Impact of Saturation on Evaporation-Driven Density Instabilities in Porous Media: Mathematical and Numerical Analysis

Evaporation from a porous medium partially saturated with saline water, causes the salinity (salt concentration) to increase near the top of the porous medium as water leaves while salt stays behind. As the density of the water increases with increased salt concentration, the evaporation leads to a gravitational unstable setting, where density instabilities can form. Whether density instabilities form, depends on a large range of parameters like the evaporation rate and intrinsic permeability of the porous medium, but also on the water saturation. As water saturation decreases, the storage, convection and diffusion of salt also decrease, which all influence the onset of instabilities. By performing a linear stability analysis on the governing equations, we give criteria for onset of instabilities, with a particular focus on impact of saturation. While decreased storage and diffusion make onset of instabilities more unstable, decreased convection has a stabilizing effect on the onset of instabilities. We find that their combined influence is that lower saturation overall gives earlier onset times. Numerical simulations give information about the further development of these instabilities. With this knowledge we can predict whether and when density instabilities occur, and how they will influence the further development of salt concentration in the porous medium.