petrophysics · water saturation
Water Saturation (Dual Water Model)
1/Rt = φt^m·Swt^n·(Swt−Swb)/Swt·(1/Rw) + Swb/Swt·(1/Rwb)) / a
click formula to derive ↑
Inputs
fraction
fraction
fraction
Ω·m
Ω·m
—
—
Ω·m
Description
The Dual Water model separates pore water into clay-bound water (high conductivity, Rwb~0.04 Ω·m) and free (formation) water, computing an effective water resistivity that blends the two. It is the most physically rigorous shaly-sand Sw model and is preferred for high-clay intervals where both Simandoux and Indonesia may be inaccurate.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Swt | fraction | Total Water Saturation |
| Swe | fraction | Effective Water Saturation |
| φt | fraction | Total porosity including clay-bound water. Use neutron-density crossplot or NMR total porosity — do NOT use effective porosity (PHIE) here. |
| Vcl | fraction | Volume fraction of clay from GR or spectral log. |
| φclay | fraction | Porosity (water content) of the pure shale endmember — typically 0.30–0.40 for smectite, 0.05–0.15 for illite. Estimated from the shale baseline on the density log. |
| Rwb | Ω·m | Resistivity of clay-bound water at formation temperature. Typically ~0.04 Ω·m in the Gulf Coast; set by the double-layer water chemistry adjacent to clay surfaces. |
| Rw | Ω·m | Formation free water resistivity at reservoir temperature, from the Rw temperature correction calculator. |
| m | — | Cementation exponent based on total porosity system. |
| n | — | Saturation exponent; 2.0 is the water-wet default. |
| Rt | Ω·m | Deep true formation resistivity, corrected for invasion. |
Assumptions
- Clay-bound water has uniform resistivity Rwb (~0.04 Ω·m) independent of clay type — smectite and illite bound water have slightly different resistivities
- Swb is constant and set by the clay mineralogy; it is not mobile during production
- Total porosity from logs is reliable and properly distinguishes clay-bound water from free-fluid pore space
Limitations
- Requires φclay — the clay porosity endmember — which is not directly measured and must be estimated from a shale baseline on the density log
- Rwb is difficult to measure directly; the assumed value of 0.04 Ω·m may be off in highly saline or unusual clay-mineral environments
- Computationally iterative — not suitable for quick hand calculations; use when Simandoux or Indonesia give questionable results
Use Cases
- → Tight shaly-gas sands (Haynesville, Barnett): These gas shales have high total porosity but much of it is clay-bound; Dual Water separates the bound volume from the free-gas pore space that drives production.
- → Deeply buried Wolfcamp siltstones: Deep Permian Basin intervals with Vcl 0.20–0.35 and variable clay type benefit from the physically motivated Rwe term rather than a fixed Rsh from a distant shale.
- → NMR-guided total porosity interpretation: NMR delivers φt directly and separates CBW; feeding NMR-derived φt and Swb into Dual Water gives the most self-consistent Sw in shaly formations.
Related Calculations
Region Notes
Permian Basin
Wolfcamp and Bone Spring: Rwb typically 0.03–0.05 Ω·m at BHT ~200–250°F; φclay ≈ 0.30–0.35 for smectite-illite mix common in the western Delaware Basin.
Gulf of Mexico
Unconsolidated Miocene sands: Rwb as low as 0.02–0.03 Ω·m due to high-salinity connate water; φclay ≈ 0.35–0.45 for smectite-dominant young shales.
North Sea
Brent Group shales: Rwb 0.04–0.07 Ω·m at 180–230°F; mixed smectite/chlorite mineralogy means φclay is variable (0.15–0.30) and should be core-calibrated.
Haynesville
Very high temperature (~320°F) and pressure; Rwb ~0.02 Ω·m; total porosity 8–12%, much of which is clay-bound — Dual Water is critical to avoid inflating Sw estimate.
Global
When Dual Water and Simandoux disagree by more than 10 pu, the divergence usually signals an error in φclay or Rwb; cross-check against core water saturation measurements.
References
Primary source
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