Surfactant-Alternating-Gas (SAG) utilizes foam to reduce gas mobility and improve reservoir sweep efficiency in gas-injection enhanced oil recovery and carbon capture and storage. Although SAG is known to have many benefits that increase hydrocarbon recovery, liquid injectivity is typically very poor during a SAG process. Conventional foam simulators use the Peaceman model to estimate injection-well pressure. However, because they assume uniform saturation in the grid block, they do not account for near-wellbore saturation distribution that improves gas and liquid injectivities during a SAG process. We use a conventional foam simulator to test the impact of grid refinement on injectivity. We compare simulation results to those with fractional-flow theory (FFT) using the a model very widely used in simulations. In addition, we test the effect of complete foam collapse at irreducible water saturation (S_wr), of neglecting the Peaceman model, and of disallowing foam in the injector grid block. We compare the transient behaviors and the average injectivities, calculated during one pore volume of injected fluid. Our results show that in a conventional simulation (including the Peaceman model) grid refinement increases gas and liquid injectivities. However, the results do not match FFT predictions. The assumption of complete foam collapse at S_wr increases gas injectivity (still without matching FFT results); however, it has a smaller impact on liquid injectivity and grid refinement results in an increase in gas and liquid injectivities. Excluding the Peaceman model reduces the error in simulated injectivities at coarse grid refinements but still without matching the FFT prediction. Finally, the procedure of excluding foam in the injection-well grid block gives average injectivities like our FFT calculations without requiring extraordinary grid refinement.