Foam has been used as an effective displacing fluid for gas mobility control in enhanced oil recovery (EOR) and subsurface remediation. In this study, a series of core flooding experiments are performed on cores with a wide permeability ranging from 3.3 to 2749 mD to evaluate the impact of foam quality and permeability on foam performance. It is found that the steady-state foam mobility control factor is related to permeability in a non-linear, non-monotonic manner. A full physics, mechanistic foam model is proposed by incorporating a novel flowing foam fraction relation grounded-up from pore-level observations, and a new kinetic expression of foam coalescence rate by oil based on pinch-off foam rupture mechanism into the population-balance framework of Almajid et al. (Advances in Water Resources, 2021, 150: 103877). The proposed model is applied to match foam flow experimental results in the absence and in the presence of oil. Results show that our model captures the high-quality and low-quality foam regimes observed in previous oil-free foam flow experiments. Within the medium permeability range, in the absence of oil, lower gas mobility is observed in the lower permeability core due to faster foam film thinning at higher capillary pressure, while in the presence of residual oil, the difference in foam mobility fades away due to the insignificant impact of capillary pressure on the stability of pseudoemulsion films.