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Excessive emissions of greenhouse gases, such as carbon dioxide, can cause severe global climatic changes, which may include an increase in the global temperature, rise of the sea level, increase in wildfire, floods, and storms, in addition to changes in the amount of rain and snow. The global mitigation strategies that can be envisioned to reduce the release of greenhouse gas emissions to the atmosphere include retrofitting buildings with more energy-efficient systems, increasing the dependency on renewable energy sources in lieu of fossil fuels, increasing the use of sustainable transportation systems that rely on electricity and biofuels, and adopting globally more sustainable uses of land and forests. To reduce global climatic changes, the excess amount of carbon dioxide in the environment needs to be captured and stored in deep underground sedimentary reservoirs. The sedimentary reservoirs that contain water in the rock matrix provide a more secure CO2 sequestration medium. The injection of carbon dioxide causes a huge increase in the reservoir pore pressure and provokes the subsequent ground uplift. The excessive increase in pore pressure may also cause leakage of carbon dioxide into the potable water layers and to the atmosphere, thus leading to severe global climatic changes. In order to maintain the integrity of the sequestration process, it is crucial to inject a safe quantity of carbon dioxide into the sequestration site. Accordingly, the injection period and the safe values of injection parameters, like flow rate and injection pressure, need to be calculated a priori to ensure that the stored carbon dioxide will not leak into the atmosphere and jeopardize the climate mitigation strategy. To model carbon dioxide injection in reservoirs having a base fluid, such as water, one has to perform a two-phase flow modeling for both the injected and base fluids. In the present investigation, carbon dioxide is injected into Biyadh reservoir, wherein the two-phase flow through the reservoir structure is taken into account. This investigation aims to estimate the safe parameter values for carbon dioxide injection into the Biyadh reservoir, in order to avoid leakage of carbon dioxide through the caprock. In this context, the two cases of a fractured and non-fractured caprock are considered. To ensure a safe sequestration mechanism, the coupled reservoir stability analysis is performed to estimate the safe values of the injection parameters, thus furnishing data for a reliable global climate change mitigation strategy. The obtained results demonstrated that the injection of carbon dioxide has caused a maximum pore pressure increase of 25MPa and a ground uplift of 35mm.