Gas–water displacement characteristics in rough-walled fractures: The effects of fractal dimension and capillary number

Gas–water displacement in rough fractures critically influences unconventional energy recovery, yet current models fail to quantify geometry-fluid-inertia coupling mechanisms that govern trapping efficiency. To resolve this, we integrate in situ profilometry and multiphysics simulations to decipher how fractal dimension (D) and capillary number (Ca) control two-phase dynamics in Qinshui Basin coal fractures. Key discoveries reveal: (1) Residual gas fraction follows a Boltzmann distribution with Ca, exhibiting a sensitive transition zone (10−2 < Ca < 10−1) where trapping surges by 18%–28%; (2) increasing D from 1.5 to 1.72 elevates residual gas by 28.5% and prolongs breakthrough via power-law scaling (R2 > 0.98); and (3) aperture transitions reduce hydraulic apertures by 13%–28% through capillary-driven fingering. These quantified mechanisms provide a predictive framework for optimizing gas recovery in fracture-dominated reservoirs.