Fluid flow and transport phenomena during geological sequestration of carbon dioxide

Geological sequestration of carbon dioxide (CO2) is one of the key technological options that can play a substantial role in mitigating greenhouse gas emissions in the short term. The long-term fate of CO2 injected into geological formations is dictated by the interplay of many physical phenomenon. Obtaining an understanding of these fundamental processes is crucial to guaranteeing security of the storage sites.;This dissertation makes contributions towards three different problems associated with geological storage of carbon dioxide. First, the idea of Non-modal Stability Analysis is used to study the physical mechanism governing the onset of density-driven convection over a transient base-state in homogeneous porous media. Non-modal stability theory is a generalization of the normal-mode approach designed to study the transient growth of perturbations. The results of the stability calculations will be shown to match extremely well with those obtained using spectral simulations of the non-linear governing equations. The second contribution is an extension of the non-modal stability calculations to flow in anisotropic and horizontally layered porous media. For a given variation of permeability in the vertical direction, non-modal analysis is used to calculate the growth of perturbations over all possible initial conditions. These amplifications are compared with Finite-Volume computations of onset of instability in heterogeneous porous media. It is shown that the theory provides good results as long as the gradients of permeability in the horizontal direction are less that those in the vertical direction by at least a factor of 4.;The final contribution is a downscaling technique called Renormalized Numerical Simulations (RNS), used to obtain the effective permeabilities of porous media exhibiting scale-invariance in their geometry. This approach is designed to exploit the scale-invariance property by estimating sub-grid scale contributions through simulations resolving only the large length scales. It will be shown that for simple test cases based on the Sierpinski carpet geometries, RNS simulations on a coarse-grid give results with errors of the order of 2% compared to completely resolved simulations on much finer grids.