Carbon capture and sequestration (CCS) is an engineering-based approach for mitigating excess anthropogenic CO2 emissions. Deep brine aquifers and basalt reservoirs have shown outstanding performance in CO2 storage based on their global widespread distribution and large storage capacity. Capillary trapping and mineral trapping are the two dominant mechanisms controlling the distribution, migration, and transportation of CO2 in deep brine aquifers and basalt reservoirs. Understanding the behavior of CO2 in a storage reservoir under realistic conditions is important for risk management and storage efficiency improvement. As a result, numerical simulations have been implemented to understand the relationship between fluid properties and multi-phase fluid dynamics. However, the physics-based simulations that focus on the uncertainties of fluid flow dynamics are complicated and computationally expensive. Machine learning method provides immense potential for improving computational efficiency for subsurface simulations, particularly in the context of parametric sensitivity. This work focuses on parametric uncertainty associated with multi-phase fluid dynamics that govern geologic CO2 storage. The effects of this uncertainty are interrogated through ensemble simulation methods that implement both physics-based and machine learning modeling strategies. This dissertation is a culmination of three projects: (1) a parametric analysis of capillary pressure variability effects on CO2 migration, (2) a reactive transport simulation in a basalt fracture system investigating the effects of carbon mineralization on CO2 migration, and (3) a parametric analysis based on machine learning methods of simultaneous effects of capillary pressure and relative permeability on CO2 migration.