## 4 Applications
### Effect of Relative Permeability Hysteresis on Hydrogen Storage
According to experimental measurements by [PERSON] [103], a significant difference is observed in the hysteresis level during the wetting phase, typically showing smaller hysteresis effects in the wetting phase of other systems, but in hydrogen-prime systems, the hysteresis effect of liquid phase relative permeability is more pronounced. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**Author** & **Time** & **Software** & \begin{tabular}{c} **Hydrogen** \\ **Storage Site** \\ \end{tabular} & **Model** & \begin{tabular}{c} **Whether** \\ **Hysteresis Exists** \\ \end{tabular} & **Main Finding** \\ \hline [PERSON] et al. [104] & 2015 & Eclipse & Saline layer & [PERSON] & \begin{tabular}{c} Porous media hydrogen storage must \\ address issues such as the resistance of \\ caprock rocks to hydrogen permeation and \\ gas diffusion. \\ \end{tabular} \\ \hline [PERSON] et al. [105] & 2015 & [PERSON] & aquifers & [PERSON]–Corey & No & \begin{tabular}{c} For low injection rates, gravitational forces \\ dominate hydrogen movement, while for \\ high injection rates, viscous forces become \\ dominant, and displacement becomes \\ unstable. \\ \end{tabular} \\ \hline [PERSON] et al. [106] & 2016 & DuMux, COMSOL & \begin{tabular}{c} Depleted gas \\ reservoir \\ \end{tabular} & Brooks–Corey & No & \begin{tabular}{c} The gravitational override and viscous \\ fingering in the aquifer structure \\ complicate the effective displacement of \\ natural fluids. \\ \end{tabular} \\ \hline [PERSON], [PERSON] et al. [107] & 2017 & COMSOL & saline layer & [PERSON]–Corey & No & \begin{tabular}{c} If there are several shallow oil wells \\ beneath the caprock, a large amount of H2 \\ can be recovered. Rising appears to be the \\ main limitation for brine aquifer storage in \\ the absence of other buffering gases. \\ \end{tabular} \\ \hline Katarzyna [108] & 2020 & \begin{tabular}{c} petraSim- \\ TOUGH2 \\ \end{tabular} & aquifers & Van Genuchten- & No & \begin{tabular}{c} Maximum hydrogen saturation occurs \\ around the injection well, and hydrogen \\ diffuses along the top surface of the \\ reservoir in contact with the caprock, likely \\ due to the lack of viscous fingering and the \\ low viscosity and density of hydrogen, \\ which may impact the geometry of \\ underground storage. \\ \end{tabular} \\ \hline [PERSON] et al. [101] & 2021 & Eclipse & \begin{tabular}{c} Depleted \\ field \\ \end{tabular} & Field data & No & \
\begin{tabular}{c} When injecting pure hydrogen only, most \\ injected hydrogen (\textgreater{}84\%) remains \\ underground as a buffering gas. \\ Unrecovered hydrogen accumulates in the \\ uppermost layer. Injecting formation gases \\ as buffering gases leads to higher \\ hydrogen recovery rates. \\ \end{tabular} \\ \hline [PERSON], et al. [109] & 2021 & TOUGH2 & Water layer & van Genuchten- & Gas-liquid \\ Mualem & & hysteresis &
\begin{tabular}{c} Caprock and injection rates have \\ significant impacts on hydrogen leakage, \\ as well as on the amount of hydrogen \\ captured and recovered. Without caprock, \\ higher injection rates increase H\({}_{2}\) leakage. \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 5: Relative permeability hysteresis on hydrogen storage application statistics.