We develop a model for the determination of gas and water relative permeabilities from pore size distribution functions. The model originates from percolation ideas, and considers two situations: (a) gas and liquid without surfactant, and (b) gas and liquid with a surfactant.
In the first case, we show that the relative permeabilities are coherent with those obtained in past studies. This proves the consistency of our model.
In the second case, the surfactant leads to the dispersion of gas in the liquid phase (foam). We determine the ensuing partitioning of mobile and immobile gas. Then we show that foam relative permeability increases with the permeability. We argue that the decline of foam mobility with increasing permeability is probably due to dominant increase of foam effective viscosity. However, at the present stage, the model could not confirm the dependence of foam mobility on a (−1/2) power of the permeability.