petrophysics · water saturation
Water Saturation (Waxman-Smits)
Sw² + (B·Qv·Rw)·Sw − (F*·Rw/Rt) = 0, F* = a/φᵐ
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Inputs
—
Ω·m
fraction
—
Ω·m
meq/mL
S·cm²/meq
Description
The Waxman-Smits equation corrects Archie's Sw for the excess conductivity contributed by clay counterions in the double layer around clay particles, using core-measured cation exchange capacity (Qv) rather than a shale-resistivity proxy. It is the same shaly-sand family as Modified Simandoux and Indonesia, but is anchored to a direct, core-calibrated clay conductivity term instead of an adjacent-shale resistivity read.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Sw | fraction | Water Saturation |
| a | — | Empirical tortuosity constant; 1.0 is standard for most sandstones. |
| Rw | Ω·m | Formation water resistivity at reservoir temperature. Use the rw_temp calculator to correct from surface to BHT before entering here. |
| φ | fraction | Effective porosity of the formation used in the interconnected-porosity formation factor F* = a/φᵐ. |
| m | — | Cementation exponent — same as Archie; 2.0 is the clean-sand default, calibrate from core when possible. |
| Rt | Ω·m | Deep-reading true formation resistivity, corrected for invasion effects. |
| Qv | meq/mL | Cation exchange capacity per unit pore volume, from core CEC measurements. Clean sands run near 0; shaly sands typically 0.1–1.0 meq/mL depending on clay type and volume. |
| B | S·cm²/meq | Equivalent conductance of clay exchange cations. Entered directly rather than derived in-app — Waxman & Thomas (1974) give B as a function of Rw and reservoir temperature; look up or fit B from that correlation (or lab measurement) before entering it here. |
Assumptions
- Saturation exponent n=2 — the general Waxman-Smits form is nonlinear in Sw for n≠2 and requires iterative solution, not implemented here
- Qv is a core-measured or independently estimated cation exchange capacity per unit pore volume, not derived from logs in this calculator
- B (equivalent conductance of clay counterions) is entered directly. Waxman & Thomas (1974) document B as a function of Rw and temperature; no lookup/correlation for B is built into this calculator — supply a value from that reference or from lab measurement
- No independently verified published numeric example (with a stated Sw result) was located during research for this calculator; the golden vector below is hand-derived from the calculator's own documented formula, not cross-checked against an external published case — flagged as a verified-tier gap, not a published-tier match
Limitations
- Requires core CEC data (Qv) that is often unavailable without a dedicated core program — where Qv is unknown, Simandoux or Indonesia (calibrated from GR-derived Vcl and shale resistivity) are more practical alternatives
- Fixed n=2 does not capture non-Archie saturation-exponent behavior seen in some shaly or mixed-wettability formations
- B is temperature- and salinity-dependent; using a single fixed B across a logged interval with varying Rw or temperature will bias Sw
Use Cases
- → Core-calibrated shaly sand Sw: Use when core CEC (Qv) measurements are available from an offset or pilot well — Waxman-Smits gives a more physically direct clay correction than shale-resistivity-based methods like Simandoux.
- → Cross-check against Simandoux/Indonesia: Run alongside the shale-resistivity-based methods; large divergence signals that the Rsh proxy used by those methods is not representative of the actual clay conductivity in this formation.
- → Low-resistivity pay evaluation: In laminated or dispersed-clay low-resistivity pay zones, Waxman-Smits Sw calibrated to core Qv can distinguish genuine low-Sw pay from clay-conductivity-masked water zones that Archie would flag as wet.
Related Calculations
Region Notes
Permian Basin
Wolfcamp/Bone Spring core studies report Qv 0.1–0.5 meq/mL in productive silty benches; use core CEC where available rather than the schema default.
Gulf of Mexico
Unconsolidated Miocene/Pliocene shaly sands: higher Qv (0.3–0.8 meq/mL) common with smectite-rich dispersed clay; B tends toward the higher end of its range at these formation temperatures.
Global
Where no core CEC program exists, Hill-Shirley-Klein or Normalized-Qv log-derived estimates are common substitutes for a direct core Qv — treat those as lower-confidence inputs than lab-measured Qv.
References
Primary source
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