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Unsaturated Hydraulic Conductivity of Structured Porous Media

A Review of Liquid Configuration–Based Models

^a Department of Plant, Soil & Entomological Sciences, University of Idaho, Moscow, Idaho 83844-2339
^b Department of Plants, Soils & Biometeorology, Utah State University, Logan, Utah 84322-4820

View larger version (149K): [in a new window]   Fig. 1. (a) Thin section of Devonian Sandstone (Roberts and Schwartz, 1985) revealing angular pore space. (b) Scanning electron micrograph (SEM) of calcium-saturated montmorillonite.

View larger version (26K): [in a new window]   Fig. 2. Unit cell for pore space representation comprising an angular central pore attached to slit-shaped spaces.

View larger version (31K): [in a new window]   Fig. 3. Definition sketch for (a) a unit fracture element representing a partially saturated fracture with liquid retained in crevices and adsorbed liquid films; (b–e) various combinations of scale parameters and surface mating based on the same geometrical definitions as in (a).

View larger version (59K): [in a new window]   Fig. 4. Conceptual sketch for the simplified approach (SYL). The radius of interface curvature r(µ) is shifted by the thickness h(µ) of the adsorbed liquid film. Note that r(µ) and h(µ) are functions of the matric potential µ.

View larger version (49K): [in a new window]   Fig. 5. A sketch illustrating liquid–vapor interfacial configurations in a unit cell with triangular central pore during transition from adsorption to capillary-dominated imbibition. (a) Partially saturated unit cell with adsorbed films and liquid accumulated in corners of the central pore, (b) liquid configuration after slit snap-off, (c) liquid saturation at pore snap-off when capillary menisci form an inscribed circle, and (d) completely liquid saturated unit cell after pore snap-off.

View larger version (16K): [in a new window]   Fig. 6. A sketch illustrating liquid configurations and critical potentials during fracture drainage. (a) Three-step transition for geometries where the capillary meniscus is first anchored at the pit edges after interface separation and then recedes into the surface pit (note that the second transition was introduced for mathematical tractability). (b) Two-step transition for geometries where the capillary meniscus immediately tangents the pit walls after interface separation.

View larger version (28K): [in a new window]   Fig. 7. Conceptual sketch of considered flow regimes under various cell-filling stages in (a) matrix, and (b) fracture unit elements.

View larger version (57K): [in a new window]   Fig. 8. Three-dimensional representation of corner and film flow regimes within (a) a partially saturated matrix unit cell and (b) a unit fracture element.

View larger version (97K): [in a new window]   Fig. 9. Images of (a) fractured rock, (b) macroporous and, (c) aggregated soils with conceptual sketches for dual continuum pore space representation. Note the pore size disparity between the two domains.

View larger version (40K): [in a new window]   Fig. 10. Definition sketch showing the applied upscaling scheme. (a) Gamma distribution of central pore lengths with = 2, and six hypothetical bins (note the inverse relationship between ß and L). (b) Cell-filling stages for a population of unit cells (represented by L1 to L6) defined at three matric potential values, µ1 to µ3 (dry to wet).

View larger version (31K): [in a new window]   Fig. 11. (a) Limits of integration for determining the expected values of liquid saturation for pores in various stages of filling. (b) Integration limits expressed in terms of pore length L as a function of potential µ.

View larger version (17K): [in a new window]   Fig. 12. Critical aperture sizes determining expected fracture-filling stages at different matric potentials.

View larger version (38K): [in a new window]   Fig. 13. A conceptual flow chart of the parameter estimation scheme. Assumed matrix pore geometry and measured matrix liquid retention data are used as input parameters to estimate free matrix model parameters while imposing surface area and porosity constraints, resulting in liquid saturation and hydraulic conductivity. Assumed fracture geometry and measured aperture-size distribution in combination with fracture porosity and saturated fracture permeability are used to determine fracture model parameters for calculating the continuous liquid saturation curve and predicting fracture hydraulic conductivity as a function of matric potential. Note that the individual contributions of the matrix and fracture domains are superimposed and weighted by matrix and fracture porosities to receive the composite response of the fractured porous medium.

View larger version (24K): [in a new window]   Fig. 14. (a) Calculated liquid saturation for a sandy loam. (b) Predicted relative hydraulic conductivity. (Note that 1 J kg-1 10-2 bar.)

View larger version (19K): [in a new window]   Fig. 15. (a) Calculated liquid saturation for Gilat loam. (b) Predicted relative hydraulic conductivity.

View larger version (20K): [in a new window]   Fig. 16. Calculated saturation and predicted permeability curves for the Tiva Canyon welded tuff (TCwt) unit. Note the corner and film flow contributions within the matrix and fracture domains. (Note that 1 J kg-1 10-2 bar.)

View larger version (23K): [in a new window]   Fig. 17. Permeability curves for Tiva Canyon welded tuff (TCwt) under nonequilibrium conditions.

View larger version (26K): [in a new window]   Fig. 18. (a) Fitted liquid saturation for silt loam soil with biological macropores. (b) Predicted relative hydraulic conductivity. (Note that 1 J kg-1 10-2 bar.) (Data source: Mohanty et al., 1997.)

View larger version (25K): [in a new window]   Fig. 19. (a) Fitted liquid saturation for aggregated loam soil. (b) Predicted relative hydraulic conductivity. (Smettem and Kirkby, 1990.)