Diffusion migration behavior of gas in unsaturated fractured soils: Fractal analytical study

Gas diffusivity is a crucial parameter for modeling the mass flow and transport in the fields of engineering, agriculture and environment. However, existing models were only developed for single-porosity media and underestimated the diffusivity of gas in fractured or cracked media. This study develops a fractal diffusion model of gas in unsaturated dual-porosity media. Based on statistical characteristics, the fracture length is assumed to obey the fractal law and the aperture is defined as a power function of its length. The transition regime of molecular diffusion is adopted to derive the upscaling diffusion model. The developed model considers the heterogeneity of porosity and water distribution by calibrating the relationship between local and bulk properties. 19 sets of data are used to evaluate the robustness of the proposed fractal model. The results show that in dual-porosity media, fractures will serve as preferential channels and significantly enhance gas migration. Besides, the heterogeneity distribution of water content inhibits molecular diffusion by potentially decreasing effective diffusion paths. The influence of fractures on gas diffusion is not only related to fracture volume but also to its scaling fractal dimension and other structures parameters. Finally, the superiority of the proposed fractal model can also be found from the comparison with other models.