Stoneley Wave Propagation across Borehole Permeability Heterogeneities

An important application of borehole acoustic logging is the determination of formation permeability using Stoneley waves. Heterogeneous permeable structures, such as fractures, sand-shale sequences, etc., are commonly encountered in acoustic logging. The purpose of this study is to investigate the effects of the permeability heterogeneities on the borehole Stoneley wave propagation, We have studied the effects of formation permeability heterogeneities on the Stoneley wave propagation when the heterogeneity changes in radial and azimuthal directions (Zhao et aL, 1993). To further study the problem of acoustic logging in heterogeneous porous formations, we study the case where the formation permeability varies in the borehole axial and radial directions. This is a very important problem because vertical heterogeneity variations are commonly encountered in acoustic logging applications. Using the finite difference approach, such heterogeneities as random heterogeneous permeability variations, multiple fracture zones, permeable (sand) non-permeable (shale) sequences, can be readily modeled, and the results are presented. Our numerical simulation results show that the continuous permeability variations in the formation have only minimal effects on the Stoneley wave propagation. Whereas the discontinuous variation (e.g., permeable sand and non-permeable shale sequences) can have significant effeces on the Stoneley wave propagation. However, when the Stoneley wavelength is considerably large compared to the scale of heterogeneity variations, the Stoneley wave is sensitive only to the overall fluid transmissivity of the formation heterogeneity, To demonstrate the effects of heterogeneity on the Stoneley wave propagation. an experimental data set (Winkler et aI., 1989) has been modeled using a randomly layered permeability model. The heterogeneous permeability model results agree with the data very well, while the data disagree with the results from homogeneous permeability models. The numerical technique for calculating Stoneley wave propagation across permeability heterogeneities has been applied to interpret the acoustic logging data across a heeerogeneous fraceure zone (paillet. 1984). The modeling technique, in conjunction with a variable permeability model, successfully explains the non-symmetric patterns of the Stoneley wave attenuation and reileceion at the top and bottom of the fracture