Permeability from STONELEY WAVE
Stoneley waves are dispersive (velocity varies with frequency), and are generated from the interaction between borehole and formation. At low frequency, it is called a tube-wave. A Stoneley waveform has a frequency content of 0.1 to 3 KHz, with most of the energy in the late arrivals at about 500 Hz.
Stoneley waves are usually detected between 0 to 20 ms on the sonic waveform. In contrast, the shear waveforms are usually detected between 0 to 5 ms and are concentrated around 4 KHz.
The Stoneley slowness increases due to fluid movement in porous media and mud cake around the borehole. The mud cake effect on slowness is usually a constant shift if the mud cake thickness is constant and if the mud is of one type. One of the major factors affecting Stoneley slowness is grain modulus. If the lithology is changing from pure calcite to dolomite or to more siliciclastic, the effect on slowness will vary. In addition, Stoneley wave is affected by pore fluid modulus. For instance, if fluid is changing from liquid to gas, the predicted permeability increases by two decades.
Stoneley wave is affected by porous media fluid and by shear modulus
at low frequency. Stoneley wave slowness can be modeled in
non-permeable zones as follows:
By cross-plotting DTST^2 versus DTS^2 / DENS across a zero permeability zone, the slope of the straight line is DENSfluid and Y-intercept is DTCfluid^2. There is one condition on the linear fit: all data on thecross plot should be above or on the fitted line.
The Stoneley permeability
index is estimated by taking the ratio of actual measured Stoneley
slowness and modeled slowness as per above model. The formula can be
written as follows:
Flow Zone Index (FZI)
Stoneley permeability index is not a permeability estimation, but it is an index of fluid movement in porous media around the borehole. Since fluid movement is a function of pore throat distribution, pore shape, and pore size, the Stoneley permeability index is a tortuosity index only. These factors can be combined in a concept called Flow Zone Index (FZI).
The Stoneley permeability
index Kist is a direct measurement of FZI. Since FZI approaches to
zero when Stoneley permeability index approaches to 1 in
non-permeable zones, and both of them approach to infinity when
permeability approaches to infinity, then a simple relationship can
be derived between FZI and STI as following:
With this equation, the only
empirical factor to match actual permeability profile is IMF. Since
the grain modulus has an effect on Stoneley slowness, IMF can be
computed in the probabilistic model by summing the volume
weighted IMF for eaach individual mineral in the model. Note: the
Schlumberger report does not indicate how the individual IMF
parameters were derived. Values quoted were:
Stoneley permeability can be
computed by using effective porosity and FZI with the following:
This method is valid for the following conditions:
• Single-phase fluid in
This method is limited to the DSI vertical resolution of 3.5 ft. The volume measured by the DSI is 0.5 to 1 ft thick with 3.5 ft long cylinder.
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