One concern regarding the underground storage of carbon dioxide (CO2) is its potential leakage from reservoirs. Over short period of time, the leakage risk is related mainly to CO2 as a separate supercritical fluid phase. However, over longer periods upon complete dissolution of injected CO2 in the fluid, the leakage risk is associated with dissolved phase CO2. Over the geological time scales, large-scale groundwater motion may cause displacement of brine containing dissolved CO2 along the conducting pathways. In this paper, we present a comprehensive modeling framework that describes the reactive transport of CO2-saturated brine along a fracture in the clay caprock based on the future, hypothetical leakage of the dissolved phase CO2. This study shows that the transport of leaked dissolved CO2 is significantly retarded by a combination of various physical and geochemical processes, such as mass exchange between conducting fracture and the neighboring rock matrix through molecular diffusion, sorption and calcite dissolution in the rock matrix. Mass stored in aqueous and adsorbed states in the rock matrix caused retention of dissolved CO2 along the leakage pathway. Calcite dissolution reaction in the rock matrix resulted in consumption of leaking dissolved CO2 and reduced its mass along the leakage pathway. Consumption and retention of dissolved CO2 along the leakage pathway have important implications for analyzing the potential reduction of CO2 fluxes from storage reservoirs over large periods and long travel pathways.