| Summary: | The measurement of in-situ permeability is very important in exploration and
production logging. Observed data show that tube wave attenuation in full waveform
acoustic logs is correlated with formation permeability. It is postulated that
attenuation is due to fluid flowing away from the borehole into the formation. In this
paper we investigate the theoretical relationship between tube wave attenuation
and permeability using two different models. The first is a simple model of a borehole
with absorbing walls, and the second is a borehole with a Biot porous medium in the
formation. Both models give qualitatively similar results. Tube wave attenuation
increases with increasing permeability. Attenuation also increases with increasing
frequency and porosity. We have also investigated the relative effects of intrinsic
formation attenuation (anelasticity) and permeability on the attenuation of tube
waves. Intrinsic attenuation was introduced into the models by means of complex
velocities. It is found that in rocks with low to medium permeability (less than 100
millidarcies), intrinsic attenuation is the major contributor to tube wave attenuation.
However, in high permeability (greater than 100 millidarcies) rocks, fluid flow
associated with in-situ permeability is as important as intrinsic attenuation in
controlling tube wave attenuation. In either case, if one can estimate the intrinsic
formation attenuation from the other parts of the full waveform (such as the P wave
or the psuedo-Rayleigh wave), an estimate of the permeability of the formation can
be obtained. We tested the models using published data on core permeability and
tube wave amplitudes. By assuming an average value of intrinsic attenuation
appropriate to the formations under study, we obtained a good agreement between
theory and data.
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