A numerical model was developed using CrunchFlow to simulate reactive transport and porosity and permeability changes of sandstone and carbonate rock samples taken from the Lower Tuscaloosa Formation and the Selma Chalk Formation, Jackson County, MS, USA. The model predicted a permeability decrease from 2190 mD to 2038 mD for the Lower Tuscaloosa Sandstone sample in a static batch reactor after 180 days of exposure to CO2‐saturated brine, which is consistent with measured permeability results. The model predicted a negligible permeability change from 2.00 mD to 2.08 mD for the Selma Chalk carbonate sample after 180 days of exposure to CO2‐saturated brine. Based on model prediction, key mineral dissolution and precipitation reactions in the Lower Tuscaloosa Sandstone sample include dissolution of quartz, chlorite, and feldspar, as well as precipitation of amorphous silica and kaolinite. For the Selma Chalk carbonate sample, key predicted reactions include dissolution of calcite, quartz and chlorite, and precipitation of kaolinite and amorphous silica. Initial porosity, initial feldspar content and the exponent n value (related to pore structure and tortuosity) used in permeability calculations were three important factors affecting permeability evolution of sandstone samples under CO2 sequestration conditions. The small permeability change predicted for both the Lower Tuscaloosa Sandstone and the Selma Chalk caprock after exposure to CO2‐saturated brine suggests that poro‐permeability changes during CO2 injection into the Lower Tuscaloosa Formation are not likely to significantly affect reservoir and seal quality. © 2017 Society of Chemical Industry and John Wiley & Sons, Ltd.