We formulate conservation laws governing steam and nitrogen injection in a one-dimensional porous medium containing water. Compressibility, heat conductivity and capillarity are neglected. We study the condensation front and shock waves arising in the flow. We find that there are four possible types of solutions for the initial and boundary conditions of interest. We describe a simple construction in the temperature saturation plane that determines the complete solution for the given conditions. Applications of the theory developed here are in clean up of soil contaminated with nonaqueous phase liquids. We show that a substantial cold gaseous zone develops in all solutions of practical interest, thus counteracting downward migration of the pollutant.