Original synthetic study
Brooks Corey versus van Genuchten on a shared synthetic case
Brooks–Corey and van Genuchten can describe different capillary-curve shapes on a shared effective-saturation basis. Matching one point does not make their parameters equivalent.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Normalize the comparison explicitly
The study uses dimensionless Pc relative to a selected pressure scale and common effective saturation values. Parameters are synthetic, and both curves are evaluated away from singular endpoints.
Brooks–Corey's entry-pressure form and van Genuchten's smooth form have different endpoint behavior. Comparing raw coefficients without those definitions is misleading.
Keep curve comparison separate from calibration
An overlay can show shape differences but cannot determine which model fits a rock without measured Pc–saturation data. A shared scale is a control, not evidence of equal physical entry pressure.
Use the site's separate calculators with their documented units and exponent conventions. Parameter symbols can differ between implementations.
Explain endpoint limits
At low effective saturation, idealized capillary pressures can grow very large. At high saturation, the models can approach different limiting forms.
The dataset preserves the selected domain and exact equations so another reader can reproduce the comparison without interpreting the curves as laboratory measurements.
Explore the example
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
Select one of 5 recorded scenarios. Intermediate states are not interpolated.
Effective saturation = 0.5. Brooks–Corey normalized Pc: 1.41421356; van Genuchten normalized Pc: 1.73205081.
- Brooks–Corey normalized Pc
- van Genuchten normalized Pc
Worked example
Normalized capillary-model comparison
Brooks–Corey λ = 2 and van Genuchten m = 0.5. Both selected pressure scales are 5 psi; report Pc divided by that scale.
Relation and unit basis
Pc,BC/5 = Se^(−1/2); Pc,VG/5 = (Se^−2 − 1)^0.5
The shared scale is a mathematical normalization, not evidence of identical measured entry pressure.
1. Define the baseline
Effective saturation = 0.5
Brooks–Corey λ = 2 and van Genuchten m = 0.5. Both selected pressure scales are 5 psi; report Pc divided by that scale.
2. Select the relation
Pc,BC/5 = Se^(−1/2); Pc,VG/5 = (Se^−2 − 1)^0.5
The shared scale is a mathematical normalization, not evidence of identical measured entry pressure.
3. Substitute the values
At Se = 0.5: BC = 1/√0.5 = 1.41421356; VG = √(0.5^−2 − 1) = √3 = 1.73205081
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Brooks–Corey normalized Pc = 1.41421356; van Genuchten normalized Pc = 1.73205081
The shapes and endpoint limits differ; this is not a laboratory fit or accuracy ranking.
Result and interpretation
Brooks–Corey normalized Pc = 1.41421356; van Genuchten normalized Pc = 1.73205081
The shapes and endpoint limits differ; this is not a laboratory fit or accuracy ranking.
The table compares normalized pressure, not fit accuracy. No field curve is used to rank the models.
Study data and reproduction
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Effective saturation | Brooks–Corey normalized Pc | van Genuchten normalized Pc |
|---|---|---|
| 0.1 | 3.162278 | 9.949874 |
| 0.25 | 2 | 3.872983 |
| 0.5 | 1.414214 | 1.732051 |
| 0.75 | 1.154701 | 0.8819171 |
| 0.95 | 1.025978 | 0.3286841 |
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 a visually close overlay establish interchangeable parameter values?
Show the worked answer
No. Different equations can match part of a range while having different endpoint behavior and parameter meanings.
2. Reproduce the baseline Brooks–Corey normalized Pc without rounding intermediate values.
Show the worked answer
At Se = 0.5: BC = 1/√0.5 = 1.41421356; VG = √(0.5^−2 − 1) = √3 = 1.73205081. Brooks–Corey normalized Pc = 1.41421356. The shapes and endpoint limits differ; this is not a laboratory fit or accuracy ranking.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Effective saturation changes from 0.1 to 0.95. Other controls remain as stated in the premise. Brooks–Corey normalized Pc changes from 3.16227766 to 1.02597835.
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. The shared scale is a mathematical normalization, not evidence of identical measured entry pressure. The shapes and endpoint limits differ; this is not a laboratory fit or accuracy ranking.
Before using the result
- Use one effective-saturation convention.
- State the pressure normalization.
- Do not rank accuracy without independent data.
The shapes and endpoint limits differ; this is not a laboratory fit or accuracy ranking.
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.