The paper presents the characteristics of potential structures that can be used for hydrogen storage. The criteria for selecting the optimal structure were formulated. They include estimated sequestration capacity, range of historical reservoir pressures, fracturing pressure, transport properties of the rock, activity of the underlying water, type of reservoir fluid, reservoir temperature. After applying these criteria, a natural gas field structure, currently functioning as a UGS (underground gas storage) facility, was selected. In order to find the characteristics of the selected structure as a UHS (underground hydrogen storage), a compositional reservoir model was constructed. For this purpose, a multicomponent model of the formation fluid described by the Soave-Redlich-Kwong equation of state was built and supplemented with compositional hydraulic models of wells. The complete model of the field was effectively calibrated using historical operational data, including the production rate from the gas field, gas injection and withdrawal under the UGS operation and the pressures measured at the bottom of the production wells. The verified model was used for multiple simulations of the hydrogen storage process using realistic constraints for gas injection and withdrawal, i.e., injection and withdrawal times, limits for the total amount of injected hydrogen and withdrawn gas, maximum acceptable contamination of the withdrawn hydrogen. Consequently, simulation scenarios differed in the details of the UGS - UHS conversion and withdrawn gas composition. The basic geological properties resulted from the original structure properties were not subject to modification, while the unknown but significant dispersion parameter determining the mixing of the injected gas with the original gas was subject to changes. The quantitative results of the UHS operation forecasts were supplemented with a detailed analysis of the distribution of hydrogen saturation at various stages and in different operation cycles of the storage schedule. The study investigated the influence of the dispersion phenomenon on the results of storage operation by implementing the phenomenon of numerical dispersion, verifying the correctness of the correlation between dispersion and migration speed, and identifying the dispersion values for various reservoir models. Basic conclusion was derived from the obtained simulation results.