A Model for Hydraulic Properties Based on Angular Pores with Lognormal Size Distribution

Abstract:

Soil water retention and unsaturated hydraulic conductivity curves are mandatory for modeling water flow in soils. It is a common approach to measure few points of the water retention curve and to calculate the hydraulic conductivity curve by assuming that the soil can be represented as a bundle of capillary tubes. Both curves are then used to predict water flow at larger spatial scales. However, the predictive power of these curves is often very limited. This can be very easily illustrated if we measure the soil hydraulic properties (SHPs) for a drainage experiment and then use these properties to predict the water flow in the case of imbibition. Further complications arise from the incomplete wetting of water at the solid matrix which results in finite values of the contact angles between the solid-water-air interfaces. To address these problems we present a physically-based model for hysteretic SHPs. This model is based on bundles of angular pores. Hysteresis for individual pores is caused by (i) different snap-off pressures during filling and emptying of single angular pores and (ii) by different advancing and receding contact angles for fluids that are not perfectly wettable. We derive a model of hydraulic conductivity as a function of contact angle by assuming flow perpendicular to pore cross sections and present closed-form expressions for both the sample scale water retention and hydraulic conductivity function by assuming a log-normal statistical distribution of pore size. We tested the new model against drainage and imbibition experiments for various sandy materials which were conducted with various liquids of differing wettability. The model described both imbibition and drainage experiments very well by assuming a unique pore size distribution of the sample and a zero contact angle for the perfectly wetting liquid. Eventually, we see the possibility to relate the particle size distribution with a model which describes the SHPs.