petrophysics · water saturation
Cementation Exponent Back-Solve (Pickett Plot)
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Inputs
Paste one row per line — separate columns with a comma or tab: Porosity (fraction), True Resistivity (Ω·m)
⚠ Needs at least 3 valid rows to calculate — 0 so far.
Description
Back-solves the Archie cementation exponent (m) from a set of clean, 100%-water-saturated (Sw=1) porosity/resistivity points via a Pickett plot: on log-log axes, Ro = a·Rw·φ⁻ᵐ is a straight line whose slope is −m and whose intercept (at φ=1) is a·Rw. A least-squares linear regression on log10(φ) vs. log10(Rt) recovers both directly from real field data, instead of assuming the common default m=2 sw_archie ships with.
Variables
| Symbol | Unit | Description |
|---|---|---|
| m | — | Cementation Exponent |
| a·Rw | Ω·m | a×Rw Product |
| φ, Rt | — | One row per clean, 100%-water-saturated (Sw=1) zone: porosity and true resistivity (which equals Ro in these zones). At least 3 points are required for a meaningful least-squares fit of the Pickett plot's log(φ) vs. log(Rt) trend — sw_archie already renders this same trend as a chart, this calculator regresses actual data against it to back-solve the cementation exponent instead of assuming m=2. |
Assumptions
- Every input point is from a clean (negligible clay), 100%-water-saturated (Sw=1) zone — the same clean/water-wet assumptions sw_archie itself carries, since this back-solve assumes Rt=Ro at every point.
- A single cementation exponent applies across all pasted points — a formation with genuinely varying pore geometry (e.g. mixed vuggy/intergranular carbonate) would need separate regressions per rock type, not one combined fit.
- Points span a real range of porosity — a regression through a narrow porosity cluster is statistically weak even with a high R², since a short line segment poorly constrains the slope.
Limitations
- Cannot separate 'a' (tortuosity factor) and Rw individually from wet-zone data alone — only their product (a·Rw, the line's intercept at φ=1) is recoverable; an independent Rw estimate is still needed to isolate 'a', or vice versa.
- Sensitive to including a non-clean or non-100%-water-saturated point by mistake — a single hydrocarbon-bearing row pulls Rt up off the true Ro trend and biases both slope and intercept.
- A least-squares fit assumes the scatter around the trend is genuine measurement noise, not systematic non-Archie pore-geometry behavior (e.g. dual-porosity carbonates) — a low R² is flagged, but does not itself diagnose which assumption is failing.
Use Cases
- → Calibrating m from field data instead of a default: Replace sw_archie's default m=2 assumption with a value back-solved from this formation's own clean, water-bearing zones, before running Sw across the full logged interval.
- → Quality-checking an assumed cementation exponent: Plot a candidate set of wet-zone φ/Rt points and check the fitted m and R² against a value already in use — a poor fit (low R²) signals the points aren't as clean/wet as assumed, or that m genuinely varies across the interval.
Related Calculations
Region Notes
Global
m=2.0 is the standard clean-sandstone default, but carbonates with vuggy or fracture porosity commonly show m=2.0-2.5+ — a field-specific back-solve from real wet-zone data is materially more reliable than a textbook default in these settings.
References
Primary source
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