Gas transport in partially-saturated sand packs

Understanding gas transport in porous media and its mechanism has broad applications in various research areas, such as carbon sequestration in deep saline aquifers and gas explorations in reservoir rocks. Gas transport is mainly controlled by pore space geometrical and morphological characteristics. In this study, we apply a physically-based model developed using concepts from percolation theory (PT) and the effective-medium approximation (EMA) to better understand diffusion and permeability of gas in packings of angular and rounded sand grains as well as glass beads. Two average sizes of grain i.e., 0.3 and 0.5 mm were used to pack sands in a column of 6 cm height and 4.9 cm diameter so that the total porosity of all packs was near 0.4. Water content, gas-filled porosity (also known as gas content), gas diffusion, and gas permeability were measured at different capillary pressures. The X-ray computed tomography method and the 3DMA-Rock software package were applied to determine the average pore coordination number z. Results showed that both saturation-dependent diffusion and permeability of gas showed almost linear behavior at higher gas-filled porosities, while deviated substantially from linear scaling at lower gas saturations. Comparing the theory with the diffusion and permeability experiments showed that the determined value of z ranged between 2.8 and 5.3, not greatly different from X-ray computed tomography results. The obtained results clearly indicate that the effect of the pore-throat size distribution on gas diffusion and permeability was minimal in these sand and glass bead packs.

💡 Research Summary

The paper investigates gas transport in partially saturated porous media by combining percolation theory (PT) with the effective‑medium approximation (EMA). Five well‑sorted packings were prepared: angular sand (Granusil) and rounded sand (Accusand) at two grain sizes (0.3 mm and 0.5 mm), plus spherical glass beads (0.5 mm). All packs were packed in a 6 cm‑high, 4.9 cm‑diameter column to a bulk porosity of approximately 0.40. By varying the imposed capillary pressure (0–90 cm H₂O) the water content was adjusted, allowing measurement of the gas‑filled porosity (e), the effective gas diffusion coefficient (D), and the gas permeability (k) for each saturation state.

The authors adopt a unified analytical expression (Eq. 3) that merges the universal scaling law of PT (a power‑law dependence on (e‑e_c)² below a crossover) with the linear EMA scaling above a crossover porosity e_x. The model contains three physically meaningful parameters: the critical gas‑filled porosity e_c (percolation threshold), the crossover porosity e_x (where the scaling changes from PT to EMA), and the average pore coordination number z (average number of throats per pore body). By fitting Eq. 3 to the experimental D(e) and k(e) data, the authors simultaneously retrieve e_c, e_x, and z for each packing.

X‑ray computed tomography (CT) was performed on dry samples, and the 3DMA‑Rock software was used to extract the pore‑throat network and compute the geometric‑mean coordination number. The CT‑derived z values follow a log‑normal distribution and lie between 2.8 and 5.3, which matches the values obtained from the PT‑EMA fits, confirming that the model can recover a key topological descriptor from transport measurements alone.

Capillary‑pressure curves were fitted with a fractal‑based model (Eq. 4) to quantify the pore‑throat size distribution. The fitted fractal dimensions d_f range from 0.98 to 1.76, considerably lower than typical natural soils or rocks (2 < d_f < 3), indicating a relatively narrow throat size distribution in these laboratory packs. The authors argue that such narrow distributions justify the use of a single crossover porosity and support the applicability of the universal PT scaling.

Key experimental findings:

• For all packings, D(e) and k(e) are nearly linear at high gas‑filled porosities (e > 0.2), but deviate strongly from linearity as e approaches the percolation threshold.
• Critical porosities e_c are small (0.03–0.04), reflecting the high connectivity of the well‑sorted packs.
• Crossover porosities e_x lie between 0.17 and 0.23, marking the transition from PT‑dominated to EMA‑dominated behavior.
• The fitted coordination numbers (z ≈ 3–5) are consistent across grain shapes and sizes, suggesting that overall packing geometry, rather than individual grain angularity, controls connectivity in these systems.

The study demonstrates that the PT‑EMA framework, originally validated in lattice‑Boltzmann simulations of mono‑size sphere packs, can accurately describe real experimental data for both diffusion and permeability. By providing a physically based link between transport coefficients and microstructural parameters (z, e_c, e_x), the approach offers a practical tool for predicting gas flow in partially saturated reservoirs, carbon‑capture storage sites, and other engineering applications where gas transport through unsaturated porous media is critical.

In summary, the work validates a unified, physics‑based model for gas diffusion and permeability in partially saturated granular media, shows that the average pore coordination number can be inferred from transport measurements, and confirms that the pore‑throat size distribution has a limited impact on the scaling behavior for the studied well‑sorted packs. This contributes a robust, parameter‑light methodology for up‑scaling laboratory observations to field‑scale predictions in environmental and energy‑related subsurface processes.