## 1 Introduction  
Cement plays a crucial role in ensuring the integrity of oil and gas wells by providing zonal isolation, structural support, and protection against corrosive fluids. However, exposure to extreme conditions, such as high pressures, thermal cycles, and aggressive wellbore fluids (e.g., CO2, H2S, and brines), leads to cement degradation, cracking, and loss of well integrity. The failure of cement sheaths can result in wellbore instability, casing damage, and leakage of hydrocarbons or injected CO2 in enhanced oil recovery (EOR) and carbon capture and storage (CCS) applications [1, 2, 3]. The cement in geothermal wells is exposed to high temperatures between 100 and 400 \({}^{\circ}\)C causing deterioration in the structure of the cement. Also, the cement suffers from volumetric shrinkage during pumping in the analysis, and hardening results in microcrack development. Conventional cement is susceptible to a reduction in sealing capacity due to its brittle nature and the weakening bonding with the casing. Leakage in wells typically arises from microcracks that develop and propagate due to factors such as cement job design, downhole stresses, chemical interactions with subsurface fluids, and temperature fluctuations [4; 5; 6; 7]. These defects create undesirable pathways for subsurface fluid migration, often resulting in sustained casing pressure [8]. When CO2 is dissolved in water, carbonic acid forms and this dissolution leads to a reaction with cement and carbonation that ultimately degrades the cement. The CO2-brine solution decreases the pH to 4, while the Portland cement has a pH between 13 and 14. Thus, when the cement interacts with the CO2-brine solution, several precipitation/dissolution reactions will take place. Cement is thermodynamically unstable in CO2-rich environments and tends to degrade rapidly when exposed to acidic gases. This degradation occurs due to its reaction with calcium hydroxide, which originates from the hydration of calcium silicate phases [9]. Also, they proposed that the Portlandite [Ca(OH)2] and Calcium Silicate Hydrates (CSH) in set cement are gradually depleted, leading to the formation of calcium carbonates (aragonite, vaterite, and/or calcite), amorphous silica gel, and water. It is worth stating that during cement carbonation and degradation, four distinct zones form: the unaltered zone, the portlandite-depleted zone, the calcium carbonate precipitation zone, and the silica gel zone, where calcium leaching and C-S-H decomposition occur. This alteration in the cement can cause a significant leakage issue in both conventional wells and CCS wells. In recent years, several solutions have been proposed to ensure well integrity, such as implementing proper cement design as a proactive approach or using different cement recipes, such as calcium carbonate precipitant, polymer, and silica gels. Traditionally, as post-job remediation, the oil and gas industry has relied on techniques like top jobs or squeezing cement to address these issues. However, these methods are costly, have a low success rate of approximately 50%, are time-consuming, and require well shutdowns, leading to significant operational expenses [4]. An alternative to performing remedial squeeze jobs is to modify the mechanical properties of the cement so that the downhole sheath will be more durable and resilient to better withstand the stresses that occur from thermal/mechanical cycling. One effective way to modify the mechanical properties of cement is to incorporate elastomer particles. When added to cement slurries, elastomers lower the Young's modulus, making the cement more elastic [10]. This allows the cement sheath to better mitigate the stress and strain state encountered downhole, but the elastomer particles can lower the compressive strength of the cement [11]. There is also a practical limit regarding how much elastomer can be loaded into a particular slurry design.