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The underground storage of carbon dioxide (CO2) in deep geological formations is a critical technology for mitigating climate change by reducing atmospheric CO2 levels. This study investigates the transport mechanisms of CO2 during underground sequestration, with a particular focus on the role of rock compressibility in influencing storage efficiency and long-term containment. We present a mathematical model that incorporates the compressibility of both the CO2 phase and the surrounding rock matrix, as well as the interaction between the both. The model addresses the coupled processes of CO2 injection, migration, and pressure build-up within the reservoir, highlighting the importance of rock compaction in altering porosity, permeability, and fluid flow dynamics. Numerical simulations are used to assess the impact of rock compressibility on CO2 plume behaviour, pressure evolution, and storage capacity. Results show that compressibility significantly affects the rate of CO2 migration and the overall effectiveness of storage, with implications for optimal injection strategies and long-term monitoring. This work provides a more accurate framework for predicting the fate of CO2 in underground storage sites and for enhancing the design and management of CO2 sequestration projects.