Considering Surface Roughness Effects in a Triangular Pore Space Model for Unsaturated Hydraulic Conductivity

Quantifying the unsaturated hydraulic conductivity of a porous medium has been a great interest in the fields of hydrology, environmental engineering, and petroleum engineering. Previous research has shown that rough surfaces enhance liquid retention and conductance of flow in the form of liquid film. We present a pore-scale-based water retention and hydraulic conductivity model considering surface roughness effects. In the proposed model, a porous medium is simplified as a bundle of statistically distributed capillaries with triangular cross-sections. Surface roughness effects are characterized by a roughness factor, which accounts for increased film thickness under relatively wet conditions due to capillary effects and increased film area under relatively dry conditions. The model significantly improved the prediction of hydraulic conductivity across the entire range of matric potentials for the illustrative soils compared with the van Genuchten-Mualem model (VGM), while maintaining the same number of adjustable parameters. The improved performance of the proposed model demonstrates the advantage of incorporating surface roughness in the pore-scale-based models. Furthermore, sandy soils and loams showed distinct roughness factors and pore-size distribution functions. Sandy soils tended to have smaller roughness factors and greater mean pore sizes than loams.