## 3 Experimental Studies
### Direct Relative Permeability Measurements  
Previous studies on relative permeability experiments can be classified into three saturation history scenarios: DDI, DDI, and IDI. The naming convention proposed by [PERSON] et al. [51]. (i.e., D = Drainage and I = Imbibition) is used to name the saturation history. For example, DDI represents a scenario where water saturation decreases, oil saturation decreases, and gas saturation increases. IDI represents a scenario where water saturation increases, oil saturation decreases, and gas saturation increases, while IDIDID represents three cycles of imbibition followed by drainage. In relative permeability experiments, without considering capillary end effects, gas is trapped by water while gas permeability decreases after trapping. However, the capture of non-wetting phase during steady-state and transient drainage processes may differ. The trapped gas leads to a decrease in water relative permeability, and the slight variation in trapped gas saturation is due to changes in gas and water relative permeability. Hysteresis cycles are also irreversible, and significant errors in simulated relative permeability may occur when capillary effects are ignored ([PERSON], [PERSON], et al. [52; 53]).  
The relative permeability of the non-wetting phase in two-phase and multi-phase flows is a function of hysteresis effects. During imbibition after drainage, the hysteresis effect causes a significant decrease in CO\({}_{2}\) relative permeability. During CO\({}_{2}\) alternating injection, the increased trapped of CO\({}_{2}\) saturation increases the pressure drop during drainage and imbibition processes ([PERSON] et al. [54]). Compared to the non-wetting phase (gas), the hysteresis of the wetting phase (oil) is much smaller, and with continuous alternating imbibition and drainage cycles, the hysteresis effect on oil relative permeability weakens. In high-permeability cores, the hysteresis of the wetting and non-wetting phases is smaller than in low-permeability ones. Compared to the water-wet system, the relative permeabilities of the wetting and non-wetting phases (oil and gas) in mixed-wet systems decrease, with reductions observed in both imbibition and drainage directions ([PERSON] et al. [55]). As the number of WAG cycles increases, the relative permeability curves all show a downward shift of the equal permeability point and a narrowing of the co-flow region. The decrease in gas phase permeability with increasing cycles slows down and stabilizes, while the hysteresis effect on the water phase ([PERSON] et al. [56]) is not significant.  
Homogeneity affects phase permeability experiments. Compared to sandstone, hysteresis effects are not dominant in carbonate rocks ([PERSON] et al. [57]). In homogeneous systems, the hysteresis effect can be negligible. Due to the combined effects of different rock wettability and pore geometries, different types of rock samples exhibit different hysteresis patterns in imbibition relative permeability curves ([PERSON] et al. [58]). Salinity also affects the hysteresis effects of phase permeability experiments, with lower salinity conditions leading to more significant capillary hysteresis ([PERSON] et al. [59]). The reasons may be related to increased dissolution of minerals causing delayed contact angle or lower salinity brines making reservoir rocks more wettable.