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 the conventional bundle of capillaries representation. In this study we develop a statistical framework for upscaling pore-scale processes to represent a sample-scale response of variably saturated porous medium. The representation of pore size distribution by the gamma distribution enables derivation of closed-form expressions for sample-scale liquid retention and liquid-vapor interfacial area. The statistical framework calculates the expected values of liquid configuration as a function of pore geometry and chemical potential considerations. Media properties are used to estimate upscaling parameters 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 predictions compare favorably with measured retention data, yielding a similar close fit as obtained with the van Genuchten parametric model. Liquid-vapor interfacial area as a function of chemical potential is readily calculated using the estimated retention parameters. Model calculations of liquid-vapor interfacial area for sand show reasonable agreement with measurements obtained with surface-active tracers. The contribution of liquid films dominates the total liquid-vapor interfacial area and often surpasses the capillary contribution (curved menisci) by several orders of magnitude. This illustrates potential limitations in using cylindrical pore network modeling of interfacial area for multiphase flow predictions. The detailed picture of liquid vapor interfaces provides a sound basis for unsaturated hydraulic conductivity calculations in the sample cross section (i.e., neglecting network effects) and offers insights into microbial habitats and related exchange processes in partially saturated porous media.