An Analytical Framework for Underground Hydrogen Storage in Depleted Gas Reservoirs: Modified Material-Balance and Radial-Diffusivity Models with Numerical Validation

Underground hydrogen storage in depleted gas reservoirs is a leading option for seasonal balancing of renewable generation, yet the classical material balance and radial diffusivity equations were derived for hydrocarbon gases and misrepresent hydrogen. This work develops modified analytical formulations and benchmarks them against a fully implicit radial finite-difference reference. The material balance is recast in pore-volume form, coupling a Soave–Redlich–Kwong description of hydrogen with formation compaction, connate-water expansion, Fetkovich aquifer influx, Henry’s-law dissolution and hysteretic capillary trapping, and is solved by damped Newton–Raphson iteration. The radial diffusivity equation is written in real-gas pseudo-pressure and solved by a line-source expression yielding hydrogen-specific dimensionless type curves. Both are verified against that reference. Across 599 paired states spanning primary depletion, water drive, transient radial flow and ten storage cycles, the analytical model reproduces numerical pressure with a mean absolute percentage error of 0.06% and a coefficient of determination of 0.99997. For a 2500 m, 373 K, 50 mD reservoir, ten cycles recover 63.5% of the volume cycled, or 28.9% of total injection including the initial fill, while purity rises from 56 to 70 mol %. Losses to dissolution and trapping total 0.70% of injection, of which only 0.20% is irreversible. Capacity proves porosity- and cushion-controlled, with deliverability permeability-controlled.