van Genuchten Capillary Pressure Calculator
Calculate uncapped van Genuchten capillary pressure from pressure scale, effective wetting saturation and m. Check pressure sign and saturation endpoints.
Calculate uncapped van Genuchten capillary pressure from pressure scale, effective wetting saturation and m. Check pressure sign and saturation endpoints.
Published by PetroCalcHub Team. Linked workflow tools and revision log.
Calculation context and source notes
Evaluate positive nonwetting-minus-wetting capillary pressure from effective wetting saturation and the restricted van Genuchten shape relation m = 1 - 1/n. The pressure scale P_0 is the reciprocal of an inverse-pressure alpha, not a Brooks-Corey entry threshold.
Supply a positive pressure scale calibrated for the selected fluid system, a compatible effective wetting saturation and a shape parameter strictly between zero and one. Compare the linked Brooks-Corey curve only after matching pressure sign, saturation normalization and experimental history.
Solves for
P_c (psi)
Best next page
Formula, variables, and sourceContrast the pressure scale with an entry threshold
For P_0 = 5 psi, effective wetting saturation 0.5 and m = 0.5, the inner saturation power is four. Subtracting one and taking the square root gives sqrt(3), so pressure is 8.660254 psi. At full effective wetting saturation the pressure is zero, unlike Brooks-Corey's raw drainage branch which retains its entry threshold.
When m = 0.5, the relation simplifies to P_c = P_0 sqrt(1 - S_e squared)/S_e. This equivalent form independently checks the default and near-full-saturation behavior. Reducing effective wetting saturation increases pressure; the uncapped dry-end limit is not a finite laboratory or simulator result.
| Effective wetting saturation | Pressure (psi), P_0 = 5, m = 0.5 |
|---|---|
| 1 | 0 |
| 0.5 | 8.660254 |
Match the source's saturation and pressure conventions
A common two-phase normalization is S_e = (S_w - S_wr)/(1 - S_wr - S_nr). Some curves use a different denominator, so the residual endpoints must match the fitted parameters rather than being chosen independently. The linked relative-permeability calculators also take effective wetting saturation, not an unprocessed water-saturation log.
The INL implementation uses inverse-pressure alpha and offers a numerical maximum-pressure cap; this page evaluates the uncapped branch with P_0 = 1/alpha. A head-based fit instead needs its characteristic head converted to pressure on the appropriate density and gravity basis before entry. Shape parameters are empirical and should not be transferred to a different rock or fluid system without justification.
Learn, compare and practice
Worked explanations, controlled studies and printable exercises connected to this calculation.
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns P_c = 8.660254 psi. Defaults demonstrate the implementation; they are not recommended field values.
5
0.5
0.5
Input definitions
P_0
psiPositive Pressure Scale (Not an Entry Threshold)
S_e
fractionEffective Wetting Saturation (0 < S_e <= 1)
m
dimensionlessShape Parameter (0 < m < 1; n = 1 / (1 - m))
Output definitions
P_c
Nonwetting Minus Wetting Capillary Pressure
Engineering use, assumptions, and limits
Supply a positive pressure scale calibrated for the selected fluid system, a compatible effective wetting saturation and a shape parameter strictly between zero and one. Compare the linked Brooks-Corey curve only after matching pressure sign, saturation normalization and experimental history.
Assumptions
- The fitted effective wetting saturation and pressure scale refer to the same nonhysteretic curve and fluid system.
- The implemented shape restriction is 0 < m < 1 with n = 1/(1 - m), and pressure is nonwetting minus wetting.
Limitations
- The uncapped relation diverges at zero effective wetting saturation, which is rejected; no dry-region extension or simulator pressure cap is applied.
- No hysteresis, scanning curve, wettability correction or conversion from a measured head-based alpha is performed.
Common mistakes
- Entering total water saturation without applying the fitted endpoint normalization, or reversing the pressure sign.
- Calling P_0 an entry pressure, or treating a reciprocal-length alpha as a reciprocal-pressure alpha without converting head to pressure.
Frequently asked questions
What inputs does the van Genuchten Capillary Pressure calculator need?
The calculation uses Positive Pressure Scale (Not an Entry Threshold) (P_0), Effective Wetting Saturation (0 < S_e <= 1) (S_e), Shape Parameter (0 < m < 1; n = 1 / (1 - m)) (m). Enter values on the units shown beside each field.
What result does this calculator return?
The primary result is nonwetting minus wetting capillary pressure in psi. The formula section shows the declared relationship, variables, and a reproducible default calculation.
What should I check before using the result?
Confirm the unit basis, source applicability, and input quality. The uncapped relation diverges at zero effective wetting saturation, which is rejected; no dry-region extension or simulator pressure cap is applied. Entering total water saturation without applying the fitted endpoint normalization, or reversing the pressure sign.
Source and record status
Source metadata identifies the relationship implemented by the calculator. Check the cited edition, unit basis, and scope against the engineering case before operational use.
PorousFlowVanGenuchten.C: capillaryPressure, Idaho National Laboratory MOOSE contributors
Idaho National Laboratory MOOSE PorousFlowVanGenuchten::capillaryPressure implementation, pinned revision c2fbc1e15048f5b43a5b80018f6ca63723757e62. Positive uncapped branch with pressure scale P_0 = 1/alpha and n = 1/(1-m).
Open source reference