The SW ratio equation allows to coarsely estimate the uninvaded water saturation in clean reservoirs, without knowing the formation porosity and the Archie parameters a and m. Instead of porosity, it requires the flushed zone resistivity Rxo, and the mud filtrate resistivity Rmf converted to the reservoir temperature:
PROOF: (For the interested reader) The former equation is derived by applying the
Archie equation
for clean reservoirs —non shaly, non conductive matrix—,
both in the non invaded zone (far beyond the zone invaded by the drilling mud), and in the zone invaded by the mud (close to the
borehole wall):
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The SW ratio equation presented above is useful when dealing with clean reservoirs. But how can we deal with moderately shaly reservoirs for which either it is not known its porosity or we don't want to use inaccurate porosity estimates? In this article —first published in this geoloil.com webpage on April 2020— we introduce a correction to deal with shaly reservoirs.
For this, we may try to replace the clean SW Archie equation with some SW equations that incorporate the effect of excess of conductivity due to the presence of clays in the shale. Classical candidates for such replacement are the Simandoux equation, the Indonesia equation, and the Fertl equation. It is the Fertl equation (which reduces to the Archie equation when Vshale=0 and n=2) the one that provides the easiest mathematical treatability:
Applying now the same algebraic steps depicted for the Archie SW ratio proof, we finally get our recommended general purpose equation, with a correction for shale content:
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⚠ REMARKS: Both the original Archie SW ratio equation, and our extension introduced above with a correction for VSH are appealing. However, they require good quality data and a stable borehole to work, otherwise the results may be misleading:

The results are very sensitive to the quality of the Rxo log curve
—also to Rw and Rt—.
We occasionally have had good results with curves with the
mnemonic MSFL (Micro Spherical Focused Log), but not always. Other common curve mnemonics to try from service companies are:
RXO, RXOZ, MCFL, SFLCC, and MGL.

Discard regular short resistivity curves as replacements for Rxo. They are not close enough to the flushed zone to work.

The mud filtrate resistivity Rmf needs to be measured accurately, and corrected to the reservoir temperature.
Don't expect that a value of Rmf measured on one well can be applied to another well.

The assumed default values for the parameters β=1/5, and θ=0.30, may be not close enough. Rather
than constants, they may well behave better as curve themselves. Feel free to change them and evaluate the results.

In most of the cases, take the water saturation values computed as qualitative and look for trends. In few cases
the calculated SW curve matches nicely with regular SW estimates and core data, which validates the SW computations.
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The figure below ↓ shows the GeolOil Panel to compute Water Saturation from flushed zone resistivity
The figure below ↓ shows in a red curve SW_Rxo, the Water Saturation computed by the Archie ratio. Notice a good match beyond MD > 725 ft between the curve SW_Rxo, and the regular SW_Final curve computed by the Indonesia equation
✔ NOTE: The GLOG file workflow for this log is available for download with the set of optional interpretation
examples.
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