Carbonate reservoirs contain more than half of the world's remaining petroleum reserves and are increasingly becoming targets for water-alternating-gas (WAG) flooding as secondary or tertiary recovery. Heterogeneity in carbonate reservoirs spans from pore- to reservoir-scale. This is exacerbated by the presence of natural fractures and post-depositional dissolution. Furthermore, carbonate reservoirs tend to have variable wettability that impacts fluid flow which adds to reservoir uncertainty and renders managing WAG floods difficult. In this work, we examine the effect of rock and wettability heterogeneity on recovery profiles in naturally fractured carbonate reservoirs (NFCR). To simulate WAG flooding in NFCR with arbitrary wettability, we use saturation functions derived from a state-of-the-art pore network model to preserve multi-scale heterogeneities at the pore-scale. We study the interplay of capillary, gravity and viscous forces at an intermediate scale, then simulate WAG flooding in the presence of fractures in a heterogeneous carbonate ramp outcrop model. Adding the permeability and wettability heterogeneities impacts ultimate recoveries during water injection cycles by up to 6% and 14% absolute, respectively. Both heterogeneities affect the speed of recovery during gas injection cycles. Depending on its relation to permeability distribution, non-uniform wettability of matrix blocks can have a substantial impact on recovery during water injection cycles while recovery efficiency during the gas injection cycle can be reduced by a factor of 50%. Our work identifies the key factors that must be considered when modelling WAG floods in NFCR. We evaluate the reliability of conventional dual-porosity/dual- permeability numerical simulation approaches for NFCR by comparing results with multi-stage upscaled models through which we capture the fundamental controls on multi-phase flow. Hence, we can offer explanations for possible NFCR responses to WAG flooding and novel ways to improve the predictive ability of field-scale numerical simulation models.@en