## 3 Results and Discussion
### Porosity and Saturation Influence  
The dissolution rate of CO\({}_{2}\) is defined as the CO\({}_{2}\) molar flux, which acts as an important indicator of the residual and solubility trapping mechanism [6]. The CO\({}_{2}\) dissolution is controlled by both diffusion and dispersion mechanisms, but the CO\({}_{2}\) dispersivity is commonly one to two orders of magnitude greater than the molecular diffusion coefficient. When brine imbibes to contact with CO\({}_{2}\), the dispersion between CO\({}_{2}\) and brine dominates and therefore the dissolution rate of this period is increased. As both dispersion and diffusion are active under a supercritical state, the dissolution rate follows the analogous definition of the pseudo-diffusion coefficient (Dps) which can be used for quantification of the dissolution rate of CO\({}_{2}\) in water [28]. In the case of the dissolution in porous media, it was calculated based on the rate of loss of CO\({}_{2}\) from the CO\({}_{2}\) phase,  
\[\text{Dps}(x,t)=\frac{\text{C}(0,t)}{\Delta t}-\frac{\rho_{g}*\Delta\theta* \Delta x}{\Delta t^{2}*U} \tag{1}\]  
Figure 3: Time-lapse images of gaseous CO\({}_{2}\) (red) at different positions for 0.04 mL/min. where \(\text{Dps}(x,t)\) is the CO\({}_{2}\) dissolution rate, C(0,\(t\)) is the concentration of CO\({}_{2}\) at the inlet of the core, \(\Delta t\) is the time interval of each CT scan, \(\rho_{g}\) is the CO\({}_{2}\) density, \(\Delta\theta\) is the difference of CO\({}_{2}\) volume fraction, \(U\) is the Darcy flux, and \(\Delta x\) is the distance of brine imbibition below the inlet of the core. The dissolution rate values at different PVs and their correlations with porosity are shown in Figure 4. The dissolution rate of supercritical CO\({}_{2}\) was about two or three orders of magnitude greater than that of gaseous CO\({}_{2}\), indicating the prominent properties of the supercritical CO\({}_{2}\) during the dissolution process. In addition, the value distribution of the dissolution rate of CO\({}_{2}\) under the supercritical state was similar to that of gaseous CO\({}_{2}\) and spanned about four orders of magnitude. The dissolution rate of supercritical CO\({}_{2}\) increased as the flow path of the brine gradually expanded, and decreased as the isolated bubbles gradually dissolved due to the diffusion mechanism. By contrast, the dissolution rate of gaseous CO\({}_{2}\) dropped rapidly, and the value differences were approximately one order of magnitude at different PVs. This can be attributed to the difference in the critical time of dissolution expansion. In the cases of supercritical and gaseous CO\({}_{2}\), the dissolution rate was maintained at a relatively large value during the domination of the dissolution expansion, and changed slightly with brine injection. Then, the dissolution rate of gaseous CO\({}_{2}\) decreased more dramatically because of the diverse number of residual CO\({}_{2}\) bubbles. The features correspond to the flow development which is shown in Figures 2 and 3. The porosity was defined by the following equation, as given in [29],  
\[\varphi=\frac{Vc}{V} \tag{2}\]  
where \(\varphi\) is the porosity, \(Vc\) is the void space in the pore structure, and \(V\) is the volume of the core sample. In our experiments, an adequate threshold was chosen to extract the pore space from the original CT images. The porosity profiles were generated from the CT scans of the dry core. The dissolution rate of supercritical CO\({}_{2}\) decreased as porosity increased, and this trend increased with the increment of porosity. Simultaneously, the relatively small dissolution rate, which was located in the region of large porosity, decreased faster, and the descending trends between PVs had significant differences. In the previous study, a larger porosity heterogeneity may have led to more significant changes to the dissolution rate [30], while a simple relationship between the CO\({}_{2}\)-brine dissolution rate and cross-sectional area of adjoining pores would therefore not necessarily be expected [31].