The Riemann solution for thermal flows with mass transfer between phases

Dan Marchesin | Lambert, Wanderson

Keywords: Balance laws | conservation laws | Riemann problem | asymptotic expansion | porous medium | steamdrive | local thermodynamic equilibrium | geothermal energy | multiphase flow

We are interested in solving systems of balance equations under the approximation of local thermodynamical equilibrium except at very localized locations. This equilibrium occurs for states on a stratified variety called the 'thermodynamical equilibrium variety', which is obtained as the domain of the zero-order approximation of an asymptotic expansion for these balance laws. Waves far from thermodynamical equilibrium occur in thin regions of physical space and they form shocks connecting sheets of the stratified variety. In this scenario, we develop the general theory for fundamental solutions of a large class of systems of balance equations. We study all bifurcation loci, such as coincidence and inflection locus and develop a systematic approach to solve problems described by similar equations. For concreteness, we exhibit the bifurcation theory for a representative system with four equations. This class of equations models thermal flow with mass interchange between phases in porous media appearing in oil recovery. We find the complete solution of the Riemann problem for two-phase thermal flow in porous media with two chemical species to simplify the physics, the liquid phase consists of a single chemical species. We give an example of steam and nitrogen injection into a porous medium initially saturated with water, with applications to geothermal energy recovery.

Anexos:

• nitromatematica11.pdf