Engineering lesson
Clean sand versus shaly sand choosing a saturation model
Use a clean-rock saturation model only where its electrical assumptions are appropriate. Conductive shale can contribute current that Archie would otherwise attribute to connected water.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Make model choice an evidence question
Archie describes a nonconductive rock matrix with conduction through pore water under calibrated exponents. Shaly-sand models introduce additional conductive contributions and require their own inputs.
A low Rt alone does not quantify shale conductivity. Clay distribution, shale resistivity, porosity basis and water properties all affect the interpretation.
Use the clean-rock threshold as a diagnostic
The interactive example deliberately applies Archie through a range of Rt values. The Sw > 1 region exposes a violated combination of inputs or assumptions.
It does not prove that shale is the cause. Incorrect Rw, porosity or log conditions can produce the same symptom. Do not tune Vsh until the answer falls inside zero to one.
Follow the broader comparison when inputs are available
The existing shaly-sand guide covers the Indonesian equation and its variables. This supporting lesson provides a decision checklist and an original invalid-result exercise rather than repeating that equation as a second calculator.
Compare models using the same depth interval and documented input basis. Disagreement is diagnostic evidence, not an automatic ranking of correctness.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/archie-water-saturation-from-resistivity-logs. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
True Formation Resistivity (ohm m) = 1. S_w (fraction): 1.58113883.
- S_w (fraction)
Worked example
Archie Water Saturation from Resistivity Logs
Fixed controls: a = 1 dimensionless; phi = 0.2 fraction; m = 2 dimensionless; R_w = 0.1 ohm m; n = 2 dimensionless. R_t is varied as shown.
Relation and unit basis
S_w = ((a / phi^m) * (R_w / R_t))^(1 / n)
a: Tortuosity Factor (dimensionless). phi: Porosity (fraction). m: Cementation Factor (dimensionless). R_w: Formation Water Resistivity (ohm m). R_t: True Formation Resistivity (ohm m). n: Saturation Exponent (dimensionless).
1. Define the baseline
True Formation Resistivity (ohm m) = 1
Fixed controls: a = 1 dimensionless; phi = 0.2 fraction; m = 2 dimensionless; R_w = 0.1 ohm m; n = 2 dimensionless. R_t is varied as shown.
2. Select the relation
S_w = ((a / phi^m) * (R_w / R_t))^(1 / n)
a: Tortuosity Factor (dimensionless). phi: Porosity (fraction). m: Cementation Factor (dimensionless). R_w: Formation Water Resistivity (ohm m). R_t: True Formation Resistivity (ohm m). n: Saturation Exponent (dimensionless).
3. Substitute the values
a = 1; phi = 0.2; m = 2; R_w = 0.1; R_t = 1; n = 2 → S_w = 1.58113883 fraction
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
S_w (fraction) = 1.58113883
The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
Result and interpretation
S_w (fraction) = 1.58113883
The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
The panel demonstrates the clean-rock failure signal. Open the linked Indonesian calculator only with its required shale inputs.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/archie-water-saturation-from-resistivity-logs. Original synthetic inputs; engine outputs are saved in the downloadable record.
| True Formation Resistivity (ohm m) | S_w (fraction) |
|---|---|
| 1 | 1.581139 |
| 2 | 1.118034 |
| 2.5 | 1 |
| 5 | 0.7071068 |
| 10 | 0.5 |
Scroll the table to see all columns. The highlighted row is the worked baseline. Downloads retain full numerical precision.
Test your understanding
Work through the question before revealing its answer. Use the stated assumptions and include units in every numerical step.
1. Does Sw > 1 prove that an Indonesian model is correct?
Show the worked answer
No. It identifies inconsistency in the supplied Archie case; alternative causes and the extra model inputs must be checked.
2. Reproduce the baseline S_w (fraction) without rounding intermediate values.
Show the worked answer
a = 1; phi = 0.2; m = 2; R_w = 0.1; R_t = 1; n = 2 → S_w = 1.58113883 fraction. S_w (fraction) = 1.58113883. The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
True Formation Resistivity (ohm m) changes from 1 to 10. Other controls remain as stated in the premise. S_w (fraction) changes from 1.58113883 to 0.5.
4. What would be needed to apply this example to a different physical system?
Show the worked answer
Replace the synthetic controls with compatible documented inputs and check the relation's assumptions. a: Tortuosity Factor (dimensionless). phi: Porosity (fraction). m: Cementation Factor (dimensionless). R_w: Formation Water Resistivity (ohm m). R_t: True Formation Resistivity (ohm m). n: Saturation Exponent (dimensionless). The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
Before using the result
- Check conductive-mineral evidence.
- Use consistent depth and porosity basis.
- Do not choose a model solely to bound the output.
The full-water threshold is Rt = 2.5 Ω·m. Sw above one remains visible as an input/model inconsistency, not a physical saturation.
Continue learning
Start with the broader workflow guide
Sources and method
The explanation and synthetic examples are original PetroCalcHub teaching material. The references below support the definitions and model context. They do not supply field validation for the synthetic scenarios.