Fractal-based model for gas diffusion in multi-branch tree-like bifurcation networks: Decoupling the effects of asymmetry and tortuosity

The gas diffusion coefficient is a vital research parameter across multiple domains, including energy development, materials science, and chemical engineering. Most studies, when simulating tree-like bifurcation networks, often only consider the symmetric double-branch structure and neglect the impact of the complex internal structure of fractures on the gas diffusion. This paper employs a novel multi-branch tree-like bifurcation network model to more accurately characterize the fracture system, taking into account the effects of asymmetry and tortuous on gas diffusion, and derives an analytical expression for the relative gas diffusion coefficient. The study finds that the relative gas diffusion coefficient is positively correlated with porosity, the diameter ratio, and the number of branches, while it is negatively correlated with the tortuosity fractal dimension, the length ratio, and the total number of levels. By comparing with experimental data and existing models, the reliability of this model is verified. The model can effectively reveal the diffusion mechanism of gas in fracture-type multi-branch tree-like bifurcation networks, providing a theoretical support for understanding the diffusion mechanism of gas in fracture-type networks.