Relative Permeability Modeling for Underground Hydrogen Storage: A Comparative Analysis of Hysteresis Effects

The transition towards a sustainable and low-carbon future introduces the necessity to develop efficient energy storage systems. H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf>, with its high energy density and environmental benignity, emerges as a pivotal element in this energy transition. Nevertheless, the efficient storage of H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> is impeded by substantial obstacles, which requires the development of innovative solutions. Underground H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> storage (UHS) in depleted hydrocarbon reservoirs is a promising solution for large-scale H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> energy management that is essential for the transition to an H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> economy. This paper investigates the mathematical modeling and curve fitting of experimental measured relative permeability hysteresis data for H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and water during drainage, imbibition processes on reservoir-scale performance. This study evaluates the performance of several relative permeability models—Brooks-Corey (BC), Van Genuchten (VG), and Modified Brooks-Corey-variable Corey (BC-vC)—using experimental data for H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> and water during drainage and imbibition processes. Error metrics, including Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE), and the coefficient of determination (R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>), are calculated to assess model accuracy. The results indicate that the VG model provides the best fit for H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> during drainage, while all models perform comparably for water drainage. The VG model is a more suitable option for H<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> in terms of imbibition. The study underscores the importance of model selection in accurately describing multiphase flow in porous media.