Seminar on Qualitative Theory of Differential Equations - Radoslav Hurtiš (2.12.2021)
Thursday 2.12.2021 at 14:00, Lecture room M 223
By: Pavol Quittner
The Elder problem with reactive infiltration effects
The occurrence of buoyancy-driven flow and reactive solute transport in a fluid-saturated porous medium can be induced by either various human activities or natural processes. A typical example is groundwater salinization in coastal carbonate aquifers. In the current work, using the Elder problem geometry, we consider a two-dimensional porous-medium model with local chemical interactions between the solute and a mineral structure of the solid, in which the solute and the minerals are consumed and reaction products in the liquid are generated without any dissolution effects on porosity and permeability. Based on the model, we analyze and explain the impact of the geochemical processes on the flow and mass transport. For the reactive system in the regime dominated by the diffusive mass transport, we find a decrease in the net solute concentration compared to the non-reactive case. This decrease is pronounced at higher values of the Damk\"ohler number when the solute reaction rate becomes larger than the solute diffusion rate. Furthermore, we find that the structure of the flow is affected by the products present in the system when the Rayleigh number for the products is sufficiently high. In that case, numerical simulations show the formation of diluted fluid tongues exhibiting damped periodic oscillations about a non-zero mean. The pseudospectral code used to obtain the numerical simulations was verified against an analytical solution for a non-reactive and purely diffusive case.