## 6 Results and Discussion
### Phase Volume Changes and Mineral Transformations  
The phase volume evolution data, illustrated in Figure 6, further supports the robustness of the self-healing cement formulations. Key findings include the following:  
1. ECSH2 (a highly reactive C-S-H phase) exhibits consistent volume stability, reaffirming its role in continuous cement reinforcement and crack-sealing functionality. 2. Pozzolan and Chalcedony dissolution contribute to secondary silicate formation, validating their self-healing role through silica gel formation and subsequent precipitation. 3. Calcite and Aragonite display controlled precipitation behavior, suggesting a balance between dissolution and secondary reprecipitation, which is critical for maintaining cement integrity in CO\({}_{2}\)-rich environments. 4. Minimal volume loss in key binding phases such as C2S and C3S confirms the structural durability of the cement, as these phases provide essential strength and long-term sealing capabilities in wellbore applications. Variations in phase volume changes, spanning up to three orders of magnitude, arise from differences in initial phase abundance and mineral dissolution-precipitation kinet  
Figure 6: Phase volume changes in key minerals over time, demonstrating the stability of ECSH2 and Chalcedony in self-healing cement formulations under CO\({}_{2}\)-rich conditions, ensuring sustained mechanical integrity and resistance to degradation. Observable volume evolution in Calcite, Quartz, C2S, C3S, Vaterite, Portlandite, and Pozzolan confirms active dissolution–precipitation reactions. Barite and Montmorillonite exhibited negligible volume change during the simulation. ics. Phases with higher initial volume fractions, such as C-S-H and Portlandite, show relatively stable behavior, while minor phases exhibit larger relative volume shifts due to their lower starting amounts. These findings validate the effectiveness of the self-healing cement, demonstrating sustained phase stability, mineral transformations conducive to crack healing, and prolonged durability under wellbore conditions. The results from the porosity evolution analysis emphasize the critical role of advanced self-healing cement formulations in ensuring long-term wellbore integrity in CO\({}_{2}\) injection and storage applications. As depicted in Figure 7, cement formulations containing Barite, Pozzolan, and Zeolite demonstrate superior resistance to CO\({}_{2}\)-induced degradation compared to conventional cement, which exhibits a continuous increase in porosity over time when exposed to CO\({}_{2}\)-rich reservoir fluids. The Design of Experiment (DOE) approach was employed to optimize the percentage composition of Barite, Pozzolan, and Zeolite, ensuring that the best formulation was identified under severe CO\({}_{2}\) conditions. The DOE findings confirm that specific mineral combinations significantly reduce porosity within the first 7-14 days, enabling early-stage self-sealing while maintaining long-term chemical and mechanical stability. The porosity evolution trends of cement formulations (Figure 7) reveal distinct behaviors distinguished by color-coded curves. The self-healing cement systems--Barite  
Figure 7: Porosity evolution over time for different cement systems under CO\({}_{2}\) conditions. The conventional cement (teal) shows significant porosity increase (\(\sim\)12–18%), while the Barite–Pozzolan–Chalcedony mix (blue) maintains lower porosity (\(\sim\)3%) and the Barite–Pozzolan–Zeolite mix (green) remains slightly higher (\(\sim\)4%), both with minor increases over time. Pozzolan-Chalcedony (blue) and Barite-Pozzolan-Zeolite (green)--show an initial slight reduction in porosity, followed by gradual stabilization. This behavior is attributed to secondary hydration reactions involving Pozzolan and Zeolite, resulting in the formation of calcium silicate hydrate (C-S-H) gels, which effectively seal microcracks and reduce permeability.