Theoretical modeling of hydrogen relative permeability relevant to underground hydrogen storage

Abstract

Underground hydrogen storage (UHS) is a potential technology that can resolve renewable energy supply-demand challenge at seasonal (terawatt-hours) scales. Enabling this technology and optimizing its performance require a wide range of analyses from hydrodynamics to geomechanics and biogeochemistry, among which understanding the transport (and trapping) of hydrogen in porous rocks stands out. A key parameter in quantification of hydrogen transport in partially brine-saturated geological formations is its relative permeability (k_rh). In this study, we develop a theoretical k_rh model using upscaling concepts from effective medium approximation and percolation theory. Our theoretical model, developed based on pore-scale characteristics, estimates k_rh from pore size distribution, capillary pressure curve or mercury intrusion capillary pressure curve, and critical hydrogen saturation, S_hc, at which k_rh approaches zero. We evaluate the proposed model using eight experimental datasets and eleven pore-network simulations. Discrepancies are observed for some of the carbonate samples, likely due to secondary porosity effects (e.g., presence of vugs and/or fractures), and in some of the sandstone rocks, possibly due to imprecise S_hc estimation. These observations highlight the importance of improving pore structure characterization to better account for such heterogeneities and enhance model accuracy for reliable quantification of the k_rh relevant to UHS applications. These findings also highlight the critical role of accurate parameter estimation, such as determining the S_hc in estimating k_rh. Overall, the study demonstrates that the proposed approach provides a cost-effective and practical alternative to extensive experiments and simulations, offering a promising tool for quantifying k_rh relevant to UHS applications.