Research on Establishment and Solution of the Model of Drill String Vertical Vibration

Abstract

Aiming at the problem of the drill string vertical vibration on rotary drilling, the dynamic model of the drill string vertical vibration which caused by the interaction of drill bit and rock and elastic deformation of drill string is established by the theory of flexibility pole and cell method. The finite difference method is used to solve the drill string vertical vibration model under the given initial conditions and boundary conditions. In this study, MATLAB is employed to calculate results of displacement, velocity and acceleration of drill string vertical vibration in order to lay theoretical basis for further studying actual law of movement and dynamics performance of the drill string vibration. The drill strings are under some heavy and complex dynamic loadings. These loadings may result in excess vibrations, even more than the predicted limits and led to premature failure(1). The drill string vibration is a major factor of resulting in drill string failure and fatigue breakdown, which undergoes four kinds of vibrations during the drilling operation, including lateral vibration, vertical vibration, torsional vibration and hydraulic vibration(2). (3) shows that the drill string lifespan is most affected by the drill string vertical vibration, resulting in the vertical impact force up to 840kN, which is mainly caused by periodic upward vibration of roller-cone core bit. With the increasing difficulties of the drilling for oil resources, a number of new drilling technique and technology are widely used to predict and control the law of movement and dynamic performance of downhole drill bit and the drill string. How to reasonably and effectively improve the strength of drill string and to achieve the precise control of well locus are the key technical issues of drilling engineering(4). Therefore, one of the methods is to establish a rational and reliable drill string dynamic model in order to solve these problems. In this paper, the model of drill string vertical vibration is built and the finite difference method is used to calculate the numerical solution of displacement, velocity and acceleration of the drill string vertical vibration. This study is significant to correctly understand the actual law of movement and dynamics performance of drill string, to