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, non-clayey, 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 web-page 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:

Comparisons of porosities from core, density, neutron porosity, sonic, and micro-resistivity porosity

Computation panel to estimate porosity for flushed zone, invaded Rxo resistivity in shaly sands

Related articles: How to estimate effective porosity from Rt deep resistivity How to estimate water saturation from Rxo flushed zone resistivity How to estimate fracture porosity How to estimate the cementation porosity exponent m

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