On the possibility of propagation of pipe and lemb waves in cylindrical wells filled with liquid

This work is devoted to the study of the propagation and dispersion of natural waves in oil-gas wells. A detailed analysis of well-known works devoted to this problem is given. In this work, a mathematical formulation and a methodology for studying the propagation, dispersion and attenuation of tube and Lamb waves in a well filled with liquid have been developed. To solve the problem and assess the damping properties of tube and Lamb waves in a well filled with liquid, the following methods were used: separation of variables, the theory of potential functions, an orthogonal sweep and central difference schemes. The complex roots (phase velocities) of the dispersion equation are determined by the methods of Mueller and Gauss. A number of new mechanical effects have been identified that have practical significance: the interference and dispersion of Lamb waves depends on the parameters of the well; the presence of a sliding contact between the pipe and the medium leads to the appearance of pipe and Lamb waves, and taking the viscoelastic properties of the pipe into account leads to a damping effect; with a system of zero frequency, despite the contact conditions between the elements of the system, both L and T waves have the same speed, and with an increase in the frequency of oscillations, the difference in the phase velocities of these waves increases.