Density-driven convection and chemical infiltration in saturated porous media

Convection and chemical dissolution in porous media are observed in many hydrogeological processes such as seawater intrusion in coastal aquifers, CO₂ sequestration in saline aquifers and heat transport in geothermal reservoirs. When a porous medium is infiltrated by a fluid contaminated with a reactive solute, convection is accompanied by dissolution of the porous matrix through chemical reactions between the solute and minerals contained in the porous solid, generating reaction products. Here we study how density-driven convection and reactive infiltration affect the transport of the solute and products in the porous medium. Convection and dissolution are modelled by coupled equations describing flow, transport of the solute and products, and mineral dissolution in a two-dimensional rectangular domain with a solute source located along half of the upper boundary. We quantify the average solute flux from the source in unsteady flows and analyze its development towards a steady-state value computed in [1]. Numerical experiments on the temporal development of convective flow and concentration fields are reported (see [2] for more details). The full numerical solutions are augmented with asymptotic analysis in a weakly convective and reactive regime performed in the limit of small Rayleigh and Damköhler numbers.

Acknowledgement:

This work was supported by the Slovak Research and Development Agency under the contract no. APVV-18-0308, and the VEGA project no. 1/0339/21 and the GUK project no. UK/355/2023.

References:

[1] van Reeuwijk, M., Mathias, S. A., Simmons, C. T., and Ward, J. D.: Insights from a pseudospectral approach to the Elder problem, Water Resources Research, 45, W04416, https://doi.org/10.1029/2008WR007421, 2009.

[2] Hurtiš, R., Guba, P., and Kyselica, J.: Simulation of reactive groundwater flow and salinization in carbonate-rock aquifers, 2022 International Conference on Electrical, Computer and Energy Technologies (ICECET), Prague, Czech Republic, 20–22 July 2022, pp. 1–4, https://doi.org/10.1109/ICECET55527.2022.9872944, 2022.