We propose a new workflow to evaluate the impact of three-phase relative permeability models on the simulation of Water-Alternating-Gas (WAG) injection – define a root-mean-square error to quantify differences between the models; introduce a high-uncertainty region on a ternary saturation diagram; and map simulation saturation-time paths in this ternary diagram. The display of the saturation paths, along with the high-uncertainty region, allows us to systematically analyze and understand the impact of three-phase models on recovery predictions. We apply the workflow to immiscible and miscible WAG injection, simulated using black-oil and compositional models. Both 2D homogeneous cases (with various reservoir conditions and injection scheduling), and realistic 3D field sector models are considered. We show that the three-phase relative permeability models can have a strong impact on recovery predictions for immiscible WAG injection, and the impact depends on initial conditions and displacement history. For compositional simulation of multi-contact miscible WAG injection, the impact of three-phase models depends on the size of the three-phase flow region before the miscibility fully develops. Simulation of CO2 flooding on a 3D field sector model reveals that the uncertainty in recovery predictions due to the various three-phase models is secondary compared with other sources of uncertainty (e.g., the input two-phase relative permeability data), and this may be the case in other field studies.