Comparison of dispersive relation of the oil well with that of the fluid cylinder and the hollow in solid

Abstract

Acoustical well logging is a widely used technique in oil fields to investigate the formation outside wells and the quality of wells. The knowledge of the acoustical behavior of the wells is important to the technique and has been widely studied. The wells are usually modeled as a fluid filled cylindrical borehole in an infinite solid medium. This structure with an infinite section, sometimes called as open waveguide, is more difficult to study than the typical acoustical waveguide with finite section and free or rigid boundaries. In this presentation the well is studied as a coupled vibration system consisted of the fluid cylinder inside the well and the solid formation outside the well. The dispersive relations of 3 systems, i.e., the circular fluid cylinder with rigid boundary, the circular hollow in solid medium and the fluid filled borehole in solid, are numerically calculated and compared.