Geologic storage of carbon dioxide (CO2) is considered a viable strategy for significantly reducing anthropogenic CO2 emissions into the atmosphere; however, understanding the flow mechanisms in various geological formations is essential for safe storage using this technique. This study presents, for the first time, a two-phase (CO2 and brine) flow visualization under reservoir conditions (10 MPa, 50 °C) for a highly heterogeneous conglomerate core obtained from a real CO2 storage site. Rock heterogeneity and the porosity variation characteristics were evaluated using X-ray computed tomography (CT). Multiphase flow tests with an in-situ imaging technology revealed three distinct CO2 saturation distributions (from homogeneous to non-uniform) dependent on compositional complexity. Dense discontinuity networks within clasts provided well-connected pathways for CO2 flow, potentially helping to reduce overpressure. Two flow tests, one under capillary-dominated conditions and the other in a transition regime between the capillary and viscous limits, indicated that greater injection rates (potential causes of reservoir overpressure) could be significantly reduced without substantially altering the total stored CO2 mass. Finally, the capillary storage capacity of the reservoir was calculated. Capacity ranged between 0.5 and 4.5%, depending on the initial CO2 saturation.