Fractures in caprocks overlying CO2 storage reservoirs can adversely affect the sealing capacity of the rocks. Interactions between acidified fluid and minerals with different reactivities along a fracture pathway can affect the chemically induced changes in hydrodynamic properties of fractures. To study porosity and permeability evolution of small-scale (millimeter scale) fractures, a three-dimensional pore-scale reactive transport model based on the lattice Boltzmann method has been developed. The model simulates the evolution of two different fractured carbonate-rich caprock samples subjected to a flow of CO2-rich brine. The results show that the existence of nonreactive minerals along the flow path can restrict the increase in permeability and the cubic law used to relate porosity and permeability in monomineral fractured systems is therefore not valid in multimineral systems. Moreover, the injection of CO2-acidified brine at high rates resulted in a more permeable fractured media in comparison to the case with lower injection rates. The overall rate of calcite dissolution along the fracture decreased over time, confirming similar observations from previous continuum scale models. The presented 3D pore-scale model can be used to provide inputs for continuum scale models, such as improved porosity-permeability relationships for heterogeneous rocks, and also to investigate other reactive transport processes in the context of CO2 leakage in fractured seals.