Air entry-based characteristic length for estimation of permeability of variably compacted earth materials

The permeability k of a porous medium is a geometrical pore space attribute required for quantifying fluid flows and transport processes for hydrological, civil, agriculture, and petroleum engineering applications. Permeability is often expressed as proportional to a characteristic length squared and inversely proportional to factors accounting for porosity, pore shape, and tortuosity effects. Compaction and diagenesis reduce porosity, mean pore size, and connectivity, resulting in decrease in k. Permeability prediction relies on suitable selection of a characteristic length that may vary from simple hydraulic radius approximation of Kozeny-Carman to more complex critical path analysis to identify flow-limiting pore size. For porous media undergoing significant changes in pore space (e. g., compaction due to anthropogenic activities), the proper choice of a robust characteristic length is particularly challenging. We propose using the air entry pressure, a natural characteristic length that gauges the largest drainable pore size. This choice of a characteristic length is compatible with the Aissen formula that provides robust estimates of k for complex pore shapes. Additionally, the model considers geometrical (tortuosity) factors and links relative changes in porosity to concurrent changes in k. The model was tested against experimental data for sands, sandstones with different cementing agents, and unconsolidated soils. For unconsolidated sands and soils the model provides reasonable predictions of permeability for the entire range of porosities determined in laboratory or field experiments. However, for sandstones, and especially those containing cementing agents such as clay, the model is valid up to a critical porosity where hydraulic connectivity is lost, resulting in drastic reduction in k. The geometrical factor for soils was influenced by silt-to-clay ratio, while for sands, it was correlated with mean grain diameter. The model offers improvement in predicting k and provides a means for incorporating critical pore size and connectivity information in addition to porosity.