A new model for relative gas permeability considering the dynamics of pore-scale water distribution

Abstract

Investigating gas flow through unsaturated soils is crucial for various geoscientific and engineering applications. Traditional statistical permeability models, based on capillary-law theory, often overestimate gas permeability. While recent efforts have extended gas permeability functions into the adsorption region, they rarely consider the dynamics of water distribution at the pore scale. This study introduces a new approach to predicting gas permeability by considering the dynamics of flow regimes as water saturation increases. This approach employs a dual-regime framework that sequentially accounts for the funicular and separate channel flow regimes. At low saturation, water forms thin films on particle surfaces, and as saturation increases, these films thicken, creating a funicular flow regime. At higher saturation levels, capillary forces gradually dominate gas flow, and gas occupies larger pores while water fills smaller ones, enabling separate channel flow regime. To mathematically represent and integrate these two physical processes, a piecewise function is used, and a model parameter of critical saturation is defined to delineate the transition between these two regimes. For verification, a dataset comprising 31 different soils, including loam, sand, loess, and clay, was compiled from various literature sources. The prediction results by the proposed model show good agreement with experimental data, yielding low RMSE and MAE values of 0.050 and 0.028, respectively. To provide a rapid method for predicting relative gas permeability based on readily available parameters, this study established an empirical relationship between critical saturation and residual saturation, which also yields satisfactory results with RMSE and MAE values of 0.085 and 0.054, respectively. The findings of this study offer a new perspective on understanding gas transport within unsaturated soils.