We investigated the theoretical relationship between propagation characteristics of Stoneley (tube) waves in a borehole and in-situ permeability by using a modified formulation of a borehole model with a formation that behaves as a Biot porous medium. We found that Stoneley-wave attenuation and phase-velocity dispersion increased with increasing permeability and porosity, and decreased with increasing frequency. In rocks with low to medium permeabilities (less than 100 mD), variations in formation velocity and attenuation were major contributors to variations in Stoneley-wave properties at normal logging frequencies. However, in high-permeability rocks (greater than 100 mD), coupling between the borehole and pore fluids associated with in-situ permeability was more important than lithological changes in controlling Stoneley-wave properties. Pore-fluid viscosity had an effect on Stoneley-wave propagation equal but opposite to permeability, and hence must be taken into account. We compared our theoretical results with published data on core permeability and Stoneley-wave phase velocities and amplitudes. The Stoneley-wave amplitude was more sensitive to the permeability of the formation than Stoneley-wave phase velocity. By assuming an appropriate average value of intrinsic attenuation, we obtained reasonable agreements between theory and the published data. We conclude that relative permeability within a formation can be determined quite well using Stoneley-wave amplitude and phase velocity, but absolute permeability determination requires accurate measurements of parameters such as the intrinsic attenuation of the formation and the viscosity and compressibility of the pore fluid.

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