Foam greatly reduces the mobility of gas in porous media, both by increasing the effective viscosity of the gas phase and by trapping a substantial fraction of the gas in place. Mechanistic models for foam mobility split the effect of foam into an effective viscosity and an effective relative permeability, which includes the effect of gas trapping. The effective gas relative permeability is represented as a function of the volume fraction of gas that flows, which depends on the pressure gradient. We test various models for effective gas relative permeability using realistic network models of a sphere pack and a sandstone. We represent the gas phase as a Bingham plastic, a Herschel-Bulkley fluid, or using two other simple models. We show the relation between the pressure gradient, gas flowing fraction, and gas mobility for these cases. Results for all the models differ strikingly from those based on the conventional percolation theory and bundle-of-tubes models as well as those used in current mechanistic foam simulators. No simple scaling law fits the relation between the flowing fraction and pressure gradient for both the sandstone and the sphere pack. A new model for gas superficial velocity as a function of pressure gradient fits our results for one fluid model in one pore network reasonably well.