Hydrogen (H2) is an attractive energy carrier to move, store, and deliver energy in a form that can be easily used. Field proven technology for underground hydrogen storage (UHS) is essential for a successful hydrogen economy. Options for this are manmade caverns, salt domes/caverns, saline aquifers, and depleted oil/gas fields, where large quantities of gaseous hydrogen have been stored in caverns for many years. The key requirements intrinsic of a porous rock formation for seasonal storage of hydrogen are: adequate capacity, ability to contain H2, capability to inject/extract high volumes of H2, and a reliable caprock to prevent leakage. We have carefully evaluated a commercial non-isothermal compositional gas reservoir simulator and its suitability for hydrogen storage and withdrawal from saline aquifers and depleted oil/gas reservoirs. We have successfully calibrated the gas equation of state model against published laboratory H2 density and viscosity data as a function of pressure and temperature. Comparisons between the H2, natural gas and CO2 storage in real field models were also performed. Our numerical models demonstrated more lateral spread of the H2 when compared to CO2 and natural gas with a need for special containment in H2 projects. It was also observed that the experience with CO2 and natural gas storage cannot be simply replicated with H2.