Theoretical Models Relating Acoustic Tube-Wave Attenuation To Fracture Permeability - Reconciling Model Results With Field Data

Abstract

Several recent investigations indicate that tube-wave amplitude attenuation in acoustic full-waveform logs is correlated with permeability in fractured rocks. However, there are significant differences between predictions based on theoretical models for tubewave propagation and experimental waveform amplitude data. This investigation reviews the results of existing theoretical models for tube-wave attenuation in fractured rock and compares model predictions with acoustic full-waveform data where extensive independent fracture-permeability data are available from straddle-packer permeability tests. None of the tube-wave models presented in the literature predicts attenuation at fracture apertures as small as those producing attenuation in the field; and most models predict tube-wave reflections, which are rarely measured at frequencies greater then 5 kHz. Even the unrealistic assumption that all of the tube-wave energy loss is caused by viscous dissipation in fracture openings does not result in predicted apertures being as small as those indicated by packer permeability measurements in most situations. On the basis of these results, it is concluded that plane-fracture models cannot account for the measured tube-wave attenuation where natural fractures intersect fluidfilled boreholes. However, natural fractures are fundamentally different from plane parallel passages. This difference appears to explain the small equivalent flow apertures and lack of reflections associated with fractures in waveform-log data. Permeable fracture openings modeled as irregular tubes embedded between asperities along the fracture face are predicted to produce significant tube-wave attenuation when tube diameters exceed 1.0 cm, but arrays of such tubes conduct fluid flow equivalent to that through plane fractures less than 2 mm in effective flow aperture. Although the theory predicts some reflection from simple cylindrical passages, scattering from irregular distributions of natural fracture openings probably accounts for the infrequency with which coherent tube-wave reflections occur in field data.