Abstract Underground gas storage supports the energy transition, enabling long‐term CO2 ${text{CO} }{2}$ sequestration and seasonal H2 ${mathrm{H} }{2}$ storage. A key process shaping the fate of injected gases is Ostwald ripening—the curvature‐driven mass transfer between trapped ganglia—yet its behavior in confined porous structures remains poorly constrained. We present ultra‐high‐resolution microfluidic experiments that track residually trapped hydrogen for weeks in realistic heterogeneous pore networks. The data show rapid local equilibration among neighboring bubbles, followed by slow global depletion driven by long‐range diffusion. We develop a continuum model that couples pore‐scale capillary pressure–saturation relationship, derived using the pore‐morphology method, with macroscopic diffusion. The model predicts saturation evolution without fitting parameters and collapses results across diverse conditions. Reservoir‐scale estimates indicate that local equilibration far outpaces convective dissolution for CO2 ${text{CO} }{2}$ and occurs on timescales comparable to seasonal H2 ${mathrm{H} }{2}$ storage. Because minimal redistribution is required to reach local capillary equilibrium, residual trapping remains stable in the absence of sinks.