Geochemical reactions add complexity to the characterization and prediction of fracture hydraulic properties because they depend on factors that are highly heterogeneous, such as mineral composition. However, systematic analyses of fracture evolution in mineralogically heterogeneous systems are still limited. In this study, we investigated fracture evolution in multimineral systems using a reduced dimension reactive transport model. The model was developed and tested based on experimental studies and addresses the complex morphological and geochemical changes that arise from the presence of multiple minerals of different reactivities. Numerical experiments were performed using randomly generated initial fracture geometries based on representative geostatistics, different categories of mineral composition, and a range of flow rates that are relevant to geologic carbon storage systems. The simulation results showed distinct dissolution regimes at different flow rates, each of which produced characteristic dissolution patterns and temporal evolutions of chemical reactions and fracture hydraulic properties. Overall, as flow rate increases, fracture evolution shifts from compact dissolution to fracture channelization to uniform dissolution. The corresponding flow rate for a given dissolution regime, however, varies considerably with mineral composition. Fracture evolution, especially in the flow regime that induces fracture channelization, is also affected by initial fracture geometry. The numerical experiments were used to develop a multireaction Damköhler number (mDa) for the prediction of fracture evolution, and fracture channelization in particular, in multimineral systems. The multireaction Damköhler number also provides a useful framework for the evaluation of caprock integrity in geologic carbon storage systems.