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Carbonate rock reservoirs are dominated by heterogeneity across a large and continuous range of spatial scales. We study the impact of heterogeneities on relative permeability and residual trapping for three carbonate rocks selected for their distinct spatial scales of rock texture. The Indiana limestone comprises millimeter scale heterogeneities, the Estaillades limestone consists of half‐centimeter scale heterogeneities, and the Edwards dolomite includes decimeter scale heterogeneity. Along with routine characterisation of rock samples, steady‐state N₂ ‐ deionized water drainage relative permeability measurements are made for each rock at two distinct total flow rates, at least one order of magnitude apart. The variation in flow potential across the core results in observations of fluid distribution, core‐average relative permeability, and residual trapping obtained for a range of continuum‐scale capillary number . The relative permeability curves for all rocks shift to the right of the water saturation axis with increasing flow potential; the nitrogen relative permeability increases while the water relative permeability decreases. However, the magnitude of the shift depends on the spatial scale of heterogeneity. An inspection of 3D saturation distributions in the cores and estimation of the capillary numbers of flow shows the rock with the largest heterogeneity is capillary flow dominated throughout the range of injection rates tested; Observations in the Indiana and Estaillades carbonates traverse capillary to viscous dominated flow regimes, with commensurate flow rate dependence in the relative permeability. In all cases, residual trapping is poorly described by the Land model.

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