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Sample Scale Liquid Retention and Liquid-Vapor Interfacial Area

Sample Scale Liquid Retention and Liquid-Vapor Interfacial Area Dani Or & Markus Tuller Dept. of Plants, Soils and Biometeorology Utah State University, Logan, Utah. Outline for Section 2.

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Sample Scale Liquid Retention and Liquid-Vapor Interfacial Area

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  1. Sample Scale Liquid Retention and Liquid-Vapor Interfacial Area Dani Or & Markus TullerDept. of Plants, Soils and Biometeorology Utah State University, Logan, Utah

  2. Outline for Section 2 • How can we use simplified Y-L expressions in a unit cell to represent a population of pores (i.e., a soil sample)? • Statistical representation of pore size distribution (normal, log-normal, and Gamma) • Relationships between psd and soil water characteristic curve • Measurable soil attributes that provide constraints for psd estimation • A proposed estimation scheme • Examples for various soils – capillary and film water content • Liquid-vapor interfacial area – an important function for gas exchange processes (e.g., bioremediation)

  3. Statistical representation of soil pore size distribution • From Brutsaert (1966) to Assouline (2000) many have proposed to represent soil pore size distribution by various statistical PDF’s such as: normal, log-normal, Gamma, and Weibul PDF’s. • For example, Kosugi (1994) proposed a log-normal expression: • There are some subtle differences between f(r) and f(r3) – psd of size usually pertains to pore radii and not volume distribution… • Relationships between psd and SWC – water capacity (d/d) with f(r) based on the capillary rise equation.

  4. Statistical representation of soil pore size distribution • Pore size (radii) distribution is calculated by taking the derivative of the SWC (d/dh); and • By employing the capillary rise equation (r=a/h) Water Content - q - [m3 m-3] Matric Potential - h - [m]

  5. Gamma Distribution for L Slits f(L) L4 L5 L1 L2 L3 L6 Dry Wet L1 L2 L3 L4 L5 L6 m3 m1 m2 Upscaling from Pore-to Sample-Scale • A statistical approach using Gamma distributed cell size is employed to represent a sample of a porous medium. • Gamma distribution – facilitates analytical solutions and preserves the observed skewness in psd. • In developing “upscaled” equations for liquid retention, one must keep track of portions of pore population at various filling stages (due to differences in their pore size).

  6. L1= L2= Limits of Integration for the Upscaling Scheme Filling Stage Boundary Cell Size Lmin Full Cells Full Slits-Partially-Filled Pores Partially-Filled Slits & Pores Lmax

  7. full cells corners pore full slits films pore films pore +slits The application of Limits of Integrationin the Upscaling Scheme

  8. Measured Media Properties ProvideConstraints for Geometry and PSD • Measured soil specific surface area and the “dry end” of the SWC curve provide constraints for  and  parameters. • The “bubbling pressure” defines the largest pore to be considered. • The smallest pore size is bounded by slit-spacing.

  9. Millville Silt Loam Measured and Modeled Water Retention Curve films corners/ full pores

  10. Salkum Measured and Modeled Water Retention Curve

  11. Measured and Predicted Liquid-Vapor Interfacial Area Sand

  12. An Overview of the Proposed Scheme

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