Riemann solutions of balance system with phase change for thermal flow in porous media.
Balance laws | phase change | porous medium
This work encompasses two types of results. First we present a new general theory which deals with Riemann solution for a large class of balance equations. This class of equations has interest because it can be applied to model thermal flow with mass interchange between phases in porous media, with important applications in oil recovery. As applications of this theory, we present three models of steam injection in a horizontal porous media. The systems of equations are based on mass balance, energy conservation and Darcy law of force. We neglect compressibility, heat conductivity and capillarity effects. In first example we consider steam/water/oil flow in porous medium. We only prepare the formalism for this class of equations. In second example we consider steam/water/nitrogen flow into a porous medium. We develop the general theory for a $4\times 4$ system of balance equations. We solve the Riemann problem with application to recovery of geothermal energy. A rarefaction evaporation wave is observed. In third example we consider the steam/water injection into a porous medium. We completely solve the Riemann problem associated with this model. We obtain a rich class of bifurcations in the solutions. A new type of shock, the evaporation shock, is identified in the Riemann solution.