Wave generation and source energy distribution in cylindrical fluid-filled waveguide structures

Abstract

The paper deals with an analytically based computer simulation of wave fields generated by a monopole source in a multilayered fluid-filled tube waveguide in an elastic or porous-elastic space. The mathematical problems considered relate to various practical applications ranging from a micro scale for fibers and nano-tubes to a macro scale for seismo-acoustics and well production. To be specific, the presentation is given for borehole waveguides, aiming at estimating the efficiency of an in-hole source for various surrounding media. The time-harmonic and transient solutions are obtained in terms of inverse Fourier integrals. The tube, body, and leaky waves propagating from the source to infinity are derived from those path integrals as an asymptotic contribution of the residues, stationary points, and approaching complex poles and stationary points. On this basis, the wave energy radiation from the source, which is dependent on the geometry and material properties of a cased fluid-filled borehole and formation, is numerically studied. The analysis is focused on the peculiarities of the source power distribution among the generated waves as well as between the radial and axial directions of wave propagation. A qualitative difference in source energy radiation modes for hard and soft environments and the role of leaky waves in the power transport into a soft formation are discussed. The emergence of additional tube waves due to a fluid saturation of porous interlayers is revealed.