This study presents a three-dimensional reactive transport model to simulate upward and lateral migration of CO₂ plumes under different scenarios through a leaky section of a plugged and abandoned well at a hypothetical CO₂ storage site into the Texas Gulf Coast Aquifer (TGCA). The TGCA is the most active region in research and operation of carbon capture, utilization, and storage, with the largest technically accessible resource of CO₂ storage, in the United States. The results suggest that dissolved inorganic carbon (DIC) concentration and pH, better than Cl concentration (or total dissolved solids), can be indicators for leakage detection in the TGCA; DIC has earlier detection time than pH. The modeling results show that detection of CO₂ leakage in the shallow aquifers may take hundreds of years because of the confining unit in the TGCA, suggesting that (1) monitoring wells should be placed as deep as possible and (2) characterization of confining units in the overlying aquifer system is critical. Regional hydraulic gradient and groundwater pumping in the TGCA are important factors for monitoring well placement. While this study was conducted in the TGCA, the results provide valuable information for groundwater monitoring at other geological carbon sequestration sites.