The success of engineered geologic carbon dioxide storage hinges on our ability to identify optimal sites and forecast their long-term security. This ability, in turn, relies upon predictive models for assessing the relative effectiveness of carbon dioxide migration and sequestration processes (isolation performance) as a function of key target-formation and cap-rock properties (screening criteria). Our recent modeling work has focused on applying our unique computational toolbox to address this central issue of long-term hydrodynamic seal capacity in geologic carbon dioxide storage sites. In the present contribution, we review the methodology and fundamental results of this research; i.e., the reactive transport modeling approach, geochemical and geomechanical contributions to cap-rock permeability evolution during and after carbon dioxide influx, and a new conceptual framework for evaluating the net impact on long-term cap rock integrity of these contributions.