Spatially varying fractional flow in radial CO₂-brine displacement

[1] In analytical modeling of two-phase flow problems in porous media, the saturation profile for a fixed time can be obtained by using the method of characteristics (MOC). One of the basic assumptions in the application of the MOC is that the fractional flow is a function of saturation only. However, when gas is injected, it is often flowing under nonlinear flow conditions and inertial losses are significant in the near-well region. Therefore, in a radial displacement non-Darcy flow applies at the injection well, but as the saturation front gets further away, its velocity will decrease and the fractional flow curve will vary with the distance along the streamline. This paper presents the extension of the Buckley-Leverett analytical solution when the injected gas phase flow is governed by the two-phase extension to the Forchheimer equation and the fractional flow function depends both on the saturation and radial distance from the well. The behavior of a gas-liquid system under non-Darcy flow conditions is shown for carbon dioxide injection into saline aquifers. Finally, this analytical solution is tested against the corresponding finite difference numerical model and the limitations of the approach are discussed.