the influence of lateral inertia effect, can be obtained
Summary
In oil and gas drilling engineering, the drill string is a slender structure connecting downhole tools and drilling rig. For the solutions of drill string vibration analysis methods with complex influence factors and boundary conditions, the related researches include taking the drill string as elastomer, or obtaining vibration equations with dynamics FEM (finite element method), or analyzing longitudinal vibration considering the coupling effects of wellbore friction or the hydrodynamic interaction of drilling fluid [9,10,11,12,13,14]. With the search results of reference articles, previous research work was not found about the lateral inertia effect on drill string longitudinal vibration. The influence of the lateral inertia effect on the drill string longitudinal vibration is discussed in this paper. According to well structure and drill string working conditions, the longitudinal vibration models whether considering the lateral inertia or not are established. With the presented analysis models and solution equations, the influences of considering the lateral inertia effect or not on drill string longitudinal vibration are discussed. The research results can present theoretical and actual value for optimization of downhole tools design and safety evaluation of drilling operations
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