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.

气体扩散率是工程、农业和环境领域中用于模拟质量流和传输的关键参数。然而，现有模型仅针对单孔隙度介质开发，并低估了气体在裂缝或破裂介质中的扩散率。本研究建立了气体在不饱和双孔隙度介质中的分形扩散模型。基于统计特征，假设裂缝长度服从分形定律，孔径定义为其长度的幂函数。采用分子扩散的过渡机制来推导放大扩散模型。所开发的模型通过校准局部和整体特性之间的关系来考虑孔隙度和水分布的异质性。19组数据用于评估所提出的分形模型的稳健性。结果表明，在双孔隙度介质中，裂缝将作为优先通道，显着促进气体运移。此外，含水量的不均匀分布通过潜在地减少有效扩散路径来抑制分子扩散。裂缝对气体扩散的影响不仅与裂缝体积有关，还与裂缝的尺度分形维数等结构参数有关。最后，从与其他模型的比较中也可以看出所提出的分形模型的优越性。裂缝对气体扩散的影响不仅与裂缝体积有关，还与裂缝的尺度分形维数等结构参数有关。最后，从与其他模型的比较中也可以看出所提出的分形模型的优越性。裂缝对气体扩散的影响不仅与裂缝体积有关，还与裂缝的尺度分形维数等结构参数有关。最后，从与其他模型的比较中也可以看出所提出的分形模型的优越性。