Steam injection into water-saturated porous rock

We formulate conservation laws governing steam injection in a linear porous medium containing water. Heat losses to the outside are neglected. We find a complete and systematic description of all solutions of the Riemann problem for the injection of a mixture of steam and water into a water-saturated porous medium. For ambient pressure, there are three kinds of solutions, depending on injection and reservoir conditions. We show that the solution is unique for each initial data.