A potential geologic target for CO2 storage should ensure secure containment of injected CO2. Traditionally, this objective has been achieved by targeting reservoirs with overlying seals-regionally extensive, low permeability units that have been proven capable of retaining buoyant fluid accumulations over geologic time. However, considering that the amount of CO2 is limited by a decadal injection period, vertical migration of CO2 can be effectively halted by a composite system of discontinuous shale/silt/mudstone barriers in bedded sedimentary rocks. Here, we studied the impact of depositional architectures in a composite confining system on CO2 migration and confinement at reservoir scale. We stochastically generated lithologically heterogeneous reservoir models containing discontinuous barriers consistent with statistical distributions of net-sand-to-gross-shale ratio (NTG) and horizontal correlation lengths derived from well log data and observations of producing hydrocarbon fields in Southern Louisiana. We then performed an extensive suite of reservoir simulations of CO2 injection and post-injection to evaluate the sensitivity of CO2 plume migration and pressure response of the composite system to a series of geologic and fluid parameters including the lateral continuity of barriers, NTG, permeability anisotropy within the sand body, and capillary pressure contrast between the sand and shale facies. The results indicate that lateral continuity of barriers and NTG are the dominant controls on CO2 plume geometry and pressure build-up in the reservoir, while the impact of NTG is particularly pronounced. The significance of intraformational barriers becomes apparent as they facilitate the local capillary trapping of CO2. Those barriers improve the pore space occupancy by promoting a more dispersed shape of the plume and ultimately retard the buoyancy-driven upward migration of the plume post injection.