No abstract

Carbon dioxide (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 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 dioxideloaded 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.

In this article, we report 3D numerical simulations of highly conductive nonmagnetic particles dispersed in a moderately conductive matrix, subject to an AC magnetic field in a range of several hundred kHz. We address the issue of the scaling of current loops and heating power with respect to the volume fraction of the dispersed phase. Simulations are performed in two steps. First, a static electric potential gradient is imposed between two opposite faces of the simulation domain and an effective conductivity is computed in good agreement with percolation models. Second, the particles are constrained in a spherical subregion and an AC magnetic field is imposed at the boundary of the domain. For small volume fractions, the induced Joule power is in good agreement with an analytical model of dilute dispersions. As the volume fraction increases, wider current loops form, until the percolation threshold is reached. Then the induced power in the spherical aggregate is well described by the power induced in an equivalent sphere with a volume-fraction-dependent conductivity.