This paper focuses on the modeling of hydrogen (H2) storage in subsurface formations, particularly focusing on the equilibrium between H2 and brine and its implications for hydrogen transport properties in black-oil reservoir simulations. Initially, we evaluate and calibrate various equations of state (EoS) for H2-water and H2-brine mixtures. Our analysis ranges from the molecular-level Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation to a more explicit version of the Redlich-Kwong cubic EoS, and concludes with an empirical Henry-Setschenow (HS) model. These models are compared in terms of their ability to predict mutual solubilities with validation against experimental data. This study compares the strengths and limitations of each thermodynamic model, highlighting their overall good predictability across various temperatures, pressures, and salinity levels with a relatively moderate number of adjustable parameters. Subsequently, we apply these thermodynamic models to generate Pressure-Volume-Temperature (PVT) phase equilibrium data for use in black-oil simulations, focusing on the behavior of H2 in saline aquifers. Our investigation examines the effects of salt concentration, H2 solubility, molecular diffusion, and the impact of cycling frequency, injection and withdrawal rates on the storage and recoverability process. We present three numerical examples to illustrate these concepts: a 2D aquifer model, a modified benchmark originally designed for simulating the conversion of natural gas to hydrogen storage, and a 3D anticlinal dome-shaped aquifer model. These examples cover a range of complexities, such as heterogeneous permeability, porosity variations, and diverse rock types with specific entry pressures, providing a comprehensive overview of the factors influencing H2 storage in subsurface formations.