Engineering lesson
Explore saturation curve parameters without changing the rock data
A saturation-curve parameter changes a selected model's shape; it does not change the underlying rock measurements. Keep observed points fixed while comparing parameter choices.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Define effective saturation first
The van Genuchten–Mualem wetting relative-permeability model uses effective saturation and shape parameters. The common m = 1 − 1/n linkage is a model choice, not a measured identity for every rock.
The explorer varies the supported shape parameter at a fixed effective saturation. It keeps the endpoint convention unchanged so the curve-shape effect can be isolated.
Do not fit by moving the observations
Measured saturation and permeability pairs should remain in their original coordinates. Changing residual saturation transforms the model coordinate and must be documented as part of fitting.
Several parameter combinations may fit a narrow range similarly. Examine endpoint behavior and held-out points rather than only the visually best overlay.
Respect the numerical domain
Effective saturation must remain between zero and one for the stated real-valued model. Fractional powers can become invalid outside that interval.
The teaching scenarios avoid singular endpoints and show exact tabulated evaluations. They do not calibrate a rock curve or supply an uncertainty distribution.
Explore the example
Replayed with the same equation record and calculation engine as /calculators/van-genuchten-mualem-wetting-relative-permeability. Original synthetic inputs; engine outputs are saved in the downloadable record.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless) = 0.5. k_rw (fraction): 0.0126919957.
- k_rw (fraction)
Worked example
van Genuchten-Mualem Wetting Relative Permeability
Fixed controls: S_e = 0.5 fraction. m is varied as shown.
Relation and unit basis
S_e: Effective Wetting Saturation (fraction). m: Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless).
1. Define the baseline
Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless) = 0.5
Fixed controls: S_e = 0.5 fraction. m is varied as shown.
2. Select the relation
S_e: Effective Wetting Saturation (fraction). m: Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless).
3. Substitute the values
S_e = 0.5; m = 0.5 → k_rw = 0.0126919957 fraction
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
k_rw (fraction) = 0.0126919957
Effective saturation remains 0.5; m changes curve shape under the linked model's m–n convention.
Result and interpretation
k_rw (fraction) = 0.0126919957
Effective saturation remains 0.5; m changes curve shape under the linked model's m–n convention.
Only the curve-shape parameter changes. The fixed evaluation saturation and endpoint basis stay visible.
Exact scenario data
Replayed with the same equation record and calculation engine as /calculators/van-genuchten-mualem-wetting-relative-permeability. Original synthetic inputs; engine outputs are saved in the downloadable record.
| Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless) | k_rw (fraction) |
|---|---|
| 0.2 | 2.8330e-5 |
| 0.35 | 0.001814151 |
| 0.5 | 0.012692 |
| 0.65 | 0.04069058 |
| 0.8 | 0.08843216 |
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 changing n in a model alter the original measured rock data?
Show the worked answer
No. It changes the predicted curve. The observations should remain fixed for comparison.
2. Reproduce the baseline k_rw (fraction) without rounding intermediate values.
Show the worked answer
S_e = 0.5; m = 0.5 → k_rw = 0.0126919957 fraction. k_rw (fraction) = 0.0126919957. Effective saturation remains 0.5; m changes curve shape under the linked model's m–n convention.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless) changes from 0.2 to 0.8. Other controls remain as stated in the premise. k_rw (fraction) changes from 0.0000283296131 to 0.0884321561.
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. S_e: Effective Wetting Saturation (fraction). m: Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (dimensionless). Effective saturation remains 0.5; m changes curve shape under the linked model's m–n convention.
Before using the result
- State the effective-saturation transform.
- Keep measurements fixed.
- Check parameter and endpoint domains.
Effective saturation remains 0.5; m changes curve shape under the linked model's m–n convention.
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.