Simultaneous Brine and Heat Transport in Porous Media: Non-Boussinesq Semi-Analytical Solutions

Simultaneous heat and brine transport in a porous medium is considered. Both heat and brine affect the fluid density. In this particular case, the equations describing the flow and transport processes are: mass balance equation for the fluid, mass balance equation for salt (dissolved in the fluid), thermal energy conservation equation, Darcy's Law, and an equation of state. The equation of state relates fluid density to temperature and salt concentration. Note that the full mass balance equation for the fluid is taken into account. For this non-Boussinesq case, semi-explicit solutions for one-dimensional problems can be constructed, using a variety of transformation techniques. These solutions gain insight in the non-Boussinesq volume effects, inducing enhanced flow in the porous medium. These volume effects are due to the presence of both brine and heat in the flow domain. The produced semi-analytic solutions are extremely accurate and therefor useful for computer code verification.