Aqueous Relative Permeability Description (G)

The aqueous relative permeability functions relate phase saturations with aqueous relative permeability. The Aqueous Relative Permeability Card is used to specify model options and parameters. Every rock/soil type defined in the Rock/Soil Zonation Card must be referenced. With the IJK Indexing option, node dependent parameters are entered via external files and node independent parameters are entered directly on the card. The Mualem and Burdine aqueous relative permeability functions are also dependent on the saturation function type and are strictly applicable to the van Genuchten (1980) and Brooks and Corey (1966) functions. For these functions, either the van Genuchten ‘m’ parameter or the Brooks and Corey ‘λ’ parameter can be defaulted to the values entered or defaulted with the saturation function. Functional forms for the aqueous relative permeability-saturation functions are preferred, but tabular input is acceptable. By default, tabular data will be interpolated using linear interpolation, whereas values beyond the table limits will be assigned either the table minimum or maximum values appropriately.

Anisotropy in relative permeability or unsaturated hydraulic conductivity is represented using the tensorial-connectivity-tortuosity model (Zhang et al. 2003; Raats et al. 2004). The concept of directional permeability can be applied to any of the relative permeability models, but is described here as applied to the Modified Mualem model.  With the assumption of pore continuity and connectivity, Burdine (1953) and Mualem (1976) proposed relationships for unsaturated hydraulic conductivity (or relative permeability) in terms of water content or pressure head.  A general expression of the two can be written as (Hoffmann-Riem et al. 1999):

 

 

 

This equation reduces to the Burdine (1953) relationship when β_tct = 2 and γ_tct = 1 and to the Mualem (1976) relationship when β_tct = 1 and γ_tct = 2.  When the Directional Aqueous Relative Permeability is applied to the Modified Mualem model, L can be specified in each of the three coordinate directions. If this parameter is assumed to be homogeneous in all coordinate directions (i.e., isotropic), then the Aqueous Relative Permeability Card can be used in place of the Directional Aqueous Relative Permeability Cards (~X Aqueous Relative Permeability, ~Y Aqueous Relative Permeability and ~Z Aqueous Relative Permeability).

 

References

Brooks, RH and AT Corey. 1966. "Hydraulic Properties of Porous Media Affecting Fluid Flow," Proc. ASCE J. Irrig. Drain. Div. , 92:61-68.

Burdine, NT. 1953. "Relative Permeability Calculation from Size Distribution Data," Trans. AIME, 198:71-78.

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.

Mualem, Y. 1976. "A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media," Water Resources Research, 12:513-522.

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.

van Genuchten, MT. 1980. "A Closed-Form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils," Soil Science Society of America Journal, 44:892-898.

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.

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