On singular points for convex permeability models

Pablo CastaĆ±eda | Frederico Furtado | Dan Marchesin

**Keywords:**Conservation laws | Riemann problem | umbilic point | WAG injection | petroleum engineering | flow in porous media | Corey permeability model

We focus on a system of two conservation laws representing a large class of models relevant for petroleum engineering, the domain of which possesses singular points. It has been conjectured that the structure of the Riemann solution in the saturation triangle is strongly influenced by the nature of the umbilic point. In the current work we show that features originally related to umbilic points actually belong to a distinct point, the new Equal-Speed Shocks point. Even though the location of the umbilic point is known, for the first time, we relate the umbilic point to a physical property, namely, the minimum of the total mobility for any Corey model.