van Genuchten Nonwetting Permeability Calculator
Calculate normalized van Genuchten nonwetting relative permeability from effective wetting saturation and m, using a fixed connectivity exponent of one half.
Calculate normalized van Genuchten nonwetting relative permeability from effective wetting saturation and m, using a fixed connectivity exponent of one half.
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Calculation context and source notes
Calculate the INL van Genuchten nonwetting relative-permeability branch using effective wetting saturation and a fixed nonwetting connectivity exponent of one half. This completes the available wetting/nonwetting pair without treating all published nonwetting exponent variants as interchangeable.
Enter effective wetting saturation and the same shape parameter used by the selected normalized curve. The result describes the nonwetting phase with endpoint unity, not absolute permeability or mobility. Confirm the residual-saturation normalization and exponent convention before comparing with another simulator.
Solves for
k_rn (fraction)
Best next page
Formula, variables, and sourceCheck the nonwetting phase convention
At effective wetting saturation 0.5 and m = 0.5, the bracket is 1 - 0.5 squared = 0.75 and its exponent is one. Multiplication by sqrt(0.5) gives 0.530330086. At zero wetting saturation the nonwetting normalized endpoint is one; at full wetting saturation it is zero.
The INL source takes its nonwetting phase's own effective saturation s_n and evaluates sqrt(s_n)[1 - (1 - s_n)^(1/m)]^(2m). Substituting s_n = 1 - S_e gives the expression on this page. The input convention matches the site's other saturation calculators, and the source-argument transformation is tested independently.
| Effective WETTING saturation | Normalized k_rn, m = 0.5 |
|---|---|
| 0 | 1 |
| 0.5 | 0.530330086 |
| 1 | 0 |
Keep the exponent variant and phase properties explicit
The square-root prefactor corresponds to nonwetting connectivity exponent one half. A relation using (1 - S_e)^(1/3) has a different prefactor and is not the same implemented model. Select and calibrate the convention rather than changing a numerical exponent merely to match one data point.
The two relative-permeability outputs do not sum to one: the default wetting value is 0.012691996 while this nonwetting value is 0.530330086. Each is a normalized flow-property curve, not a complementary volume fraction. Computing phase mobility additionally requires viscosity, and computing phase flow needs absolute permeability, geometry and a driving-pressure model.
Related source-backed guides
Formula, variables, and default calculation
Reproducible default result
With the default values shown below, the calculation returns k_rn = 0.53033 fraction. Defaults demonstrate the implementation; they are not recommended field values.
0.5
0.5
Input definitions
S_e
fractionEffective WETTING Saturation
m
dimensionlessShape Parameter (0 < m < 1; n = 1 / (1 - m))
Output definitions
k_rn
Normalized Nonwetting Relative Permeability
Engineering use, assumptions, and limits
Enter effective wetting saturation and the same shape parameter used by the selected normalized curve. The result describes the nonwetting phase with endpoint unity, not absolute permeability or mobility. Confirm the residual-saturation normalization and exponent convention before comparing with another simulator.
Assumptions
- Two-phase effective wetting saturation is between zero and one on the fitted curve's residual-endpoint basis.
- The nonwetting connectivity exponent is fixed at 1/2, the endpoint multiplier is one, and m = 1 - 1/n.
Limitations
- No free connectivity exponent, endpoint fitting, hysteresis, trapping or three-phase extension is provided.
- Some nonwetting variants use exponent 1/3 rather than 1/2; those are different models and need not return the same curve.
Common mistakes
- Entering the nonwetting phase's saturation in this interface, which deliberately takes effective wetting saturation.
- Assuming wetting and nonwetting relative permeabilities must sum to one, or interpreting the result as a permeability in mD.
Frequently asked questions
What inputs does the van Genuchten Nonwetting Relative Permeability calculator need?
The calculation uses Effective WETTING Saturation (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 normalized nonwetting relative permeability in fraction. 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. No free connectivity exponent, endpoint fitting, hysteresis, trapping or three-phase extension is provided. Entering the nonwetting phase's saturation in this interface, which deliberately takes effective wetting saturation.
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.h: relativePermeabilityNW, Idaho National Laboratory MOOSE contributors
Idaho National Laboratory MOOSE PorousFlowVanGenuchten::relativePermeabilityNW, pinned revision c2fbc1e15048f5b43a5b80018f6ca63723757e62. Source effective saturation is NONWETTING; substitute s_n = 1 - S_e to use WETTING saturation. Fixed nonwetting connectivity exponent 1/2, not a 1/3 variant.
Open source reference