A reactive fluid flow and geochemical transport numerical model for evaluating long-term CO2 disposal in deep geologic formations has been developed. The numerical model is needed because alteration of the predominant host rock aluminosilicate minerals is very slow and is not amenable to laboratory experiment under ambient deep-formation conditions. Using this model, we performed numerical simulations for a commonly encountered Gulf Coast sediment under natural and CO2 injection conditions in order to analyze the impact of CO2 immobilization through carbonate precipitation. Under conditions considered in our simulations, CO2 trapping by secondary carbonate minerals such as calcite (CaCO3), dolomite (CaMg(CO3)2), siderite (FeCO3), and dawsonite (NaAlCO3(OH)2) could occur in the presence of high pressure CO2. Variations in the precipitation of secondary carbonate minerals strongly depend on rock mineral composition and their kinetic reaction rates. Using the data presented in this paper, the CO2 mineral-trapping capability after 10,000 years is comparable to CO2 dissolution in pore waters (2--5 kg CO2 per cubic meter of formation). The addition of CO2 mass as secondary carbonates to the solid matrix decreases porosity. A small porosity decrease can result in a significant decrease in permeability. Despite simplifications in the current model, a comparison between initial model results and field observations for natural diagenesis of Gulf Coast sediments is instructive. Most of the simulated mineral alteration pattern is consistent with the observations. Some inconsistencies are noted, which can help identify issues, limitations, and areas where the conceptual model requires improvement. The numerical simulations described here provide useful insight into potential sequestration processes, and their controlling conditions and parameters.