Carbonate reservoirs are rich in hydrocarbon resources. However, carbonate reservoirs usually have strong pore structure heterogeneity, and thus it is necessary to understand the effect of heterogeneity on pore-scale fluid distributions during CO2 enhanced oil recover (CO2-EOR) process. We thus conducted water-alternating-gas (CO2-WAG) injection in the three carbonate samples with strong to weak heterogeneity. The 15 sets of images showed that the fractured-vuggy carbonate with the strongest heterogeneity had the highest additional oil recovery. CO2-WAG injection significantly changed the residual oil distribution, and further oil production can be achieved by increasing the number of CO2-WAG cycles. For CO2 geological storage, with the increase of carbonate heterogeneity, CO2 capillary-trapping capacity decreased, CO2 dissolution trapping potentiality decreased, but the stability of CO2 capillary trapping enhanced. These key parameters related to CO2 storage were described through the saturation of trapped gas, the types of trapped gas, and the surface area-volume relationship of CO2 clusters. For example, the higher amount of network gas is detrimental to the stability of CO2 capillary trapping because the network gas is easily displaced when the hydrodynamic force is enhanced. The specific surface area of CO2 cluster determines dissolution dynamics, and a higher specific surface area is beneficial for CO2 dissolution. Another interesting phenomenon - Ostwald ripening, is related to long-term CO2 transport. The CO2 concentration gradient in aquifer generates a vertically upward diffusive flux, causing CO2 remobilization. By calculating the height of the transition zone and the time to reach gravity-capillary pressure equilibrium, we found that as carbonate heterogeneity increased, the height of transition zone (the area where CO2 is trapped by capillary pressure) increased, while equilibrium time shortened. By comparing the results of previous gas-water two-phase flow experiments, we believe that the relationship between CO2 storage characteristics and carbonate heterogeneity summarized in this paper are universally applicable.