Understanding pure H2 and H2/CH4 adsorption and diffusion in earth materials is one vital step toward a successful and safe H2 storage in depleted gas reservoirs. Despite recent research efforts such understanding is far from complete. In this work we first use Nuclear Magnetic Resonance (NMR) experiments to study the NMR response of injected H2 into Duvernay shale and Berea sandstone samples, representing materials in confining and storage zones. Then we use molecular simulations to investigate H2/CH4 competitive adsorption and diffusion in kerogen, a common component of shale. Our results indicate that in shale there are two H2 populations, i.e., free H2 and adsorbed H2, that yield very distinct NMR responses. However, only free gas presents in sandstone that yields a H2 NMR response similar to that of bulk H2. About 10 % of injected H2 can be lost due to adsorption/desorption hysteresis in shale, and no H2 loss (no hysteresis) is observed in sandstone. Our molecular simulation results support our NMR results that there are two H2 populations in nanoporous materials (kerogen). The simulation results also indicate that CH4 outcompetes H2 in adsorption onto kerogen, due to stronger CH4-kerogen interactions than H2-kerogen interactions. Nevertheless, in a depleted gas reservoir with low CH4 gas pressure, about ∼30 % of residual CH4 can be desorbed upon H2 injection. The simulation results also predict that H2 diffusion in porous kerogen is about one order of magnitude higher than that of CH4 and CO2. This work provides an understanding of H2/CH4 behaviors in deleted gas reservoirs upon H2 injection and predictions of H2 loss and CH4 desorption in H2 storage.