Empirical and numerical modelling of gas-gas diffusion for binary hydrogen-methane systems at underground gas storage conditions

The physical process in which a substance moves from a location with a higher concentration to a location with a lower concentration is known as molecular diffusion. It plays a crucial role during the mixing process between different gases in porous media. Due to the petrophysical properties of the porous medium, the diffusion process occurs slower than in bulk, and the overall process is also affected by thermodynamic conditions. The complexity of measuring gas–gas diffusion in porous media at increased pressure and temperature resulted in significant gaps in data availability for modelling this process. Therefore, correlations for ambient conditions and simplified diffusivity models have been used for modelling purposes. In this study, correlations in dependency of petrophysical and thermodynamic properties were developed based on more than 30 measurements of the molecular diffusion of the binary system hydrogen–methane in gas storage rock samples at typical subsurface conditions. It allows reproducing the laboratory observations by evaluating the bulk diffusion coefficient and the tortuosity factor with relative errors of less than 50 % with minor exceptions, leading to a strong improvement compared to existing correlations. The developed correlation was implemented in the open-source simulator DuMu x and the implementation was validated by reproducing the measurement results. The validated implementation in DuMux allows to model scenarios such as Underground Hydrogen Storage (UHS) on a field-scale and, as a result, can be used to estimate the temporary loss of hydrogen into the cushion gas and the purity of withdrawn gas due to the gas–gas mixing process.