An important application of borehole acoustic logging is the determination of formationpermeability 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. anexperimental data set (Winkler et aI., 1989) has been modeled using a randomly layeredpermeability model. The heterogeneous permeability model results agree with the datavery well, while the data disagree with the results from homogeneous permeabilitymodels.The numerical technique for calculating Stoneley wave propagation across permeabilityheterogeneities has been applied to interpret the acoustic logging data across aheeerogeneous fraceure zone (paillet. 1984). The modeling technique, in conjunctionwith a variable permeability model, successfully explains the non-symmetric patternsof the Stoneley wave attenuation and reileceion at the top and bottom of the fracturezone, while it is difficult to explain these patterns using a homogeneous permeable zonemodel. The technique developed in this study can be used as an effective means forcharacterizing permeability heterogeneities using borehole Stoneley waves.
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