Seminar 2.12.2021: Radoslav Hurtis

[quittner]

Seminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations

Thursday 2.12.2021 at 14:00

Radoslav Hurtiš (KAMŠ FMFI UK):
The Elder problem with reactive infiltration effects

MS-Teams link:
https://teams.microsoft.com/l/meetup-jo ... 0ff7%22%7d

Abstract:
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.