Hydrogen gas migration modeling through water-saturated engineering barriers and the host rock of a deep geological repository for radioactive waste is of concern for safety assessment of such facilities. A two-phase two-relaxation-time lattice Boltzmann model using the Rothman and Keller approach was parallelized on graphic processing units to simulate hydrogen gas migration in a 3D image obtained by X-ray microtomography of Opalinus clay microfractures. A dimensional analysis combined with a grid refinement analysis was carried out to set the model parameters to reproduce the realistic viscous, capillary and inertial forces of the natural system. Relative permeabilities curves were first calculated in a simple regular fracture with different initial two-phase configurations. We observed that segmented gas flow configurations led to a drop in the relative gas permeability by two orders of magnitude as compared to parallel flow configuration. The model was then applied to 4 refined 3D images. For lower water saturation values (), hydrogen gas migrated through continuous gas paths oriented in the flow direction. At high water saturation values (), the relative gas permeability dropped to zero because the hydrogen phase segmented into gas pockets that were stuck in local narrow throats of the clay fracture. The study pointed out that the high capillary forces prevented the gas bubbles from distorting themselves to pass through these narrow paths.