Effects of hydrodynamic dispersion on the stability of buoyancy-driven porous media convection in the presence of first order chemical reaction

Carbon dioxide (\(\text {CO}_2\)) sequestration is one of several long-term solutions suggested to decrease the amount of greenhouse gases in the atmosphere. Among different methods of carbon dioxide sequestration, the dissolution of \(\text {CO}_2\) in deep saline aquifers is considered one of the most effective. A significant number of studies are currently being carried out to provide a good understanding of the physical mechanisms involved in this type of storage. The present work focuses on the hydrodynamic part of the problem: setting a model for carbon dioxide-loaded flows in an idealised two-dimensional geometry. It considers the impact of hydrodynamic dispersion in porous media on the development of convective instabilities. Particular attention is paid to the mathematical form of the dispersion tensor widely used in porous media studies, and a new type of bifurcation is investigated. We show that the analysis of bifurcations from the no-flow steady-state solution is a continuous but non-smooth problem, which is a key feature of the analysis. Although the problem is non-smooth, it is also shown that the basic behaviours of linear stability analysis are observed in its solution.