## 4 Results
### Effect of Leakage Rate (Cases 1, 2, and 3/Bubble Size = 20 mm, Leakage Area = 20,000 m)  
Figure 7 shows contour maps of some variables on the center plane in the x direction (x = 1000 m) of the small-scale domain, 30 days after the start of leakage. From the distribution of void rate and cell-averaged number densities of CO\({}_{2}\) bubbles, it can be seen that all CO\({}_{2}\) bubbles leaking from the depth of 190 m would be dissolved at a depth of 70 m before reaching the free surface. Because the initial diameter of the CO\({}_{2}\) bubbles are the same, but the leakage rates are different for these cases, the void rates of the bubbles near the leakage depth are higher than other depths and become lower as the depth becomes shallower due to the rising and dissolution of the bubbles to the surrounding seawater. The reason for the higher values of the number densities near the depth of 100 m is that the density of the bubbles is almost the same as that of seawater, and the volume of the bubbles is very small, which makes the buoyant force zero. Although the velocity vector fields or contour maps of the velocities are not presented, one may know that complex flows exist owing to the rising of the CO\({}_{2}\) bubbles with surrounding seawater and tidal flows from the distribution of the DCO\({}_{2}\) shown in Figure 7c. Since more bubbles exist and dissolution lasts for a longer time as the leakage rate increases, relatively higher values and wider areas of dispersed DCO\({}_{2}\) are observed, as shown in the figure. Comparing the contour maps of DCO\({}_{2}\) with those of the changes in DCO\({}_{2}\) (\(\Delta\)DCO\({}_{2}\)) due to the dissolution of the bubbles, no large discrepancy is observed because the background DCO\({}_{2}\) is much smaller. The contour maps of \(\Delta\)pCO\({}_{2}\) on the center planes of the x, y, and z directions of the small-scale domain are depicted in Figure 8, where not only the diffusion but also the advection of \(\Delta\)pCO\({}_{2}\) by the tide are clearly shown. A high \(\Delta\)pCO\({}_{2}\) is observed near the leakage depth, and the maximum \(\Delta\)pCO\({}_{2}\) is lower than 200 ppm and does not exceed the PNEC. It can also be seen that the distributions of \(\Delta\)pCO\({}_{2}\) shown in Figure 8a are similar to those of \(\Delta\)DCO\({}_{2}\) on the same plane (Figure 7c). The contour maps of \(\Delta\)pCO\({}_{2}\) on the constant z planes of the mesoscale domain with respect to depths and elapsed time after leakage for the most extreme case are illustrated in Figures 9 and 10, respectively, where the black rectangular box indicates the full-3D small-scale domain including the leakage area. Both figures show that high \(\Delta\)pCO\({}_{2}\) regions are placed at depths between 150 and 170 m, not in the leakage depth. This might be due to the convection of DCO\({}_{2}\) by the geostrophic flows. It can also be found that diffusion is more dominant than convection as water depth becomes deeper. The time change of maximum \(\Delta\)pCO\({}_{2}\) in the mesoscale domain is not significant, as shown in Figure 10. The maximum \(\Delta\)pCO\({}_{2}\) is lower than 50 ppm and does not exceed the PNEC. Figure 6: Velocity vector fields on the horizontal planes (upper rows: near free surface, lower rows: z = -187 m) at 28, 29, and 30 days after the start of simulation (data are skipped by 2). Figure 7: Contour maps of (**a**) void rate, (**b**) number density of undissolved CO\({}_{2}\) bubbles, (**c**) DCO\({}_{2}\), and (**d**) \(\Delta\)DCO\({}_{2}\) on the center plane in the x direction (x = 1000 m) of the small-scale domain at 30 days after the start of leakage with the same initial diameter of bubble of 20 mm and leakage area of 20,000 m\({}^{2}\) but different leakage rates. Figure 8: Contour maps of \(\Delta\)pCO\({}_{2}\) on the center planes of the x, y, and z directions of the small-scale domain at 30 days after the start of leakage with the same initial diameter of bubble of 20 mm and leakage area of 20,000 m\({}^{2}\) but with different leakage rates.