## 3 Results and Discussion
### Porosity and Saturation Influence
This also proves the more active solubility of supercritical CO\({}_{2}\). The dissolution rate of gaseous CO\({}_{2}\) gradually increased with porosity, which showed no obvious effect on the variation of the dissolution rate. For both gaseous and supercritical CO\({}_{2}\), no observable correlation existed between the ranges of the CO\({}_{2}\) dissolution rate and porosity at different PVs. However, when the porosity was between 0.36 and 0.38, the value ranges of dissolution rates under a  
Figure 4: CO\({}_{2}\) dissolution rate vs. porosity at different injection PVs for (**a**) supercritical CO\({}_{2}\) and (**b**) gaseous CO\({}_{2}\). supercritical state were greater. It is suggested that pore-size distribution will affect the dissolution rate, which is another mechanism identified for trapping as varying solubility is applicable [32]. In previous studies, CO\({}_{2}\) saturation and the CO\({}_{2}\) reduction rate originating from the CO\({}_{2}\) dissolution are generally used to calculate the CO\({}_{2}\) capacity and trapping efficiency, respectively [1; 10]. By using numerical analysis and resistivity monitoring, the computation of CO\({}_{2}\) saturation could be conducted. Also, the saturation could be indirectly obtained by isotope or acoustic data with accessible cost and convenient technicalities. The CO\({}_{2}\) saturation could be expressed as shown in Equation (3), based on the definition of porosity,  
\[S_{g}=\frac{Vg}{\varphi} \tag{3}\]  
where \(S_{g}\) is the CO\({}_{2}\) saturation, \(Vg\) is the volume of CO\({}_{2}\) phase, and \(\varphi\) is the porosity. As the CO\({}_{2}\) saturation increased, almost all CO\({}_{2}\) dissolution rates had slight variations. Consequently, after the saturation exceeded a certain threshold, the dissolution rate plummeted severely, which even varied from one to two orders of magnitude at the same PV. At high CO\({}_{2}\) saturations, concentration gradients were near zero because of the low velocities and prolonged contact with CO\({}_{2}\). This further reduced the active mass transfer from high saturation regions and illustrates the important role of low to medium saturations [20]. The plots of dissolution rate vs. saturation in Figure 5 were divided into two categories due to the significant differences of value ranges at different PVs, and the threshold of saturation was chosen as 0.1. The dissolution rate of supercritical CO\({}_{2}\) increased with the saturation decreased, which was obviously reversed with the brine injection. The dissolution rate remained less than 6 \(\times\) 10\({}^{-6}\) mol/L/s before the brine formed multiple fingerings and increased rapidly with the saturation reduction. The observed growth in the CO\({}_{2}\) dissolution rate as the CO\({}_{2}\) saturation declined has been attributed to the creation of new water-flow paths as CO\({}_{2}\) was dissolved [33; 34]. When CO\({}_{2}\) saturation was less than  
Figure 5: CO\({}_{2}\) dissolution rate vs. CO\({}_{2}\) saturation at different injection PVs for (**a,b**) supercritical CO\({}_{2}\) and (**c,d**)gaseous CO\({}_{2}\). 0.5, the dissolution rate increased by two order of magnitude. At higher saturations, the dissolution rate may reduce by an order of magnitude, and the inverse correlation of the dissolution rate with the saturation remained invariant at a certain PV. This is because the smaller bubbles have higher dissolution rates than larger clusters [35]. In the saturations between 0.1 and 0.01, the correlations between the dissolution rate and saturation were inverted at later PVs. Subsequently, the dissolution rate was maintained at a relatively large level without monotonic decreasing with brine injection at the end of the dissolution process. Only a few bubble clusters remained in porous media, as shown in Figure 2. This suggests that the CO\({}_{2}\) dissolution rate is more vulnerable to being controlled by the location and quantity of the dissolution events.