We use a method combining experimental design, sketch-based reservoir modelling, and flow diagnostics to rapidly screen the impact of sedimentological heterogeneities on CO2 migration and storage by stratigraphic trapping. Experimental design allows efficient exploration of a wide parameter space, sketch-based modelling enables rapid construction of deterministic models of interpreted geological scenarios, and flow diagnostics provide computationally cheap approximations of full-physics, multiphase simulations that are reasonable for many subsurface-flow conditions. Integrated sketch-based reservoir modelling and flow diagnostics are implemented in open source research code (Rapid Reservoir Modelling, RRM). The method is applied to two case studies: (1) the Triassic Sherwood Sandstone Group and Bunter Sandstone Formation, UK, which comprise fluvial-aeolian sandstones, floodplain and sabkha heteroliths, and lacustrine mudstones; and (2) the Jurassic Johansen and Cook formations, offshore western Norway, which record progradation of a wave-dominated delta system. Results for the two case studies are compared using effective permeability (kx, ky, kz) and pore volume injected at breakthrough time (a measure of how much injected fluid is stored in the model volume as a result of stratigraphic trapping).