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Underground hydrogen storage (UHS) in porous formations such as depleted reservoirs offers a promising solution for large-scale, long-term energy storage. A key factor controlling storage safety is the maximum hydrogen column height (MHCH) that can be retained beneath the caprock without leakage. This study investigates the geological and physicochemical parameters that govern MHCH, including pore throat size, wettability, interfacial tension, and brine salinity. Using capillary sealing theory and the Laplace equation, we establish a framework to calculate MHCH under varying conditions. Experimental data from the literature are compiled across different caprock lithologies, and a Monte Carlo simulation approach is applied to quantify uncertainties and conduct global sensitivity analysis. Preliminary results suggest that clay-rich caprocks with fine pores and hydrophilic surfaces, such as illite- and smectite-rich shales, can support significantly higher MHCH than coarser or more oil-wet rocks. Additionally, interfacial tension and brine chemistry play important secondary roles, often underestimated in traditional assessments. This work provides a data-driven, probabilistic method for evaluating site suitability and improving the design of UHS systems. By clarifying the critical controls on hydrogen containment, the study contributes to safer and more effective deployment of subsurface hydrogen storage as part of a future low-carbon energy system.