Liquid retention and interfacial area in variably saturated porous media: Upscaling from single-pore to sample-scale model

A new model for liquid configuration in angular pore space considering both capillary and adsorptive contributions was proposed as an alternative to t he conventional bundle of capillaries representation. In this study we deve lop a statistical framework for upscaling pore-scale processes to represent a sample-scale response of variably saturated porous medium. The represent ation of pore size distribution by the gamma distribution enables derivatio n of closed-farm expressions for sample-scale liquid retention and liquid-v apor interfacial area. The statistical framework calculates the expected va lues of liquid configuration as a function of pore geometry and chemical po tential considerations. Media properties are used to estimate upscaling par ameters by matching model predictions with measured retention data subject to specific surface area constraint. Additionally, a method for estimating liquid-solid adsorption behavior for the medium is proposed. Model predicti ons compare favorably with measured retention data, yielding a similar clos e fit as obtained with the van Genuchten parametric model. Liquid-vapor int erfacial area as a function of chemical potential is readily calculated usi ng the estimated retention parameters. Model calculations of liquid-vapor i nterfacial area for sand show reasonable agreement with measurements obtain ed with surface-active tracers, The contribution of liquid films dominates the total liquid-vapor interfacial area and often surpasses the capillary c ontribution (curved menisci) by several orders of magnitude. This illustrat es potential limitations in using cylindrical pore network modeling of inte rfacial area for multiphase flow predictions. The detailed picture of liqui d vapor interfaces provides a sound basis for unsaturated hydraulic conduct ivity calculations in the sample cross section (i.e. neglecting network eff ects) and offers insights into microbial habitats, and related exchange pro cesses in partially saturated porous media.