## 3 Results and Discussion
### Reynolds Number-Dissolution Rate Relationships  
The flow regime is characterized through the dimensionless number, the Reynolds number, which represents the ratio of the inertial force to the viscous force [40]. The equation of Re is written in the formula of,  
\[\mathrm{Re}=\frac{\rho_{w}*U*L}{\mu_{w}} \tag{4}\]  
where \(\rho_{w}\) is the density of the brine, \(U\) is the Darcy velocity, \(L\) is the characteristic length, and \(\mu_{w}\) is the viscosity of the brine. The Darcy velocity is proportional to the Reynolds number because the brine properties and the characteristic length are constant in the experiments. It is expected that the Darcy velocity will be affected by the saturation and the porosity at the pore scale. The Re was calculated for each position along the core since the geometry of the porous media is varied along the injection direction. In our experiments, the Re ranges from 0.001 to 1, which corresponds to laminar flows, so that the flow process was dominated by the viscous force [39]. In Figure 6, the order of the dissolution rate and the relevant range of Re varied widely at different PVs. Therefore, we adopt similar methods as the diagrams of the saturation-dissolution rate to distinguish the character of the dissolution rate when the Re distributions were concentrated in the later period of CO\({}_{2}\) dissolution. The corresponding linear relationships are presented visually in the insets. In the early period of the supercritical CO\({}_{2}\) dissolution, the dissolution rate decreased with the increase of Re, and the relationship was reversed as most bubbles were dissolved. When the Re was greater than 0.1, the dissolution rate of supercritical CO\({}_{2}\) was relatively very small. This indicated that compared with the injection flow rate, the flow development critically determines the CO\({}_{2}\) dissolution in porous media. During the dissolution expansion, the dissolution rate increased rapidly as the Re decreased, and the differences at different Re values were about one order of magnitude. The dissolution rates between solute and brine are highly variable in aquifers and depend on the flow rate of brine in the aquifer [41]. When buoyancy forces are preponderant (low injection flow rate), the dissolution rate increases with the distance of the brine imbibition, whereas a uniform dissolution could be observed at a high injection flow rate [42]. In the later period of dissolution, the Re was not greater than 0.01 at the same PV, but remained the order of magnitude similar to those in the early period of dissolution. In former studies, the highest dissolution rates were achieved during the injection and shortly after the injection periods, when CO\({}_{2}\) was still mobile and distributed over many pores before it settled underneath the caprock. The dissolution rate gradually increased with the Re, and the trend was not significantly correlated with the injected PV. This is similar to the process of phase equilibrium of CO\({}_{2}\)-brine in laminar flow. It is concluded that there is hardly any difference in dissolution rates between injection into a hydrostatic and a hydrodynamic aquifer, but with larger background flux, the dissolution rate may be higher [43]. Meanwhile, for CO\({}_{2}\) droplets, the dissolution rate increases with the flow velocity of brine, which is proportional to the Re [39]. When the Re was between 0.05 and 0.2, the dissolution rate of gaseous CO\({}_{2}\) significantly decreased with the increase of Re, and the dissolution rates were different by about two orders of magnitude at the same PV. Many bubbles resisted the accelerated dissolution; however, the overall dissolution rate for the CO\({}_{2}\) plume decreased with time because less CO\({}_{2}\) mass was associated with the dissolution [9]. The former studies showed that the initial dissolution rate constant depends on Re, the molecular diffusivity of CO\({}_{2}\) in water, and the mean pore size [44].