The storage of underground carbon dioxide (CO2) is one of the alternatives to reduce the amount of greenhouse gases in the atmosphere. However, such a process can alter the pressure distribution within geological formations, triggering rock expansion and stress changes, which can induce potential geomechanical risks. Among them, geological fault reactivation is a critical issue to consider during the injection of CO2 into the subsurface. Induced seismicity and CO2 leakage have been reported in some field operations. Several numerical models adopt the simple one-way approach to estimate the spatial evolution of fluid pressures and stresses due to fluid injection and production. However, this approach can provide inaccurate results depending on the coupling level between the mechanical and the hydraulic processes. On the other hand, the fully-implicit approach presents more accurate results, but its application in large-scale models is unviable. Sequential coupling approaches have been introduced in the literature and applied to porous media as an alternative approach. This work investigates different coupling strategies to assess the potential risk of geological fault reactivation in CO2 geological sequestration. The geological faults are represented through interface elements combined with the Mohr-Coulomb criterion to evaluate the fault reactivation mechanism. The numerical results using different coupling strategies are compared against those using the fully implicit approach. The influence of mesh discretization was investigated by performing two- and three-dimensional analyses. We also investigated the impact of fault permeability evolution on the maximum injection pressure. The results show that a sequential explicit two-way strategy can accurately estimate the maximum sustainable pressure and significantly reduce computational costs. Although the studied scenarios are synthetic, the findings add value to the research community for modeling large-scale models.