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GeolOil  How to estimate Porosity from FlushedZone Rxo invaded Resistivity
By: Oscar Gonzalez, GeolOil LLC. This paper was first published on April 2020 on geoloil.com
Porosity can be estimated from the log curve of flushed zone resistivity Rxo. Since the drilling mud invades the zone closest to the borehole wall, it displaces most of the hydrocarbons, so the local hydrocarbon saturation in such small zone can drop easily to around 20% or less.
The Archie equation can be applied then to this invaded zone —for now let's assume that the rock matrix is clean, nonclayey, and non conductive—. Replacing the deep, true far field uninvaded resistivity Rt with the flushed zone resistivity Rxo, and replacing the formation water resistivity Rw with the mud filtrate resistivity Rmf (which has to be corrected to the depth temperature), and solving for the porosity φ:
The former equation is appealing. Provided that a good quality curve for Rxo is available in a good quality and stable borehole —occasionally MSFL yields good results—, and Rmf is accurately measured and converted to the depth temperature, the estimator for porosity is useful. This φ estimate is independent of the classics density porosity, neutron porosity, and sonic porosity. It is based only on resistivity and provides yet another in situ estimate, valuable either for validation or even estimation on its own right.
The GeolOil Panel to estimate porosity on clean reservoirs from Rxo
How can we deal with clayey matrices with excess of conductivity? Certainly the Archie equation is not suitable for such cases. In this article —first published in this geoloil.com webpage on April 2020— we introduce a correction to deal with shaly reservoirs. Just take the Indonesia equation for water saturation. After following the same algebraic steps, an approximation to estimate the effective porosity φ_{e} with a correction for shale content is:
The former equation provides a correction for shale content, and may work for moderately shaly rocks (say VSH ≤ 30%). However, it requires knowledge of an additional parameter, the shale resistivity Rsh. If a nearby pure shale can not be found around the study zone —and also we must assume that such shale has a similar nature than the dispersed shales inside the target rock—, the formula is of little use.
One workaround is the use instead the Fertl equation for water saturation as a coarse approximation (it does not depend on Rsh). After following the same algebraic steps, it is found:
Both former equations can be blended into a unique estimate. Use w=1 if Rshale can be estimated with reasonable accuracy. Use w=0 if Rshale is not reliable at all, and use intermediate values around w=0.5 for a general, more robust estimate under uncertainty:
⚠ REMARKS: The techniques described 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 and the value of Rmf.
Occasionally good results are seen with curves 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 shallow resistivity curves as replacements for Rxo. They are not close enough to the flushed zone to work.
However, shallow resistivity may work if the mud invasion spans for several feet. In those cases Sxo=0.80 might be
a coarse approximartion, and Rmf may represent accurately enough the conductive (equivalent to water Rw) fluid
resistivity in the zone.

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 value for the parameters Sxo=0.80, may be not close enough. Rather
than a constant, it may well behave better as curve itself. Feel free to change it and evaluate the results.
 In most of the cases, take the porosity estimate as qualitative and look for trends. In some cases the calculated porosity curve matches nicely with regular porosity estimates and core data, which validates the computations. ∎
One robust feature of the estimated insitu microresistivity porosity, is that its value is independent of the fluids nature in the pore space —it only uses resistivity data—. This is specially useful when working with gas reservoirs, for which carefully adjustments have to be made to neutron porosity and density porosity to avoid porosity underestimation and overestimation.
Comparisons of porosities from core, density, neutron porosity, sonic, and microresistivity porosity
✔ NOTE: The GLOG file workflow for this log is available for download with the set of optional interpretation examples.
Computation panel to estimate porosity for flushed zone, invaded Rxo resistivity in shaly sands
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