Thermohaline convection in a homogeneous porous medium

The theoretical examination of the combined effect of heat and mass transfer in porous media is relevant to improve understanding thermohaline natural convection in both local- and basin-scale groundwater flow systems. Numerical model calculations were carried out to investigate the interaction of the temperature- (ΔT) and salinity-driven (Δc) natural convection in a synthetic model, as in a two-dimensional homogeneous porous medium. Effects of the non-dimensional thermal expansion (α' = αΔT = 10–3–1) and the non-dimensional relative density contrast (β' = βΔc = 10–7–0.1) were systematically studied in order to examine their influence on the temperature, the concentration and the Darcy flux field. Thus, the thermal (Rat) and the haline (Rah) Rayleigh number and the Buoyancy ratio (BR) were varied within the following ranges: 1.4 ≤ Rat ≤ 1400, 0.1 ≤ Rah ≤ 105, 10–7 ≤ BR ≤ 100, while the Lewis number was fixed, Le = 714. As the results of simulations, the Darcy flux (U), the Nusselt (Nu) and Sherwood numbers (Sh) were computed. In the examined cases, both effects facilitated the onset of natural convection. Depending on the studied parameters (α' and β'), six types of flow systems were separated in the numerical model including: 1) no convection, 2) steady-state haline convection, 3) time-dependent haline convection, 4) forced thermohaline convection, 5) steady-state thermohaline convection, 6) time-dependent thermohaline convection. However, the effect of haline term was strongly influenced by the heat transport mechanism due to the relation between the thermal and the molecular diffusivity (κ >> D0). These simulations draw attention to the importance of understanding the physical background of thermohaline convection, for instance, in aquifers separated by salt domes, in the deep (hypogene) karstified carbonates (e.g. the Buda Thermal Karst), in the case of groundwater flow induced by water pumping/injection of deep geothermal power plants, or in contaminated groundwater transport process.