Directional Aqueous Relative Permeability Options (GT)
Directional/Anisotropic Relative Permeability Options
Constant
The relative permeability is constant regardless of saturation.
Burdine
The Burdine (1953) relative permeability function is described as
Aqueous phase relative permeability can be computed as a function of aqueous saturation from knowledge of the soil-moisture retention function and the pore distribution model of Burdine [1953]. If the van Genuchten and Brooks and Corey soil-moisture retention functions are used, closed-form expressions for fluid phase relative permeability can be derived. Using the van Genuchten soil-moisture retention function, the aqueous phase relative permeability appears as shown:
Using the Brooks and Corey soil-moisture retention function, the aqueous phase relative permeability appears as shown:
Symbols
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aqueous relative permeability |
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effective aqueous liquid saturation |
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van Genuchten m parameter |
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Brooks and Corey parameter |
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capillary head, m |
Mualem
Modified Mualem
The pore scale parameter (aka tortuosity-connectivity coefficient) can be specified to be any value. The default value is 0.5.
Irreducible Mualem
There is a minimum saturation for the porous medium.
Corey Model
Free Corey
Haverkamp
Touma and Vauclin
Tabular
This option accepts tabulated relative permeability data. The default is the data of aqueous saturation and aqueous relative permeability data pairs and linear interpolation is used between data points; a cubic spline interpolation scheme can also be specified. Alternately, capillary head vs relative permeability can be provided using the keyword "head." Other interpolation schemes that can be specified for capillary head vs. aqueous relative permeability are log capillary head vs relative permeability, cubic spline, or cubic spline for log capillary head vs relative permeability.
Sub-Options
Dual Porosity/Permeability Model for Fractured Systems
IJK, JKI or KIJ Indexing
If IJK Indexing, JKI Indexing, or KIJ Indexing is specified as the Rock/Soil Name in the Rock/Soil Zonation Card, then this must also be specified as the Rock/Soil Name in the Directional Aqueous Relative Permeability Card.
IJK Indexing
If the IJK Indexing option is specified in the Rock/Soil Zonation Card, then the relative permeability models and any or all associated parameters can be specified either as a single value that will be applied to each node in the domain, or in an external file with the values for every grid-cell ordered according to the IJK indexing scheme. Units shown in the input line will be applied to all parameters in the external file.
JKI Indexing
If the JKI Indexing option is specified in the Rock/Soil Zonation Card, then the relative permeability models and any or all associated parameters can be specified either as a single value that will be applied to each node in the domain, or in an external file with the values for every grid-cell ordered according to the JKI indexing scheme. Units shown in the input line will be applied to all parameters in the external file.
KIJ Indexing
If the KIJ Indexing option is specified in the Rock/Soil Zonation Card, then the relative permeability models and any or all associated parameters can be specified either as a single value that will be applied to each node in the domain, or in an external file with the values for every grid-cell ordered according to the KIJ indexing scheme. Units shown in the input line will be applied to all parameters in the external file.
Effective Aqueous Liquid Saturation
Mobile saturations are scaled by the residual aqueous liquid saturation to determine effective saturations for use with common relative permeability models.
Symbols
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effective aqueous liquid saturation |
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actual aqueous liquid saturation |
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actual aqueous liquid residual saturation |
References
Burdine, NT. 1953. "Relative Permeability Calculation from Size Distribution Data," Trans. AIME, 198:71-78.
Corey, AT. 1977. Mechanics of Heterogeneous Fluids in Porous Media, Fort Collins, Colorado.
Fatt , I and WA Klikoff Jr. 1959. "Effect of Fractional Wettability on Multiphase Flow through Porous Media," AIME Trans, 215:426-429.
Gardner, WR. 1958. "Some Steady-State Solutions of the Unsaturated Moisture Flow Equation with Applications to Evaporation from a Water Table," Soil Science, 85:228-232.
Haverkamp, R, M Vauclin, J Touma, PJ Wierenga, and G Vachaud. 1977. "A Comparison of Numerical Simulation Models for One-Dimensional Infiltration," Soil Sci. Soc. Am. J., 41:285-294.
Hoffmann-Riem, H, MT Van Genuchten, and H Fluhler. 1999. A General Model of the Hydraulic Conductivity of Unsaturated Soils. In M.T. Van Genuchten, L.J. Leij and L. Wu Proceedings of Int. Workshop, Characterization And Measurements Of The Hydraulic Properties of UnsaturatedPorous Media, University of California Riverside, Riverside, CA.
Klavetter, EA and RR Peters. 1986. Estimation of Hydrologic Properties of Unsaturated Fractured Rock Mass, SAND84-2642, Sandia National Laboratories, Albuquerque, NM.
Mualem, Y. 1976. "A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media," Water Resources Research, 12:513-522.
Nitao, JJ. 1988. Numerical Modeling of the Thermal and Hydrological Environment around a Nuclear Waste Package Using the Equivalent Continuum Approximation: Horizontal Emplacement, UCID-2144, Lawrence Livermore National Laboratory, Livermore, CA.
Parker, JC and RJ Lenhard. 1987. "A Model for Hysteretic Constitutive Relations Governing Multiphase Flow 1. Saturation-Pressure Relations," Water Resources Research, 23(12):2187-2196.
Polmann, DJ. 1990. "Application of Stochastic Methods to Transient Flow and Transport in Heterogeneous Unsaturated Soils," PhD, Massachusetts Institute of Technology, Cambridge, MA.
Raats, PaC, ZF Zhang, AL Ward, and GW Gee. 2004. "The Relative Connectivity–Tortuosity Tensor for Conduction of Water in Anisotropic Unsaturated Soils," Vadose Zone Journal, 3:1471-1478.
Zhang, ZF, AL Ward, and GW Gee. 2003. "A Tensorial Connectivity–Tortuosity Concept to Describe the Unsaturated Hydraulic Properties of Anisotropic Soils," Vadose Zone Journal, 2:313-321.