An experimental study and mathematical formulation for hydrogen diffusion in water

Abstract

Abstract The transition to a hydrogen-based energy system requires safe and efficient large-scale storage solutions. Underground hydrogen storage (UHS) has emerged as a promising candidate, but the effectiveness and long-term security of UHS depend on a fundamental understanding of hydrogen transport mechanisms in subsurface environments. Among these, hydrogen diffusion into formation water plays a key role in governing mass loss, geochemical reactions, and microbial activity. This study presents a combined experimental and mathematical approach to quantify hydrogen diffusion in distilled water and brine at temperatures of 30 °C, 45 °C, and 60 °C, and pressures near 6.5 MPa. A new formulation is proposed that accounts for non-constant gas compressibility and enables systematic identification of the initial non-diffusive regime in pressure-time data. The methodology was validated by measuring the diffusion coefficient of CO₂ in distilled water, giving values consistent with those reported in the literature. Experimental results showed that hydrogen diffusion coefficients increase with temperature, from 3.6 $$\:\pm\:$$ 0.4 × 10⁻⁹ m²/s at 30 °C to 6.1 $$\:\pm\:$$ 0.3 × 10⁻⁹ m²/s at 60 °C. An additional series of tests on brine demonstrated that increasing salinity from 0 to 10,000 ppm of NaCl salt reduces the hydrogen diffusion coefficient to 5. $$\:8\pm\:$$ 0.2 × 10⁻⁹ m²/s at 60 °C. This methodology offers a robust framework for characterizing gas diffusion in aqueous systems, providing critical input not only for modeling hydrogen behavior in geological storage formations but also for optimizing hydrogen production via water electrolysis and its utilization in fuel cells.