## 4 Applications
### The Impact of Relative Permeability Hysteresis on CO\({}_{2}\) Sequestration  
The effect of phase trapping is described by the gas trapping and reduction in relative permeability during three-phase flow processes, which is particularly pronounced during flow reversals and holds significant importance for CO\({}_{2}\) sequestration studies. Currently, there have been some studies on the impact of phase trapping on CO\({}_{2}\) sequestration, indicating that phase trapping is beneficial for CO\({}_{2}\) sequestration. In saline aquifers, which are the primary targets for CO\({}_{2}\) sequestration, the reservoirs are typically water-wet. During water flooding, the gas saturation decreases, and the non-wetting gas phase is trapped by the wetting phase. As the wetting phase invades the pores, the non-wetting gas phase also increases. During CO\({}_{2}\) injection into the reservoir, the gas saturation increases, and due to gravitational differentiation, the gas phase moves laterally from the injection well to the top of the aquifer, forming vertical pathways. Once injection ceases, CO\({}_{2}\) continues to migrate upwards. At the front edge of the CO\({}_{2}\) slug, gas continues to displace the wetting phase during drainage, while at the rear edge, water displaces gas during imbibition, leading to gas phase fragmentation and subsequent trapping. As the slug migrates upwards, some CO\({}_{2}\) is trapped as residual immobile phase in pore spaces, effectively isolating CO\({}_{2}\) in the rock until the immobile gas dissolves over geological time [11; 73; 74; 76; 77; 85; 86; 87]. In recent years, numerical simulation techniques have been widely used, and many attempts have been made in simulating phase trapping. Table 4 shows the CO\({}_{2}\) sequestration with hysteresis consideration and various conclusions have been made:  
1. The choice of three-phase relative permeability models and phase trapping models significantly affects the prediction of CO\({}_{2}\) sequestration capacity. The impact of three-phase relative permeability models is less important than that of phase trapping models, and the choice of phase trapping models may affect the impact of three-phase relative permeability models. 2. Injecting water after gas injection disrupts connected gas clusters, as the wetting phase traps the non-wetting phase due to phase trapping, enhancing gas trapping and immobilization. In processes with strong flow reversals, the effect of phase trapping is significant, making gas-water alternation a potentially effective CO\({}_{2}\) sequestration strategy. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Author** & **Application** & \begin{tabular}{c} **Two Phase or** \\ **Three Phase** \\ \end{tabular} & \begin{tabular}{c} **Injection** \\ **Method** \\ \end{tabular} & **Gas** & **Phenomena and Conclusions** \\ \hline [PERSON]. [PERSON] & Core & & & Mixture of & As the WAG cycle increases, the hysteresis effect \\ et al. [80] (2012) & experiment & Two-phase & WAG & methane (C1) and & weakens. Compared to krw, the cyclic hysteresis of \\  & & & & n-butane (n-C\({}_{4}\)) & krg is more pronounced. \\ \hline [PERSON] et al. [81] (2016) & Core & & & Mixture of & Adding WAG hysteresis parameters during fitting \\  & experiment & Three-phase & WAG & methane (C1) and & experiments instead of using the measured values \\  & & & & n-butane (n-C\({}_{4}\)) & of these parameters can significantly reduce \\ \hline [PERSON] et al. [82] (2019) & Reservoir & Three-phase & WAG & Natural gas & \
\begin{tabular}{c} The combined effect of relative permeability \\ hysteresis and reservoir heterogeneity on WAG. \\ \end{tabular} \\ \hline [PERSON] et al. [83] (2022) & Reservoir & Three-phase & WAG & Methane (C1) &
\begin{tabular}{c} The optimal WAG parameters may be influenced \\ by the choice of hysteresis models. \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table}