Mathematics

We consider an isothermal model of flow of hydrocarbons and water in subsurface known as black-oil model. The model accounts for three phases and three components. Due to pressure changes, the gas phase may appear or disappear. Various primary unknowns are considered, and the qualitative and quantitative consequences of a choice of primary unknowns are discussed. In particular, a total compressibility is defined and a local nonlinear problem is studied. We discuss conditions on the data which guarantee a degenerate parabolic/elliptic behavior of the pressure equation as well as unique solvability of the local problem. Numerical results will illustrate the talk.