Preprint C52/2006
Riemann solutions of balance system with phase change for thermal flow in porous media.

Wanderson Lambert

**Keywords: **
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.