Greenhouse gases, like carbon dioxide, are the primary cause of global warming. Carbon Capture and Sequestration (CCS) is a novel technique developed to address this issue by injecting CO₂ into deep geological structures.
To ensure the effectiveness of CCS, we need to simulate the long-term behavior of liquid-gas fluid mixtures containing CO₂ and stored inside a porous medium. In this talk, we outline the numerical model that describes this problem.
The system of equations that we obtain shows a hybrid parabolic-hyperbolic behavior. This issue has been generally tackled either by simplifying the model or by using simpler numerical methods, resulting in instabilities or low accuracy levels.
We discuss a Discontinuous Galerkin (DG) approach to the problem that allows the preservation of a rigorous thermodynamical description. To do so, we present a splitting of the parabolic and hyperbolic fluxes, that consents to combine a Symmetric Interior Penalty DG method with an upwind evaluation of the resulting advection term. This technique allows retaining the generality of the model and the flexibility provided by DG methods.