Stoneley waves in permeable boreholes are diagnostic of formation permeability becausetheir propagation is affected by the dynamic fluid flow at the borehole wall. Wecharacterize this flow using the concept of dynamic permeability. We examined theapplicability of the dynamic permeability to porous media by applying it to a singlefracture case and found that it agrees excellently with the fracture conductivity derivedfrom an exact solution. In dealing with the interaction of a Stoneley wave witha porous formation, we decompose the problem into two parts. The first is the interactionof the Stoneley with an equivalent elastic formation without fluid flow. Thesecond is the interaction with the flow that is governed by the dynamic permeability.In this manner, we obtained a simple model for the Stoneley propagation in permeableboreholes. We compared the Stoneley wave attenuation and dispersion characteristicsfrom this model with those from the complete model of the Biot-Rosenbaum theoryin the case of a hard and a soft formation, respectively. We found that the resultsfrom both models agree very well for a hard formation, although they differ at higherfrequencies for a soft formation because of the increased solid compressibility. Thetheoretical predictions from this simple model were also compared with recently publishedlaboratory data of Stoneley wave measurements, performed at both low- andhigh-frequency regions of Biot theory. The simple model and experiment are in excellentagreement. Because of the simplicity of the model, it can be easily appliedto problems concerning Stoneley propagation in permeable boreholes, especially to aninverse problem to extract formation permeability from Stoneley wave measurements.
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