Fractal Analysis for Permeability of Multiple Shale Gas Transport Mechanisms in Dual Media with Embedded Tree-Like Branching Networks

In this study, a fractal-based model for apparent permeability is developed by embedding the tree-like branching network and capillaries within a porous matrix. The model incorporates multiple gas flow mechanisms, including slip flow and Knudsen diffusion. The results indicate that apparent permeability decreases with increasing pore pressure or decreasing maximum parent branch width. At low pressure and small maximum parent branch width, the flow is predominantly governed by Knudsen diffusion, while at high pressure and large maximum parent branch width, slip flow dominates. As pressure decreases or the maximum parent branch width decreases, the flow transitions from slip flow to Knudsen diffusion. In addition, higher porosity and larger fractal dimensions both contribute to higher apparent permeability. Moreover, the geometric parameters of the branching structure, such as the length ratio, width ratio, branch aspect ratio, and branch level, significantly influence apparent permeability. This model reveals the coupled effects of multiple transport mechanisms within the branching structure. It enhances our understanding of gas flow in the complex porous media of shale reservoirs.