High-resolution three-dimensional X-ray imaging was employed to evaluate the injection of nitrogen (N2), carbon dioxide (CO2), and hydrogen (H2) in a reservoir carbonate rock. The imaging data were analyzed to determine key properties, including wettability, gas saturation, pore occupancy, ganglia size, and connectivity throughout the sample. The experiment was conducted on a water-wet carbonate rock saturated with synthetic brine prior to and between each gas injection cycle. The work demonstrates key differences in the behavior of the gases: H2 undergoes more significant rearrangement and improved connectivity after injection compared to N2, while CO2 remains well connected but exhibits the least rearrangement. This is advantageous of hydrogen withdrawal, whereas improved connectivity is not favorable for long-term CO2 sequestration. These findings are critical when considering the design and optimization of subsurface storage projects, where enhanced gas mobility benefits H2 recovery but poses risks for CO2 leakage.