Geological hydrogen storage in depleted gas fields represents a new technology to mitigate climate change. It comes with several research gaps, around hydrogen recovery, including the flow behavior of hydrogen gas in porous media. Here, we provide the first‐published comprehensive experimental study of unsteady state drainage relative permeability curves with H 2 ‐Brine, on two different types of sandstones and a carbonate rock. We investigate the effect of pressure, brine salinity, and rock type on hydrogen flow behavior and compare it to that of CH 4 and N 2 at high‐pressure and high‐temperature conditions representative of potential geological storage sites. Finally, we use a history matching method for modeling relative permeability curves using the measured data within the experiments. Our results suggest that nitrogen can be used as a proxy gas for hydrogen to carry out multiphase fluid flow experiments, to provide the fundamental constitutive relationships necessary for large‐scale simulations of geological hydrogen storage.