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

TL;DR

This paper introduces a new fractal-based model to predict permeability in saturated and partially saturated porous media, improving accuracy by incorporating microstructural properties and validated against experimental data.

Contribution

The study develops a physically-based fractal model for permeability that accounts for microstructural features and saturation levels, advancing existing models in the field.

Findings

The model accurately predicts permeability for various porous media.

Comparison shows the model outperforms existing models.

Experimental validation confirms the model's robustness.

Abstract

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. In this study, we develop 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, we show that the proposed model estimate the permeability from the medium properties very well.