A simple model for describing hydraulic conductivity in unsaturated porous media accounting for film and capillary flow

The commonly used models for characterizing hydraulic conductivity of porous media rely on pore bundle concepts that account for capillary flow only and neglect film flow. Experimental evidence suggests that water flow at medium to low water contents in unsaturated porous media can be significantly underestimated by these capillary bundle models. We present a new model that combines a simple film flow function with the capillary flow model of Mualem. This new model can easily be coupled to any water retention function. Moreover, due to its mathematical simplicity, it can easily and efficiently be implemented in existing codes for the numerical solution of unsaturated flow problems. We investigated a set of soil water retention and conductivity data from the literature that all reached dry conditions and were poorly described by existing capillary bundle models. These data were well described with the new model if the model was coupled with an appropriate retention function. Investigation of conductivity data from the UNsaturated SOil hydraulic DAtabase (UNSODA) database showed that, in 75% of all data sets, the new model achieved the best performance using a modified version of Akaike's information criterion. The numeric simulation of an evaporation scenario using Richards's equation showed that by neglecting film flow, the evaporation rate may be underestimated by more than an order of magnitude.