## 5 Methodology and Results
### CO\({}_{2}\) Injection Flow Results  
In the simulation, the CO\({}_{2}\) was injected at a constant rate of 2200 tons per day over 20 years, followed by 50 years of monitoring, resulting in 70 years of simulation. This extended duration was chosen to simulate realistic long-term injection scenarios, reflecting the commitment to sustained carbon sequestration efforts. The total injected volume culminated in 16 million metric tons of CO\({}_{2}\), as depicted by the cumulative injection curve (Figure 5, blue curve) and the average reservoir pressure, showcasing an initial increase followed by a dissipation phase (Figure 5, red curve). The pressure increase during the injection period (Figure 5) can be interpreted as a clear response of the reservoir to the substantial volume of CO\({}_{2}\) being stored. The steep rise in pressure suggests that the aquifer has a limited capacity to accommodate the injected CO\({}_{2}\) without significant pressure buildup, which implies that the reservoir volume or the permeability may not be as large as required for the injected volumes. After reaching a peak, 20 years after the start of the injection, the pressure curve shows a gradual decline, signaling the onset of pressure dissipation. This phase transition may denote the beginning of CO\({}_{2}\) redistribution within the reservoir and potential migration into adjacent rocks, suggesting that the initial storage volume is approaching its capacity limit. The phase of  
Figure 5: Reservoir pressure and cumulative CO\({}_{2}\) injection over 20 years and subsequent 50 years of monitoring period. The blue curve indicates the total CO\({}_{2}\) injected, while the red curve shows the corresponding average pressure in the reservoir. pressure decline may also suggest that the pressure is being alleviated not just within the reservoir but also across the surrounding rock formations. This diffusion into the adjacent rocks can occur even in the absence of significant CO\({}_{2}\) migration due to the nature of pressure transmission through the pore fluids, which precedes the physical movement of CO\({}_{2}\). The pressure within a fluid-filled porous medium can propagate more rapidly than the CO\({}_{2}\) itself due to the fluid's compressibility and the interconnectedness of the pore spaces, allowing for a swift response and redistribution of pressure throughout the surrounding rocks. Figure 6 captures the evolution of reservoir pressure via delta pressure visualizations, marking changes from the initial state due to CO\({}_{2}\) injection. Figure 6A is the 3D view at the end of the 20-year injection phase, and it shows a relevant delta pressure gradient not only around the injector, with warmer hues indicating more significant pressure increases, but also within the entire confined reservoir. This confinement and the magnitude of pressure buildup at the injection end, evident from the vibrant coloration in Figure 6A, present subsequent long-term dissipation into the surrounding shaly rocks. Figure 6B's vertical cross-section near the injector after 20 years reveals the onset of this dissipation, with color transitions highlighting pressure migration beyond the reservoir boundaries. By 70 years, Figure 6C illustrates that the pressure has dissipated even further into the surrounding rocks. This extended spread of pressure, despite the absence of considerable CO\({}_{2}\) movement (Figure 7), indicates that the diffusion of pressure through the fluid phase outpaces the physical redistribution of CO\({}_{2}\), emphasizing the role of the interconnected pore network in the broader geological environment for managing injected pressures. The visual data from Figure 6B,C corroborate the effects of the injection on the adjacent rocks,  
Figure 6: Delta pressure (difference between initial and current pressure per gridblock) distribution in the reservoir and surrounding rocks. Panel (**A**) shows a 3D view of the reservoir at the end of the 20-year CO\({}_{2}\) injection phase, indicating high delta pressure near the injection well.