petrophysics · formation water
Formation Water Resistivity from Salinity
Rw = [0.0123 + 3647.5/S^0.955] × (23.9 + 21.54)/(T + 21.54)
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Inputs
ppm
°F
Description
Estimates formation water resistivity (Rw) from NaCl-equivalent salinity using the Schlumberger Gen-9 chart curve-fit, then scales it to formation temperature using the Arps (1953) relationship already used in Rw Temperature Correction. Provides an Rw estimate when no direct water sample or SP-log analysis is available, using only a salinity value from a water catalog, produced-water analysis, or offset-well data.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Rw | Ω·m | Formation Water Resistivity |
| S | ppm | Total dissolved solids expressed as NaCl-equivalent concentration in ppm, from a produced-water sample, water catalog, mud-log chloride titration, or basin water-chemistry study. Not a direct LAS curve — sourced externally. |
| T | °F | Formation (bottom hole) temperature at which Rw is needed — typically BHT from the log header or a temperature-gradient estimate. |
Assumptions
- Formation water salinity is expressed as NaCl-equivalent ppm — the standard convention for folding a mixed-ion brine composition (Na, Ca, Mg, K, Cl, SO4, HCO3, etc.) into a single conductivity-equivalent NaCl concentration.
- The salinity value represents the same water zone being evaluated with sw_archie/sw_simandoux/sw_indonesia/sw_dual_water, not a different aquifer or an averaged basin value.
- Formation temperature (T) is a reliable BHT or gradient-based estimate — the temperature correction is only as accurate as this input.
Limitations
- This is a curve-fit to a company-published chart (Schlumberger Log Interpretation Charts, Gen-9), not a peer-reviewed physicochemical derivation — treat as an engineering approximation, not a first-principles result.
- Accuracy degrades for brines with significant non-NaCl ionic content (e.g. high Ca²⁺/Mg²⁺ deep Gulf Coast brines), where the true NaCl-equivalent conversion itself carries added uncertainty — see the Gulf Coast region note below for a documented case where a formation's catalog Rw approaches the pure-NaCl saturation floor this formula implies.
- Not intended for very fresh formation water (S < ~1,000 ppm), where the Gen-9 chart's calibration is sparse and a direct SP-log or sample-based Rw is preferred.
- The temperature-correction term inherits the same scope as rw_temp's Arps (1953) relationship — not intended for extreme geothermal temperatures well beyond typical reservoir ranges.
Use Cases
- → No water sample or SP-derived Rw available: Estimate Rw directly from a produced-water salinity value reported in an offset well file, regional water catalog, or completion report, when no resistivity measurement exists for the zone being evaluated.
- → Mud-log / chemical salinity conversion: Convert a salinity value reported directly in ppm NaCl-equivalent (common in mud-log chloride titration results) into an Rw input for sw_archie, sw_simandoux, sw_indonesia, or sw_dual_water.
- → Cross-checking an SP-derived Rw: Use as an independent QC cross-check against an SP-log-derived Rw — the same chart-vs-log cross-validation used in published Rwa analysis workflows.
- → Regional Rw screening: Screen expected Rw across a basin using known formation-water salinity trends (e.g. increasing salinity with depth) without needing a resistivity log or water sample from every well.
Related Calculations
Region Notes
Global
Valid over roughly 1,000–300,000 ppm NaCl-equivalent. Example: 10,000 ppm at 75°F → Rw ≈ 0.56 Ω·m (matches standard NaCl(aq) conductivity tables within ~2%); 35,000 ppm (seawater-equivalent) at 75°F → Rw ≈ 0.18 Ω·m (matches real seawater resistivity within ~6%).
Permian Basin (Delaware Basin)
Wolfcamp C's catalog Rw_at_75F ≈ 0.043 Ω·m implies ≈206,000 ppm NaCl-equivalent by this correlation — consistent with known deep Permian brine salinities and a useful cross-check when a new salinity measurement comes in for this formation.
Gulf Coast (Cotton Valley / Haynesville-type)
Deep tight gas sandstone catalog values here (Rw 0.015–0.025 Ω·m at 75°F) sit at or below this formula's pure-NaCl saturation floor (≈0.030 Ω·m at 75°F, computed at NaCl's ~360,000 ppm solubility limit) — a sign the true brine has significant non-NaCl ionic content beyond what an NaCl-equivalent chart-fit can represent. Treat salinity-derived Rw with extra caution in this setting; prefer a direct sample.
References
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