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GeolOil  How to estimate Effective Porosity from Rt Resistivity in water zones
By: Oscar Gonzalez, GeolOil LLC. This paper was first published on March 2024, on geoloil.com
Quite often there are doubts about the accuracy and reliability of porosity estimates built from classic sources like: bulk density, neutron porosity, and sonic porosity, which heavily depends on a good borehole quality without washouts or rugosity. If the formation under study has some water bodies or zones —like aquifers and water pocket compartments—, an independent porosity estimate (valid only for those water zones) calculated from the deep, not invaded true Rt resistivity curve, should be computed for validation and comparison purposes. The original implicit Simandoux water saturation equation is:
In the water zones SW=1. Hence, by rearranging the former equation and solving for φ_{e}:
In the same token, the Indonesia PouponLeveaux water saturation equation (which works better for fresher waters) is:
Likewise, in the water zones SW=1 must be set. Rearranging the equation and solving for φ_{e}, yields:
Notice that the former Simandoux and Indonesia porosity equations, reduce exactly to the (similarly deduced) Archie porosity equation for clean rocks when Vsh=0 and SW=1:
The Indonesia and Simandoux porosity equations can be combined into a single, weighted, more general estimate. For relatively fresh formation water salinities like NaCl = 20,000 PPM or less, prefer a w weight that favours the Indonesia equation, for instance w≅1. For saltier formations, like NaCl = 100,000 PPM or higher, prefer a w weight that favours the Simandoux equation, for instance w≅0. For other cases, intermediate values around w≅0.5 might be a good choice:
∎
This is the equation implemented in GeolOil petrophysics software, whose computation boxes panel is shown below:
Computation panel to estimate effective porosity from Rt deep resistivity in water bodies for shaly rocks
The log plot shown below, illustrates how the effective porosity estimation equation φ_{e (Shaly rock)} behaves in a clastic eolian reservoir. The red PhiE_Rt curve of the blue Pore Space track shows the estimated effective porosity. At the bottom blue filled water body (depth > 9,250 ft), the porosity estimate has a good, accurate match with the classic effective density porosity estimate. Notice also that the secondary fracture porosity, was estimated by the difference between density porosity minus sonic porosity. The estimate is only valid in the water zone. For the shallower gas pay zone, and the transition gasoilwater zone (depths < 9.250 ft) the porosity is grossly underestimated, loosing half or worst of the porosity value:
Log plot of a gasoil reservoir. The Pore Space track shows in red, the estimation of effective porosity from Rt
⚠ REMARKS: The described technique require good parameter estimates, specially for Rw formation water resistivity:

Formation water resistivity Rw is probably the most important parameter in the equations.
If feasible, compute the equivalent NaCl ionic
salinity from reliable water analyses.
Then convert salinity to Rw
at reservoir temperature to get a quality estimate for Rw. It does not make much sense to
apply a PickettPlot on the water body which already is using a porosity estimate. That would
be a "deadlock" circular computation.

The porosity cementation exponent m is also quite influential for the porosity estimation.
Some eolian sandstones may have a low m value, like m=1.5, which yields different results
tham the typical m=1.8 used as default for some sandstones. Likewise, carbonates can have large
values of m. Values like m=2.4 or more are common for carbonates rocks.
Again, avoid a circular computation of m as commented before.

If the drilling mud is not too much salty, deep induction resistivity maybe robust against washouts and poor
boreholes. That means that the estimated porosity in water bodies, will be also robust against bad boreholes
and rugosity. Such quality estimate on poor boreholes can not be usually calculated from sources like bulk density, sonic transit time,
and even neutron porosity.

The porosity estimates are only valid for water bodies, like aquifers and water pocket compartments.
For pay zones, the porosity estimates will severely underestimate the correct porosity. In the log plot
shown above, the red PhiE_Rt curve yields a porosity which is 50% or more, smaller than the correct porosity.
Thus, an unusable porosity curve for hydrocarbon zones. The assumption that SW ≅ 1 no longer holds.

Notice that the rock has a low Vshale, and normal porosities in the range 8%16%.
However, the irreducible water saturation SWirr is quite high, which was measured through
laboratory capillary pressure tests. This is because the permeability
is low due to a small pore throat size, which drives the connate water saturation.
Rocks with a same porosity can have different pore throat diameters, and hence different
permeabilities.
 The computed estimated porosity is already the effective porosity. No further corrections for clay content are needed. ∎
Sugestion: It is always a good idea to search for water pockets and compute the effective porosity filtered for those water zones (even if they are thin of few feet). That would provide another reference computation for porosity, to validate and compare against classic estimates from bulk density, sonic transit time, and neutron porosity.
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