Prediction of relative and absolute permeabilities for gas and water from soil water retention curves using a pore-scale network model

Functional relationships for unsaturated flow in soils, including those between capillary pressure, saturation, and relative permeabilities, are often described using analytical models based on the bundle-of-tubes concept. These models are often limited by, for example, inherent difficulties in prediction of absolute permeabilities, and in incorporation of a discontinuous nonwetting phase. To overcome these difficulties, an alternative approach may be formulated using pore-scale network models. In this approach, the pore space of the network model is adjusted to match retention data, and absolute and relative permeabilities are then calculated. A new approach that allows more general assignments of pore sizes within the network model provides for greater flexibility to match measured data. This additional flexibility is especially important for simultaneous modeling of main imbibition and drainage branches. Through comparisons between the network model results, analytical model results, and measured data for a variety of both undisturbed and repacked soils, the network model is seen to match capillary pressure-saturation data nearly as well as the analytical model, to predict water phase relative permeabilities equally well, and to predict gas phase relative permeabilities significantly better than the analytical model. The network model also provides very good estimates for intrinsic permeability and thus for absolute permeabilities. Both the network model and the analytical model lost accuracy in predicting relative water permeabilities for soils characterized by a van Genuchten exponent n≲3. Overall, the computational results indicate that reliable predictions of both relative and absolute permeabilities are obtained with the network model when the model matches the capillary pressure-saturation data well. The results also indicate that measured imbibition data are crucial to good predictions of the complete hysteresis loop.