We investigate how efficiently oil can be recovered from a carbonate rock during surfactant based enhanced oil recovery (EOR) at the core-scale, particularly when chemical processes change wettability, and analyse how geological heterogeneities, observed at the next larger scale (centimetre to decimetre) impacts the effectiveness of surfactant-based EOR at the inter-well scale. To quantify how heterogeneity across scales impacts surfactant flooding, we combine laboratory experiments with simulation studies at the core- and inter-well scale. We first analysed a series of surfactant imbibition experiments at different surfactant concentrations (from 0 to 3 wt. %) using reservoir cores from the Wakamuk field, a carbonate reservoir in Indonesia. We then built a 3D simulation model of the laboratory experiment and matched the experimental data to identify the key physical mechanisms (e.g., reduction in interfacial tension (IFT) and wettability alteration) that lead to increased oil recovery. Next, we parametrised the surfactant models using assisted history-matching methods to calibrate the relative permeability and capillary pressure curves as a function of surfactant concentration. These models were then deployed in high-resolution simulations at the inter-well scale. These simulations captured the small-scale geological heterogeneities that are typical for a carbonate reservoir system, e.g., the Shuaiba formation in the Middle East, but are not resolved in field-scale models. Our core-scale simulations demonstrate a change from co- to counter-current flow in the laboratory experiments and indicate that the resulting increase in oil recovery is due to a combination of IFT reduction, wettability alteration from oil- to water-wet, and capillary pressure restoration; these processes need to be captured adequately at the inter-well scale model. The increase in surfactant concentration above the critical micelle concentration (CMC) (i.e., from 1 to 3 wt. %) triggered the capillary pressure restoration and dominated recovery at the early-time. The changes in relative permeability and capillary curves during the surfactant floods were best modelled using a concentration-based interpolation. There is uncertainty when calibrating surfactant models using laboratory experiments. A key question hence is if geological heterogeneity at the inter-well scale masks these uncertainties. Results from our high-resolution simulations show that large-scale heterogeneity impacts recovery predictions, but it is the coarsening of the grid, not the upscaling of permeability, that dominates the error in field-scale recovery predictions during surfactant based EOR. Indeed, the error arising from numerical dispersion during grid coarsening can be as large as the error arising when selecting an inaccurately configured surfactant model due to the lack of quality experimental data. Hence appropriate grid refinement, possibly using adaptive grid refinement, needs to be considered when setting up a surfactant based EOR simulation, along with the appropriate configuration of the surfactant model itself.