Study on Hydrogen Seepage Laws in Tree-Shaped Reservoir Fractures of the Storage Formation of Underground Hydrogen Storage in Depleted Oil and Gas Reservoirs Considering Slip Effects

Underground hydrogen storage (UHS) in depleted oil and gas reservoirs is regarded as a highly promising subsurface option due to its large storage capacity. In such reservoirs, the pore structure provides the primary space for hydrogen storage and governs matrix flow and diffusion. Tree-shaped fracture networks generated by hydraulic fracturing or cycling injection–production typically exhibit much higher transmissivity and serve as the dominant pathways. In this study, the geometry of multilevel branching fractures was parameterized, and two classes of tree-shaped fracture configurations were constructed, including point–line-type (PLTSF) and disc-shaped (DSTSF) networks. Analytical models were developed to evaluate the equivalent permeability of tree-shaped fracture networks with either elliptical or rectangular cross-sections. The Klinkenberg slip correction and a gas-type factor associated with molecular kinetic diameter were incorporated. The apparent equivalent permeability of hydrogen (k_app,H2) was quantified and compared with those of nitrogen and methane under identical conditions. The main findings were as follows: (1) the fracture width ratio (β) was identified as the primary factor controlling network conductivity, while the height ratio (α) amplified or attenuated this effect at a given β; (2) as the main-fracture aspect ratio, the branching order (n) or branching angle (θ) increased, the rectangular cross-sections were more favorable for maintaining higher permeability compared to the elliptical cross-section; (3) under typical operating pressures of 5–30 MPa, the apparent permeability of hydrogen was approximately 2–9% higher than that of methane and nitrogen; and (4) by introducing the fracture volume fraction, the REV-scale equivalent-permeability expression was derived for fractured rock masses containing tree-shaped fracture networks. The proposed framework provides a theoretical basis and parametric support for quantifying fracture flow capacity for UHS in depleted reservoirs.