Engineering lesson
Capillary pressure versus relative permeability
Capillary pressure describes a phase-pressure difference; relative permeability describes phase mobility relative to a reference permeability. Both can depend on saturation, but they are different physical quantities.
By PetroCalcHub Team · Updated October 24, 2026 · Free to read and use
Two curves, two measurements
A capillary curve relates Pc to saturation under a wettability and displacement history. Relative permeability curves describe how each phase flows as occupancy changes.
A rock can therefore have separate Pc(S) and kr(S) relationships. One should not be substituted numerically for the other just because their horizontal axes match.
Use effective saturation consistently
Residual and endpoint saturations transform raw Sw into effective saturation. Different endpoint choices change both the valid domain and the curve shape.
The synthetic comparison uses common effective-saturation values. It reports pressure and dimensionless relative permeability in separate columns rather than plotting them as one quantity.
Keep path and endpoint behavior visible
Drainage and imbibition can follow different curves. Entry pressure and residual saturation have distinct meanings and require data.
At some idealized endpoints a capillary equation diverges while relative permeability approaches a finite bound. Exclude singular inputs from numerical plotting and explain the limit rather than hiding it.
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. Capillary pressure (psi): 7.07106781; Illustrative relative permeability: 0.125.
- Capillary pressure (psi)
Worked example
Pressure and mobility at shared effective saturation
Brooks–Corey Pe = 5 psi, λ = 2; separate illustrative wetting kr = Se³. These are synthetic curves, not a jointly fitted rock model.
Relation and unit basis
Pc = 5 Se^(−1/2); krw = Se³
Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions.
1. Define the baseline
Effective saturation = 0.5
Brooks–Corey Pe = 5 psi, λ = 2; separate illustrative wetting kr = Se³. These are synthetic curves, not a jointly fitted rock model.
2. Select the relation
Pc = 5 Se^(−1/2); krw = Se³
Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions.
3. Substitute the values
At Se = 0.5: Pc = 5/√0.5 = 7.07106781 psi; krw = 0.5³ = 0.125
Retain intermediate precision. The displayed values are rounded only after evaluation.
4. Read the result
Capillary pressure (psi) = 7.07106781; Illustrative relative permeability = 0.125
Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.
Result and interpretation
Capillary pressure (psi) = 7.07106781; Illustrative relative permeability = 0.125
Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.
Read Pc and kr as separate outputs at the same effective saturation; the pressure axis is not a mobility axis.
Exact scenario data
Original synthetic teaching calculation. Equations and fixed controls are stated here; these are not field measurements.
| Effective saturation | Capillary pressure (psi) | Illustrative relative permeability |
|---|---|---|
| 0.1 | 15.81139 | 0.001 |
| 0.25 | 10 | 0.015625 |
| 0.5 | 7.071068 | 0.125 |
| 0.75 | 5.773503 | 0.421875 |
| 0.9 | 5.270463 | 0.729 |
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. Is relative permeability measured in psi?
Show the worked answer
No. Relative permeability is dimensionless. Capillary pressure has pressure units.
2. Reproduce the baseline Capillary pressure (psi) without rounding intermediate values.
Show the worked answer
At Se = 0.5: Pc = 5/√0.5 = 7.07106781 psi; krw = 0.5³ = 0.125. Capillary pressure (psi) = 7.07106781. Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.
3. Compare the first and last recorded scenarios. Which input changes?
Show the worked answer
Effective saturation changes from 0.1 to 0.9. Other controls remain as stated in the premise. Capillary pressure (psi) changes from 15.8113883 to 5.27046277.
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. Pc has pressure units and kr is dimensionless. Se uses fixed residual-endpoint assumptions. Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.
Before using the result
- Keep Pc and kr units separate.
- State residual and endpoint saturations.
- Record drainage or imbibition history.
Sharing a saturation coordinate does not make pressure and relative permeability interchangeable.
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.