petrophysics · water saturation
Saturation Exponent Back-Solve (Resistivity Index)
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Inputs
Ω·m
Paste one row per line — separate columns with a comma or tab: Water Saturation (fraction), True Resistivity (Ω·m)
⚠ Needs at least 3 valid rows to calculate — 0 so far.
Description
Back-solves the Archie saturation exponent (n) from a single core plug's desaturation sequence via the resistivity index method: I=Rt/Ro=Sw⁻ⁿ, where Ro is the plug's own directly-measured 100%-water-saturated resistivity. A log-log plot of I vs. Sw is a straight line through the point (Sw=1, I=1) by definition — not something to fit — so the regression is forced through the origin in log-log space, and its slope alone gives −n. Completes the Pickett-plot regression pair alongside cementation_exponent_backsolve, replacing sw_archie's default n=2 assumption with a value back-solved from real SCAL data.
Variables
| Symbol | Unit | Description |
|---|---|---|
| n | — | Saturation Exponent |
| Ro | Ω·m | Resistivity of the SAME core plug measured at 100% brine saturation, before desaturation begins — a directly measured lab value, not something this calculator solves for. Used to normalize each desaturation step's Rt into the resistivity index I=Rt/Ro. |
| Sw, Rt | — | One row per desaturation step of the same core plug: water saturation and the resistivity measured at that saturation. At least 3 points (beyond the initial Sw=1/Ro measurement) are needed for a meaningful fit of the resistivity-index-vs-Sw trend. |
Assumptions
- Every (Sw, Rt) row is from the SAME core plug's desaturation sequence, at the same porosity and pore geometry — mixing points from different plugs or different rock types would not share a single valid Ro or n.
- Ro is a genuine, independently measured 100%-water-saturated resistivity for that same plug, not a value back-calculated from a, m, φ, and Rw.
- A single saturation exponent applies across the full desaturation range pasted — real rocks can show two-slope (kinked) resistivity-index behavior near irreducible Sw, which a single straight-line fit would average over, not detect.
Limitations
- Requires a genuinely measured Ro for the same plug — supplying an estimated or formula-derived Ro (e.g. from a, m, φ, Rw) reintroduces exactly the uncertainty this lab method is meant to avoid.
- A single straight-line fit cannot detect or report a two-slope resistivity-index trend (common near irreducible water saturation in some rocks) — a low R² is flagged, but the specific cause (mixed rock types vs. genuine two-slope behavior vs. bad data) isn't distinguished.
- Lab resistivity-index measurements are usually made at atmospheric conditions — n measured this way can differ from true in-situ reservoir-pressure/temperature behavior, since smaller pores are proportionally over-represented at atmospheric desaturation.
Use Cases
- → Calibrating n from SCAL data instead of a default: Replace sw_archie's default n=2 assumption with a value back-solved from this rock's own special-core-analysis desaturation data, before running Sw across the full logged interval.
- → Completing a Pickett-plot parameter set: Use alongside cementation_exponent_backsolve — back-solving m from clean wet-zone field data and n from SCAL core data gives a fully calibrated a/m/n set for sw_archie, instead of relying on textbook defaults for any of them.
Related Calculations
Region Notes
Global
n=2.0 is the standard water-wet default, but oil-wet or mixed-wettability rocks commonly show n=3-4+ — a SCAL-derived back-solve is materially more reliable than the textbook default whenever wettability is uncertain or non-water-wet behavior is suspected.
References
Primary source
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