On Solution of the Riemann Problem Describing Injection of a Heated Salt Solution into an Aquifer

Abstract

The self-similar problem of breakdown of an arbitrary discontinuity is considered with reference to the processes of nonisothermal saline fluid flow through a porous medium. The possibility of salt precipitation in the form of a solid phase in the porous medium accompanied by reduction in its permeability is taken into account. The geometric method for solving the problem in plane is proposed under the assumption of incompressibility of the medium and neglecting thermal conductivity. It is shown that the solution should be constructed with the use of only the shock waves and zones with homogeneous parameter distributions whereas centered rarefaction waves cannot enter into the solution. The possible types of solutions of the problem are investigated. It is shown that three shocks propagate into the aquifer when the high-temperature saline fluid is injected, the temperature being discontinuous only on the inner shock.