Using Fractional Flow Function to Extrapolate Trapped Saturation in Two-Phase Flow in Porous Media

Abstract - In this study the fraction flow function is adapted to study the immiscible displacement of two phase flow in porous media. The viscous and capillary effect are included in the formulation, where the capillary term is simplified using a length scale suggested by [21]. At low capillary number the solution of the derivative of the fractional flow function shows a negative part, and as the capillary number increases it converges to the solution of the viscous model in which the capillary term is neglected, and there is no negative part in the solution. This negative part can not be a solution, and that limits the maximum saturation that can be displaced. Thus, the trapped saturation of the displaced fluid can be extrapolated. The study model shows that the extrapolated trapped saturation depends on the capillary number. At a very low capillary number, a maximum trapped saturation can be obtained, and as the capillary number increases the trapped saturation decreases. In addition, the study model shows that as the viscosity ratio increases, the maximum trapped saturation decreases. The capillary number and viscosity ratio effects on trapped saturation are similar to the results that achieved experimentally.