## 5 Materials and Methods
To evaluate self-healing performance, geochemical simulations were executed using PHREQC 3 and the CEMDATA thermodynamic database, capturing temperature- and pH-dependent solubility behaviors of key cementitious phases (Tables 2 and 3 in Appendix A). Simulations modeled porosity evolution, saturation index (SI) trends, and changes in solid phase volumes over periods ranging from 0.01 days to 30 years, covering both early healing kinetics and long-term mineralogical stabilization. Porosity changes were quantified by tracking dissolution and precipitation of solid phases, normalized against initial solid volumes, thereby reflecting evolving void spaces. This provided a quantitative assessment of self-sealing efficacy throughout the cement system's operational lifetime. The complete simulation workflow is illustrated in Figure 4. The Saturation Index (SI) for each mineral phase was calculated according to Equation (1):  
\[SI=Log_{10}\bigg{(}\frac{IAP}{K_{SP}}\bigg{)} \tag{1}\]  
where \(IAP\) is the ion activity product and \(K_{sp}\) is the solubility product under reservoir temperature and pressure. This formulation was adapted based on PHREEQC modeling practices [95]. \(SI\) values were used to assess mineral stability, precipitation, and dissolution behavior throughout the simulation period, enabling evaluation of self-healing potential and long-term chemical durability. The evolution of individual mineral phase volumes was determined by multiplying the simulated number of moles of each phase at each time step, extracted via the KINETICS block output of PHREEQC, by the corresponding molar volume (cm\({}^{3}\)/mol) from the CEMDATA thermodynamic database. Phase volumes were then normalized per 100 g of cementitious material to enable direct comparison across phases. Variations in phase volumes over time provided insight into mineral dissolution-precipitation dynamics, the healing contribution of each phase, and the overall stability of the cement system under CO2-rich conditions. By integrating experimental design, automated geochemical modeling, and data-driven analysis, this methodology presents a rigorous, scalable framework for developing next-generation self-healing cements tailored for CO2 sequestration, geothermal applications, and deep-well environments. The resulting cement systems exhibit enhanced  
Figure 4: Methodology workflow for self-healing cement development. The workflow illustrates the step-by-step process integrating experimental design, computational geochemical modeling, and data analysis for optimizing self-healing cement formulations. The methodology includes cement formulation, factorial design of experiments (DOE) using Python 3.13 (pandas, itertools, dexpy), geochemical modeling with PHREQC (phreetpy library), simulation execution using automated batch processing, and porosity evolution analysis leveraging Matplotlib 3.1 and CSV output processing. This workflow provides a structured approach for evaluating self-sealing efficiency, mineral stability, and long-term durability of cement in CO2-rich environments. -scaling performance, reduced permeability, and improved durability in chemically reactive conditions--supporting safer and more sustainable subsurface energy operations.