Geochemical reactions between fluids and carbonate rocks can change porosity and permeability during CO2 flooding, which may significantly impact well injectivity, well integrity, and oil recovery. Reactions can cause significant scaling in and around injection and production wells leading to high operating costs. Dissolution-induced well integrity issues and seabed subsidence have also been reported as a substantial problem at the Ekofisk field. Furthermore, mineral reactions can create fractures and vugs that can cause injection conformance issues, as has been observed in experiments and pressure transients in field tests. Although these issues are well known, there are differing opinions in the literature regarding the overall impact of geochemical reactions on permeability and injectivity for CO2 flooding. In this research, we use fully coupled reactive transport and compositional modeling to understand the interplay between multiphase flow, phase behavior, and geochemical reactions under reservoir and injection conditions relevant in the field. Simulations were carried out using a new compositional simulator (PennSim) based on an implicit pressure explicit composition (IMPEC) multiphase finite- volume formulation that is directly coupled with a reactive transport solver. The compositional and geochemical models were validated separately with CMG-GEM and CrunchFlow. Phase and chemical equilibrium constraints are solved simultaneously to account for the interaction between phase splits and chemical speciation. The Sereide and Whitson (1992) modified Peng-Robinson equation-of-state (EOS) is used to model component concentrations present in the aqueous and hydrocarbon phases. The mineral reactions are modeled kinetically and depend on the rock-brine contact area and the brine geochemistry, including pH and water composition. Injectivity changes caused by rock dissolution and formation scaling are investigated for a five-spot pattern using several common field injection boundary conditions. The results show that the type of injection scheme and water used (fresh water, formation water, and seawater) has a significant impact on porosity and permeability changes for the same total volume of CO2 and water injected. For continuous CO2 injection, very little porosity changes are observed owing to evaporation of water near the injection well. For water-alternating-gas (WAG) injection, however, the injectivity increases from near zero to 50%, depending on the CO2 slug size, number of cycles, and the total amount of injected water. Simultaneous water-alternating-gas injection (SWAG) shows significantly greater injectivity increases than WAG, primarily because of greater exposure time of the carbonate surface to CO2-saturated brine coupled with continued displacement of calcite-saturated brine. For simultaneous water-alternating-gas injection (SWAG), carbonate dissolution primarily occurs very near the injection well, where dissolution occurs out to greater distances. Carbonated water flooding (a special case of SWAG) shows even greater increases in injectivity than SWAG because more water is injected in this case, which can continuously sweep out brine saturated with calcite. The results also show that scaling can occur beyond the zone of dissolution depending on the type of water injected. For seawater injection, injectivity first increases and then decreases owing to formation of gypsum. The amount of precipitation depends on the compatibility of the injected brine with the formation water that is equilibrated with high pressure CO2 and minerals. We consider only gypsum and halite precipitation here, although other types of scale could be easily included.