Stoneley Wave Propagation in Heterogeneous Permeable Porous Formations

The propagation of borehole Stoneley waves is strongly correlated with permeability of the formation. Previous studies primarily focused on the situation where the permeability is homogeneously distributed in the formation. In many in-situ situations, however, the permeability distribution of the formation is heterogeneous, due to effects such as a damaged zone around the borehole, random variation of the formation permeability, and layering, etc. This study investigates the effects of formation permeability heterogeneity on Stoneley wave propagation. Using the theory of dynamic permeability and a finite difference technique in cylindrical coordinates, dynamic pore fluid flow in an arbitrarily heterogeneous porous medium surrounding the borehole is modeled. The effects of the flow on the borehole Stoneley waves are calculated. The calculations were performed on various types of permeability heterogeneities. For a formation having random permeability variation with various heterogeneity scale lengths (smaller than the scale of the borehole), the Stoneley wave attenuation and dispersion are only slightly higher than those calculated with a constant permeability (mean value of the random distributions). For a formation with permeability linearly increasing or decreasing away from the borehole, the Stoneley wave behaviors are also similar to those calculated with a constant permeability. Significant effects are found for a damaged zone case where the zone has much higher permeability than the virgin formation. The attenuation exhibits a peak and the Stoneley wave velocity is significantly decreased in the frequency range from 0 to 3 kHz. These features, if measured from the data, can be used as a diagnostic of the borehole condition.