Brooks-Corey Capillary Pressure Calculator
Calculate Brooks-Corey drainage capillary pressure from entry pressure, effective wetting saturation and pore-size index. Check endpoint conventions.
Calculate Brooks-Corey drainage capillary pressure from entry pressure, effective wetting saturation and pore-size index. Check endpoint conventions.
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Calculation context and source notes
Evaluate the uncapped Brooks-Corey drainage branch from positive entry pressure, effective wetting saturation and pore-size distribution index. The output is positive nonwetting-phase pressure minus wetting-phase pressure, with the entry threshold retained at full effective saturation.
Use entry pressure and exponent calibrated to a compatible drainage curve and fluid system. Enter effective saturation, not total water saturation; the effective-saturation normalization must use the same endpoints as the fitted curve.
USGS: Brooks-Corey saturation and entry-head relationSolves for
P_c (psi)
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Formula, variables, and sourceCheck the entry threshold and dry limit
With P_e = 5 psi, S_e = 0.25 and lambda = 2, the pressure is 5 divided by sqrt(0.25), or 10 psi. At S_e = 1 it is 5 psi, the entry threshold. At S_e = 0.0625 it is 20 psi; this increase follows the uncapped drainage branch.
The relation does not uniquely describe pressures below the entry threshold at full saturation. For that reason, the inverse offered here solves entry pressure for a specified branch point, not a universal saturation curve through the pre-entry region. Zero effective saturation is rejected rather than reported as a finite pressure.
| Effective saturation | Capillary pressure (psi) |
|---|---|
| 1 | 5 |
| 0.25 | 10 |
| 0.0625 | 20 |
Keep curve normalization and sign explicit
A common two-phase normalization is effective wetting saturation = (S_w - S_wr)/(1 - S_wr - S_nr), where both residual endpoints belong to the selected curve. Other conventions omit a nonwetting residual endpoint. Determine the source convention before reusing fitted entry pressure or lambda.
The official MOOSE implementation includes a maximum-pressure cap for numerical simulations. This calculator intentionally evaluates the uncapped positive branch over 0 < S_e <= 1, so it should not be expected to reproduce a capped simulator value near the dry endpoint. Preserve the fluid system, drainage history and pressure sign when comparing data.
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 = 10 psi. Defaults demonstrate the implementation; they are not recommended field values.
5
0.25
2
Input definitions
P_e
psiPositive Nonwetting-Phase Entry Pressure
S_e
fractionEffective Wetting Saturation (Not Total Saturation)
lambda
dimensionlessPositive Pore-Size Distribution Index
Output definitions
P_c
Nonwetting Minus Wetting Capillary Pressure
P_e
Nonwetting-Phase Entry Pressure
Engineering use, assumptions, and limits
Use entry pressure and exponent calibrated to a compatible drainage curve and fluid system. Enter effective saturation, not total water saturation; the effective-saturation normalization must use the same endpoints as the fitted curve.
Assumptions
- Positive entry pressure and distribution index describe the selected drainage curve.
- Effective wetting saturation is strictly positive and no greater than one; pressure is nonwetting minus wetting.
Limitations
- Does not represent an imbibition scanning curve, wettability change, hysteresis or a three-phase model.
- The raw branch diverges at zero effective saturation and has no numerical pressure cap or dry-region extension.
Common mistakes
- Entering total water saturation without applying the fitted curve's endpoint normalization.
- Expecting zero pressure at S_e = 1, reversing the pressure sign, or confusing lambda with a Corey relative-permeability exponent.
Frequently asked questions
What inputs does the Brooks-Corey Drainage Capillary Pressure calculator need?
The calculation uses Positive Nonwetting-Phase Entry Pressure (P_e), Effective Wetting Saturation (Not Total Saturation) (S_e), Positive Pore-Size Distribution Index (lambda). 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. Does not represent an imbibition scanning curve, wettability change, hysteresis or a three-phase model. Entering total water saturation without applying the fitted curve's endpoint normalization.
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.
Idaho National Laboratory MOOSE PorousFlowBrooksCorey, capillaryPressure implementation: pe*pow(seff,-1/lambda), based on Brooks and Corey (1966). This calculator evaluates the uncapped drainage branch, not MOOSE's numerical pressure cap.
Open source reference