petrophysics · water saturation
Water Saturation (Indonesia Equation)
√(1/Rt) = Vcl^(1−Vcl/2)/√Rsh + [φᵐ/(a·Rw)]^0.5 × Sw^(n/2)
click formula to derive ↑
Inputs
fraction
Ω·m
fraction
—
—
Ω·m
Ω·m
—
Description
The Indonesia (Poupon-Leveaux) equation is an empirical shaly-sand Sw model that gives lower Sw estimates than Modified Simandoux in high-clay formations, making it the preferred model for Vcl above 0.25. It uses a fractional clay exponent that tapers the clay conductivity correction with increasing Vcl.
Variables
| Symbol | Unit | Description |
|---|---|---|
| Sw | fraction | Water Saturation |
| Vcl | fraction | Volume fraction of clay derived from a GR or spectral log. The Indonesia equation is especially appropriate when Vcl > 0.25. |
| Rsh | Ω·m | Resistivity of the adjacent clean shale. Pick from a thick, laterally continuous shale near the interval of interest. |
| φ | fraction | Effective porosity. In shaly sands, use total porosity from neutron-density crossplot before applying a clay-volume correction separately. |
| m | — | Cementation exponent; 2.0 is the default for sandstones. Calibrate from core formation factor measurements. |
| n | — | Saturation exponent — the Indonesia equation explicitly supports n ≠ 2; 2.0 is the default for water-wet rocks. |
| Rw | Ω·m | Formation water resistivity at formation temperature. Correct to BHT with the rw_temp calculator before use. |
| Rt | Ω·m | Deep true resistivity, corrected for invasion; use the deepest available curve (LLD, ILD, or AHT90). |
| a | — | Tortuosity constant; 1.0 is standard for most sandstones. |
Assumptions
- Formation is a shaly sand where clay and brine conductivity paths both contribute to the measured Rt
- Rsh is measured from a clean adjacent shale and is representative of the clay mineral conductivity in the pay zone
- Vcl-to-conductivity relationship follows the empirical (1−Vcl/2) exponent form — derived from Indonesian well data
Limitations
- Empirically calibrated to Indonesian Tertiary shaly sands — may need recalibration for older, more complex clay mineralogies
- Less well-suited than Simandoux for very low-clay (Vcl < 0.10) intervals where Archie is more appropriate
- The √(1/Rt) mixing space assumption can over-correct in laminated shale-sand sequences where Thomas-Stieber or thin-bed models are required
Use Cases
- → High-clay sand intervals (Vcl > 0.25): Apply the Indonesia equation as the primary Sw model when clay volume exceeds 0.25 and Simandoux Sw is unreasonably low; Indonesia will typically give 5–10 pu higher Sw.
- → Offshore West Africa Tertiary sands: These prolific but clay-rich turbidite plays were the calibration setting for Indonesia equation; use with Rsh 1–3 Ω·m and m ≈ 2.0.
- → Comparative Sw uncertainty analysis: Run Archie, Simandoux, and Indonesia in parallel to bound the Sw uncertainty; the spread among them is a proxy for the impact of shale-model choice on reserves.
Related Calculations
Region Notes
Permian Basin
Less commonly used here than Simandoux; the Wolfcamp's mixed clay-carbonate matrix means the pure-clay assumption of Indonesia fits less well. Try both and compare.
Gulf of Mexico
Preferred over Simandoux for GOM Miocene/Pliocene sands with Vcl > 0.25 and Rsh < 2 Ω·m; the sub-linear clay exponent prevents overcorrection.
Haynesville
Used in the lower Haynesville shale-gas portions where clay content is high; expects Rsh 4–8 Ω·m for the calcareous shale interbeds.
Offshore West Africa
The primary calibration area for Indonesia equation; typical parameters: Rsh 1.5–3 Ω·m, m=2.0, n=2.0, a=1.0 for Oligocene-Miocene turbidites.
Global
When Vcl is between 0.10 and 0.25, both Simandoux and Indonesia are reasonable; use both and treat the difference as model uncertainty in reserves estimates.
References
Primary source
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