## 5 Materials and Methods  
To address degradation mechanisms in CO\({}_{2}\)-rich environments, this study incorporates a mineralogical self-healing concept based on controlled dissolution and re-precipitation. Cement degradation is initiated by the carbonation of portlandite and subsequent decomposition of calcium silicate hydrate (C-S-H) into calcite and silica gel, which weakens the cement matrix [81; 88; 89]. Initially, calcite precipitation can seal microcracks [90], but prolonged exposure to bicarbonate-rich fluids results in calcium bicarbonate formation and leaching, accelerating porosity increase and structural loss [91]. By leveraging this dissolution-precipitation cycle, the methodology promotes targeted mineral healing to enhance long-term cement integrity. The methodology for developing a novel self-healing cement follows a structured and systematic approach, integrating experimental design, geochemical modeling, and data analysis to optimize formulations for CO\({}_{2}\)-rich subsurface environments. This study evaluates three cement formulations: a novel self-healing cement containing Barite, Pozzolan, and Chalcedony; an advanced self-healing cement incorporating Zeolite for enhanced durability; and conventional cement as a baseline. Figure 3: Crack healing efficiency of various chemical-based self-healing materials, showing the maximum crack width that each material can heal. The red dashed line (500 \(\upmu\)m) represents the benchmark crack width in oil and gas cement applications, with some materials exceeding this threshold, offering potential for enhanced cement integrity [29; 32; 33; 52; 53; 54; 55; 56; 57]. The first phase involved designing a self-healing cement system aimed at enhancing mechanical stability, chemical resistance, and self-sealing efficiency. The selected components included Barite (fixed at 3.0 mol, comprising 18.9-24.2 wt.%) to increase density and reduce permeability [92], Pozzolan (0.60-0.75 mol, comprising 43.1-55.4 wt.%) to react with Ca(OH)\({}_{2}\) and form secondary C-S-H gels [93], and Chalcedony (0.25-0.40 mol, comprising 23.1-35.9 wt.%) to improve thermal and chemical stability. These components were optimized using a full-factorial Design of Experiment (DOE) approach, selected due to their critical roles in enhancing the geochemical durability of wellbore cement in CO\({}_{2}\)-rich environments, consistent with prior studies on cement behavior and mineral reactivity. The DOE formulation space was structured to maintain slurry density within the operational envelope of 1.88-1.92 g/cm\({}^{3}\), a range commonly employed in field deployments to minimize formation damage and manage hydrostatic pressure. The water-to-cement (\(w/c\)) ratio was dynamically adjusted for each formulation to achieve this target density while ensuring realistic mixing conditions. The resulting \(w/c\) ratios were consistent with industry standards and closely aligned with the benchmark value of 0.38 recommended in prior literature [89; 94]. This methodological choice ensures the designed cement systems are chemically effective and operationally feasible. A detailed summary of the DOE combinations, component mass percentages, cement-to-water proportions, and slurry properties is presented in Appendix A Table 1.  
Building upon this foundational formulation, an advanced self-healing cement was developed by incorporating Zeolite (0.10-0.50 mol, corresponding to approximately 12.7-42.7 wt%), known for enhancing CO\({}_{2}\) adsorption and promoting secondary mineral precipitation, thereby further reinforcing the cement matrix. This formulation was similarly optimized through the DOE framework, with simulations automated via a custom Python script interfacing with PHREQC 3 [95], facilitating batch simulations across varying additive concentrations. PHREQC 3 is widely used to simulate cement degradation in CO\({}_{2}\)-rich environments, enabling accurate prediction of mineral reactions and integrity loss [96; 97; 98].