CO₂ storage in reservoirs with natural and/or induced fractures is an efficient method to sequester CO₂ because of their high and sustained injectivity. Past work has focused on storage of CO₂ in the pore space and in the dissolved state within the brine. This research shows that geochemical reactions involving the CO₂ interacting with reservoir minerals (in different lithologies) can also play a very important role in sequestering the CO₂. A fully integrated 3-D reservoir simulator that includes single-phase flow, geomechanics, and geochemistry is introduced. The geochemical capability in the simulator predicts flow and geomechanical behavior due to geochemical reactions triggered by CO₂ injection. The simulation models a reservoir with an induced planar fracture. The amount of CO₂ that is sequestered and the extent of mineral dissolution and precipitation are computed. To demonstrate the impact of rock lithology, the model is used to simulate CO₂ injection into a sandstone, a limestone, and a dolomite reservoir. The paper also investigates two different CO₂ rich brines to investigate the impact of the brine composition. It is shown that the portion of the CO₂ injected that reacts with the minerals and is then converted into other mineral precipitates depends largely on the mineralogy of the reservoir and the composition of the injection fluid. Limestone and dolomite reservoirs are much more susceptible to mineral dissolution and precipitation resulting in more CO₂ sequestration and larger changes in injectivity over time when injection fluid is compatible with the host rock. It is shown that the fracture geometry determines the location of mineral dissolution and precipitation. This alteration of the mechanical and flow properties of the reservoir rock and fractures resulting from mineral alteration can also change the mechanical properties of the rock and result in more fracture growth and enhance or impede propagation of CO₂ plume or CO₂ charged water. Results showing the pros and cons of injecting CO₂ into fractured wells in sandstone and carbonate reservoirs are presented considering the brine types to charge CO₂. Our results show, for the first time, the clear differences that arise when sequestering CO₂ in limestone, dolomite and sandstone reservoirs. The impact of geochemical reactions in realistic injection well scenarios is quantified. Results are also presented to show the pros and cons of using hydraulically fractured wells for CO₂ injection in both lithologies.