The geological sequestration of carbon dioxide (CO2) is one of the options of controlling the greenhouse gas emissions. However, leakage of CO2 from the storage reservoir is a risk associated with geological sequestration. Over longer times, large-scale groundwater motion may cause leakage of dissolved CO2 (CO2aq). The objectives of this thesis are twofold. First, the modelling study analyzes the leakage of CO2aq along the conducting pathways. Second, a relatively safer mode of geological storage is investigated wherein CO2aq is injected in a carbonate reservoir. A reactive transport model is developed that accounts for the coupled hydrological transport and the geochemical reactions of CO2aq in the porous media. The study provides a quantitative assessment of the impact of advection, dispersion, diffusion, sorption, geochemical reactions, temperature, and heat transport on the fate of leaking CO2aq. The mass exchange between the conducting pathway and the rock matrix plays an important role in retention and reactions of leaking CO2aq. A significant retention of leaking CO2aq is caused by its mass stored in aqueous and adsorbed states and its consumption in reactions in the rock matrix along the leakage pathway. Advection causes a significant leakage of CO2aq directly from the reservoir through the matrix in comparison to the diffusion alone in the rock matrix and advection in a highly conducting, but thin fracture. Heat transport by leaking brine also plays an important role in geochemical interactions of leaking CO2aq.  Injection of CO2aq is simulated for a carbonate reservoir. Injected CO2-saturated brine being reactive causes fast dissolution of carbonate minerals in the reservoir and fast conversion of CO2aq through considered geochemical reactions. Various parameters like dispersion, sorption, temperature, and minerals reaction kinetics are found to play important role in the consumption of CO2aq in reactions. / <p>Research Funders:</p><p>(i) Higher Education Commission (HEC) of Pakistan</p><p>(ii) Lars Erik Lundberg Scholarship Foundation, Sweden</p>