On the growth of instabilities in groundwater due to temperature and salinity gradients

Abstract

Geothermal activity creates destabilizing temperature gradients which are significant in some aquifers. Usually, in such aquifers stabilizing salinity gradients also exist. The combination of temperature and salinity distribution in the aquifer may induce various types of hydrodynamic instabilities. We assume that the aquifer can be represented by an idealized model of a saturated porous layer, bounded on top and bottom by impermeable boundaries at which the temperature and salinity are constant. In stable and unperturbed conditions the fluid flows through this layer uniformly in the horizontal direction owing to the hydraulic gradient. By linear stability analysis it was found that three different mechanisms may lead to instability of the flow field: (a) buoyancy forces may induce convection currents (thermohaline convection), (b) the difference between the rate of heat and salinity diffusion may induce oscillations (overstable motions), (c) the difference between the velocity of propagation of heat and of salinity fronts may induce oscillations. The effect of mechanism (c) varies according to the type of aquifer. An aquifer in which the fluid is initially at rest is not affected at all by mechanism (c). In an aquifer of limited length, subject to hydraulic flow, mechanism (c) limits the growth of instabilities to planes perpendicular to the hydraulic gradient. In an aquifer of unlimited length mechanism (c) may completely neutralize the stabilizing effect of the salinity gradient and lead to thermohaline convection in planes parallel to the hydraulic gradient. Calculations of heat transfer through various types of aquifer by applying numerical simulations are presented.