Predicting water flow in fully and partially saturated porous media: a new fractal-based permeability model

Predicting the permeability of porous media in saturated and partially saturated conditions is of crucial importance in many geo-engineering areas, from water resources to vadose zone hydrology or contaminant transport predictions. Many models have been proposed in the literature to estimate the permeability from properties of the porous media such as porosity, grain size or pore size. This study develops a model of the permeability for porous media saturated by one or two fluid phases with all physically based parameters using a fractal upscaling technique. The model is related to microstructural properties of porous media such as fractal dimension for pore space, fractal dimension for tortuosity, porosity, maximum radius, ratio of minimum pore radius and maximum pore radius, water saturation and irreducible water saturation. The model is favorably compared to existing and widely used models from the literature. Then, comparison with published experimental data for both unconsolidated and consolidated samples shows that the proposed model estimates the permeability from the medium properties very well.

Automated summary

This study develops a model to predict the permeability of porous media saturated by one or two fluid phases using a fractal upscaling technique. The model takes into account microstructural properties such as fractal dimension and porosity, and performs well compared to existing models.