The study aims to quantitatively assess the risk of hydrate formation within the porous formation and its consequences to injectivity during storage of CO₂ in depleted gas reservoirs considering low temperatures caused by the Joule Thomson (JT) effect and hydrate kinetics. The aim was to understand which mechanisms can mitigate or prevent the formation of hydrates. The key mechanisms we studied included water dry-out, heat exchange with surrounding rock formation, and capillary pressure. A compositional thermal reservoir simulator is used to model the fluid and heat flow of CO₂ through a reservoir initially composed of brine and methane. The simulator can model the formation and dissociation of both methane and CO₂ hydrates using kinetic reactions. This approach has the advantage of computing the amount of hydrate deposited and estimating its effects on the porosity and permeability alteration. Sensitivity analyses are also carried out to investigate the impact of different parameters and mechanisms on the deposition of hydrates and the injectivity of CO₂. Simulation results for a simplified model were verified with results from the literature. The key results of this work are: (1) The Joule-Thomson effect strongly depends on the reservoir permeability and initial pressure and could lead to the formation of hydrates within the porous media even when the injected CO₂ temperature was higher than the hydrate equilibrium temperature, (2) The heat gain from underburden and overburden rock formations could prevent hydrates formed at late time, (3) Permeability reduction increased the formation of hydrates due to an increased JT cooling, and (4) Water dry-out near the wellbore did not prevent hydrate formation. Finally, the role of capillary pressure was quite complex, where it reduced the formation of hydrates in certain cases and increased in other cases. Simulating this process with heat flow and hydrate reactions was also shown to present severe numerical issues. It was critical to select convergence criteria and linear system tolerances to avoid large material balance and numerical errors.