Carbonate reservoirs host significant hydrocarbon, groundwater, geothermal and CO2- and H2-storage resources. However, their complex depositional, tectonic and diagenetic histories make it challenging to efficiently characterize and predict their flow behavior. Here, we use a novel, rapid and efficient screening methodology that integrates experimental design, the construction of three-dimensional (3D) reservoir models via sketch-based methods and single-phase flow diagnostics to investigate the impact of geological heterogeneity on flow patterns and displacement in an ultra-deep (>7 km) carbonate reservoir in the north-central Tarim Basin, northwest China. Eight heterogeneities are investigated: (1) strike-slip fault zone width; (2) complexity of flower structure configuration; (3) continuity of fault core lithology; fault zone rock properties related to (4) karstification and (5) late, post-karstification cementation; (6) the occurrence of fault-perpendicular fracture corridors; (7) connectivity of fracture corridors to fault zones and (8) variability in host rock porosity and permeability. Fault zone width has the most significant impact on reservoir properties, with wider fault zones increasing effective horizontal permeability along fault zone strike. Fracture corridor occurrence and connectivity to the fault zone are the principal heterogeneities controlling effective permeability perpendicular to fault zone strike. Fault zone rock properties reflecting karstification and late cementation also significantly impact effective permeability in all directions. Other heterogeneities have little effect on effective permeability and well performance. However, simulated wells in negative flower structures and the main fault zone have higher productivities on average than simulated wells in positive flower structures and the host rock, similar to published production data from the ultra-deep reservoir. This study demonstrates the value of the screening methodology for assessing the effects of uncertainty in the interpretation of geological heterogeneities in complex carbonate reservoirs, in order to narrow the focus of future, more comprehensive reservoir simulations. The screening methodology is directly transferable to low-carbon energy applications in settings with sparse data.