VIBRATION CHARACTERISTICS ANALYSIS OF MULTI-SPAN DRILL STRING SYSTEM BY MEANS OF GREEN'S FUNCTIONS

With the continuous expansion of petroleum exploration and development toward deep, deep water, and unconventional areas, the well conditions and constraints faced by drilling have become more stringent, the dynamics of the drill string have become more complex, and well failures frequently occur. In this paper, the two-way coupling dynamic characteristics of multi-span spinning drill string are quantitatively analyzed and studied by using Green’s function theory. Considering the multi-stabilizers and different constraints, taking the whole drill string as the research object, the bidirectional coupling dynamic equation of spinning drill string with generalized boundary constraints and multi-stabilizers is established by the grounds of Bernoulli-Euler beam theory and Hamilton principle. The vibration differential equations are solved by using the separation variable method, Laplace transform and, inverse Laplace transform. The Green’s functions of the transverse vibration of the spinning drill string system and the closed-form mode shapes and the implicit frequency equation of the multi-span rotating drill string system based on the Green’s functions are obtained. The influence of stabilizer position, of spring stiffness coefficient and of the number of stabilizers on the vibration characteristics of the drill string system is quantitatively analyzed. The numerical results show that the positions of stabilizers and the equivalent spring stiffness have great impacts on the natural frequencies and mode shapes of the system. The relationship curve between the stabilizer position and the natural frequency has corresponding order peaks. With the increase of the stiffness coefficient of the equivalent spring, the natural frequency of the system increases, but when the stiffness increases to a certain value, the first and second order frequencies of the system will tend to be a constant. The research results are helpful to deepen the understanding of the dynamic characteristics of multi-span rotary drill string, and to provide a new research method and theoretical basis for improving drilling speed and, reducing drill string failure, and to extend the application of drill string drilling technology.