petrophysics · water saturation
Water Saturation (Archie)
Sw = [(a × Rw) / (φᵐ × Rt)]^(1/n)
click formula to derive ↑
Inputs
—
Ω·m
fraction
—
Ω·m
—
Description
The foundational water saturation equation for clean (non-shaly), water-wet formations, relating resistivity to porosity and water resistivity through two empirical exponents. It underlies nearly all derived saturation models used in formation evaluation.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Sw | fraction | Water Saturation |
| a | — | Empirical tortuosity constant in the Archie formation factor relation. Typically 1.0 (Humble formula) or 0.62 (Archie original) for sandstones. |
| Rw | Ω·m | Resistivity of the formation water at formation temperature. Use the Rw temperature correction calc to convert a value measured at surface conditions. |
| φ | fraction | Effective or total porosity of the formation. Use effective porosity (PHIE) where a shale correction has been applied. |
| m | — | Cementation exponent describing pore geometry. 2.0 is the clean-sand default; carbonates and vuggy rocks often need 2.0-2.5 calibrated from core. |
| Rt | Ω·m | True formation resistivity from a deep-reading resistivity curve, ideally corrected for invasion. |
| n | — | Saturation exponent relating resistivity index to Sw. 2.0 is the default; oil-wet or mixed-wettability rocks can require higher values from SCAL. |
Assumptions
- Formation is clean (negligible clay/shale) — no conductive clay contribution to resistivity
- Rock is water-wet so the resistivity-saturation relationship follows the simple power law
- Rw is representative of formation water at reservoir temperature, and Rt is corrected for invasion
Limitations
- Overestimates Sw in shaly sands because clay-bound water adds conductivity not accounted for — use Simandoux or the Indonesia equation instead
- Default m=n=2 may not apply in carbonates with vuggy or fracture porosity; calibrate from core SCAL when possible
- Sensitive to Rw — an uncorrected or poorly estimated Rw propagates directly into Sw error
Use Cases
- → Clean sandstone or carbonate Sw: Primary water saturation curve for reservoir intervals with low clay content, used directly in net pay and reserves calculations.
- → Hydrocarbon pore volume estimation: Combine (1−Sw) with porosity and net pay thickness to estimate hydrocarbon volume for OOIP/GIIP volumetrics.
- → Net pay cutoff screening: Apply an Sw cutoff (e.g., Sw ≤ 0.6) alongside porosity and Vcl cutoffs to flag producible intervals.
- → Sensitivity / uncertainty analysis: Vary a, m, and n across their plausible ranges to bracket the uncertainty in Sw for reserve range estimates (P10/P50/P90).
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Spraberry: m≈1.9-2.0, n≈2.0, a≈1.0 typical; Rw varies 0.03-0.08 Ω·m at BHT depending on sub-basin (Midland vs. Delaware).
Eagle Ford
Organic-rich mudrock often uses m≈1.8-2.0 with a≈1.0; pyrite and TOC can suppress resistivity, so Archie Sw should be cross-checked against core.
Haynesville
High-pressure shale gas: Rw at BHT (~300°F+) is very low (~0.01-0.02 Ω·m); m≈2.0-2.2 is commonly used after core calibration.
Gulf of Mexico
Unconsolidated Miocene/Pliocene sands: a≈0.62, m≈2.15 (Archie original "a-0.62/m-2.15" set) is a common starting point before local calibration.
North Sea
Brent Group sandstones typically use a=1.0, m=2.0, n=2.0 with Rw ranging 0.02-0.04 Ω·m at reservoir temperature in the Viking Graben.
References
Primary source
Need geoscience support? BauerCalc is just one of the tools we build. If you're looking for independent expertise in well planning, geosteering, reservoir characterization, or opportunity evaluation, visit BauerSubsurface.com.