The energy sector actively seeks eco-friendly solutions to mitigate the environmental repercussions of oil and gas operations. One of these solutions is Carbon, Capture, and Storage technology (CCS). However, this technology is still under development by experts in the field. There have been several research studies on this behalf to study and comprehend the CO2 fluid flow behavior when traveling from the surface to the porous media. CCS is a promising technology for mitigating greenhouse gas emissions and addressing the challenges of climate change. The process involves capturing CO2, transporting it to the designated storage sites, and subsequently injecting it into subsurface formations for safe long-term geological sequestration. As CO2 flows along the wellbore from the surface to the storage formation, the CO2 undergoes different thermal processes. For example, CO2 can undergo phase transition; hydrates can form depending on the injection conditions of pressure and temperature at the surface; a cooling effect can happen when reaching the storage formation (Joule-Thomson effect); salt can precipitate in the near-wellbore area, reducing the porosity, and thus, compromising the CO2 injectivity. Effective and practical implementation of CCS in the real world requires a deep understanding of the wellbore dynamics coupled to the reservoir domain. However, most standard petroleum software focuses on multiphase fluid flow behavior under steady-state conditions, considering only the wellbore or the reservoir domain. Therefore, there is a growing imperative to develop models where transient phenomena are studied in a jointly wellbore-reservoir domain. This work investigates the transient effects associated with CO2 injection, particularly emphasizing contrasting gas and supercritical CO2 injection. The distinct behaviors impact the CO2 injectivity, especially concerning salt precipitation or hydrate formation. To achieve this, the research employs the numerical software T2Well ¿ an advanced transient simulator designed to analyze coupled wellbore-reservoir dynamics. Results showed that no matter in which state the CO2 is injected, it will reach the reservoir in the supercritical phase due to the phase transition occurring in the wellbore at early simulation time. Moreover, injecting supercritical CO2 is preferred over gas CO2. In the gas CO2 case, higher salt precipitation can be noticed, and a stronger JT-effect cooling effect is appreciated in the near-wellbore area than in the supercritical CO2 case. This Master¿s thesis contributes to an enhanced comprehension of transient processes and empowers informed decision-making for the practical application for real-world CCS technology implementation.