Foam is used in enhanced oil recovery to improve the sweep efficiency by controlling the gas mobility. The surfactant-alternating-gas (SAG) foam process is used as an alternative to the water-alternating-gas (WAG) injection. In the WAG technique, the high mobility and the low density of the gas lead the gas to flow in channels through the high permeability zones of the reservoir and to rise to the top of the reservoir by gravity segregation. As a result, the sweep efficiency decreases and there will be more residual oil in the reservoir. The foam can trap the gas in liquid films and reduces the gas mobility. The fractional-flow method describes the physics of immiscible displacements in porous media. Finding the water fractional flow theoretically or experimentally as a function of the water saturation represents the heart of this method. The relative permeability function is the conventional way to derive the fractional-flow function. This study presents an improved relative permeability model to derive the fractional-flow functions for WAG and SAG foam core-floods. The SAG flow regimes are characterized into weak foam, strong foam without a shock front and strong foam with a shock front. © 2013 Sinopec Geophysical Research Institute.