Evaluation of gas diffusion-saturation functions as inputs to multiphase flow and transport models simulating gas transport in variable saturated sand

Multi-phase multi-component flow and transport models are a key instrument for analyzing and predicting gas transport inside the vadose zone. The soil moisture distribution within the vadose zone varies in time and space. Thus, accurate gas transport prediction relies on the precise knowledge of the saturation-dependency of the transport parameters such as the effective gas diffusion coefficient D_eff. Although recent advances from typical small scale experiments (diffusion apparatus with typical soil core size of 100 cm³) show that D_eff-saturation(S)-relationships are not only dependent on general soil characteristics such as air-filled porosity and total porosity, but can also be derived from pore network characteristics, such as pore connectivity and geometry, most model frameworks rely on simple empirical formulations such as Millington & Quirk (1961), which find wide acceptance, but have been found to not be universally applicable.

The current state of research lacks extensive performance tests for the application of D_eff-S-relationships beyond the small scale and especially for realistic natural conditions, where soil moisture changes with depth and gas transport processes may be more complex than in standard laboratory setups used for the experimental determination of D_eff, which leads to unknown errors in the numerical prediction of sub-surface gas transport processes.

We test different D_eff-S-functions within a multi-phase-multi-component flow and transport model by reproducing a laboratory gas transport experiment, where a tracer gas is injected into a quasi-2D Darcy-scale sand tank with a soil moisture distribution that covers the full range from wet to dry and comparing simulated and measured gas concentrations at several locations within the tank over time. The systematic evaluation of different functions leads to the conclusion that the saturation-dependency of D_eff in the tested sand follows power law-scaling at low gas phase saturation and linear scaling above, in line with the physically based concepts of percolation theory and effective medium theory and with recent experimental results (Ghanbarian et al., 2018). Other approaches such as (Buckingham, 1904; Penman, 1940; Millington & Quirk, 1961; Moldrup et al., 2000) lead to large errors between numerical and experimental results. We demonstrate that the use of an inaccurate D_eff-S-function can lead to a misrepresentation of diffusion coefficients by a factor of up to 10⁵, which underlines the need for a correct representation of the saturation-dependency of D_eff in numerical modeling of sub-surface gas transport.