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 H2-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 CH4 and N2 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.