petrophysics · water saturation
Water Saturation (Simandoux)
Sw = √[(a·Rw/φᵐ) × (1/Rt − Vcl/Rsh)]
click formula to derive ↑
Inputs
fraction
Ω·m
fraction
—
Ω·m
Ω·m
—
Description
The Modified Simandoux equation corrects Archie's Sw for the additional conductivity of dispersed clay, making it valid in shaly sands where Archie overestimates water saturation. It assumes Vcl adds parallel conductivity without contributing to effective porosity.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Sw | fraction | Water Saturation |
| Vcl | fraction | Volume fraction of clay/shale derived from a GR or spectral log. Values above 0.35 indicate the interval is likely a shale baseline. |
| Rsh | Ω·m | Resistivity of the adjacent shale, read from a thick, clean shale interval. Typically 1–5 Ω·m in Gulf Coast shales; higher (5–15 Ω·m) in older or more siliceous shales. |
| φ | fraction | Effective porosity of the formation, ideally already shale-corrected before this equation is applied. |
| m | — | Cementation exponent — same as Archie; 2.0 is the clean-sand default, calibrate from core when possible. |
| Rw | Ω·m | Formation water resistivity at reservoir temperature. Use the rw_temp calculator to correct from surface to BHT before entering here. |
| Rt | Ω·m | Deep-reading true formation resistivity, corrected for invasion effects. |
| a | — | Empirical tortuosity constant; 1.0 is standard for most sandstones. |
Assumptions
- Clay conductivity acts as a parallel (independent) pathway and scales linearly with Vcl
- Saturation exponent n=2 — use iterative Archie-Simandoux for other values
- Rsh from the nearest thick clean shale is representative of the dispersed clay in the reservoir
Limitations
- Overestimates Sw in very high-clay formations (Vcl > 0.40) — consider Dual Water or Indonesia equation
- Assumes n=2 saturation exponent — wettability effects and non-Archie behavior are not captured
- Rsh is difficult to measure accurately in thinly laminated shale-sand sequences
Use Cases
- → Shaly sand Sw in Permian Basin siltstones: Apply when Vcl from GR is 0.10–0.35 and plain Archie Sw runs unrealistically low; Simandoux typically gives 5–15 pu higher Sw than Archie in these intervals.
- → Net pay cutoff in clay-rich sands: Use Simandoux Sw as input to the net pay cutoff (Sw ≤ 0.65) to avoid incorrectly flagging shaly sands as pay when Archie would give Sw > 1.
- → Cross-check against Indonesia equation: Run both Modified Simandoux and the Indonesia equation; where they agree within 5 pu the result is robust; larger divergence signals need for core SCAL.
Related Calculations
Region Notes
Permian Basin
Wolfcamp silty intervals: Rsh typically 2–4 Ω·m; Vcl 0.15–0.30 in productive benches. Simandoux gives 10–15% lower Sw than Archie when Vcl > 0.15.
Gulf of Mexico
Miocene/Pliocene shaly sands: Rsh 0.8–2 Ω·m (very conductive), Vcl correction is large. Indonesia equation is often preferred when Vcl > 0.20.
Eagle Ford
Organic shale matrix — Simandoux clay correction may not fully account for kerogen conductivity effects; always cross-check against core Sw where available.
North Sea
Brent Group: Rsh 3–8 Ω·m, Vcl 0.05–0.25 in net pay. Modified Simandoux generally works well; calibrate Rsh from deepest clean shale in each well.
Global
Always compare Simandoux Sw against Archie Sw: the clay correction should reduce Sw; if Simandoux gives higher Sw than Archie, Rsh is too low relative to Rt — check inputs.
References
Primary source
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