| Summary: | Recent investigations by a number of different authors have shown that the phase velocity
and attenuation of the tube (Stoneley) wave in the borehole is correlated with in situ
permeability. Specifically, velocity decreases and attenuation increases as a function of
in situ permeability. Hsui et al. (1985) presented two theoretical models relating in situ permeability to tube wave attenuation. The results obtained from one of the models, the modified Biot-Rosenbaum model, agreed well with the data of Williams et al. (1984).
We have extended the results from the modified Biot-Rosenbaum model to examine the
relationship between tube wave velocity and in situ permeability. It is found that with
an open borehole Biot-Rosenbaum model, i.e., allowing for the communication between
the pore and borehole fluid pressures, we can match the variation of tube wave phase velocity with in situ permeability in the data presented by Williams et al. and by Zemanek et al. (1985). Furthermore, by the introduction of intrinsic attenuation, i.e., attenuation not caused by Biot fluid flow mechanism, we can fit both the velocity and attenuation data simultaneously. Williams et al. had also observed that the existence of a mudcake did not appear to significantly affect the observed correlation of tube wave velocity and attenuation with permeability. In the Biot-Rosenbaum model, this is explained by the fact that a mudcake is not rigid, and there can be communication between the pore and borehole fluid pressure systems without actual fluid exchange between them. Thus if one can determine the formation P- and S-wave velocity and attenuation, the in situ permeability may be obtainable using the Biot-Rosenbaum model.
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