Abstract
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.
Highlights
Storage of CO2 in underground geological formations is a potential means of limiting greenhouse gas emissions to the atmosphere whilst continuing the use of fossil fuels [1]
In the analysis presented in [23] and [37], as well as in most works dealing with the study of stability and bifurcation maps for this type of problem, only molecular diffusion is considered instead of the hydrodynamic dispersion in porous media
In contrast to the dispersion tensor used in porous media, this tensor is quadratic in the velocity and regular in the no-flow state
Summary
Storage of CO2 in underground geological formations is a potential means of limiting greenhouse gas emissions to the atmosphere whilst continuing the use of fossil fuels [1]. Related studies, addressing the effect of chemical reaction on a Rayleigh–Taylor instability, have employed non-linear reaction terms that allow for chemical front propagation [25,26] From these works it can be concluded that a chemical reaction with the substrate significantly changes the dynamics of the system through the introduction of a steady state that prevents the solution from penetrating deep into the underlying fluid. This process delays the onset of convection, shortens the evolution time and alters the spatial patterns of velocity and concentration of solute. A similar assumption was made in most of the aforementioned works that deal with the reaction between dissolved CO2 and minerals trapped in a fixed substrate
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