The Pereriv Suite reservoir in the Azeri culmination of the ACG Oilfield is characterized by laterally continuous layers of variable net-to-gross (NTG) ratio deposited in a channel-dominated, fluvio-deltaic environment. The reservoir is being developed by down-dip water injection, with up-dip gas injection on the more steeply dipping central north flank. We use high-resolution models derived from outcrop analogue and subsurface data to demonstrate that four key sedimentological heterogeneities control recovery in both oil–water and gas–oil displacements: (1) local variations in NTG within low NTG (<55%) layers; (2) the degree of communication between low NTG layers and adjacent high NTG (>85%) layers; (3) sinuosity and (4) stacking pattern of channel-fill sandbodies in low NTG layers. The first three heterogeneities control sandbody connectivity; the fourth controls sweep efficiency in the connected sandbodies. Two further heterogeneities control recovery in gas–oil displacements in high NTG layers: (5) vertical-to-horizontal permeability ratio of channel-fill sandbodies and (6) mud clast lags at channel bases. Models which omit these small-scale features predict that sedimentological heterogeneity has little impact on water–oil or gas–oil displacements in high NTG layers, but fail to capture the effect of heterogeneity on the gravity stability of the gas–oil displacement, which significantly impacts on recovery.