Double Diffusive Natural Convection of CO2 in Brine Saturated Porous Media: Study of Non-Modal Growth of Perturbations and Heterogeneity Effects

It is important to understand the factors that drive natural convection in aquifers for assessing geologic CO₂ sequestration. This topic has been the focus of many recent studies because of its relevance to long-term solubility trapping mechanism. In this study we present non-modal stability theory to analyze the time-dependent double diffusive convection where both density and geothermal gradients along vertical direction of the aquifer are accounted. The objective is to study the linear stability analysis through non-modal stability theory and thus obtain the maximum amplification of perturbations optimized over the entire space of initial perturbations. This provides us the onset time of convection and the structure of the most-amplified perturbations as well. Then we perform numerical investigation of an anisotropic and layered porous medium having permeability variation that is impervious from the sides and is open to CO₂ at the top. This study is done using mass, momentum, energy conservation, and the Darcy laws. We show the propagation of CO₂ plumes over long periods of time analyzing different combination of problem parameters: solutal Rayleigh number (100<Ra_s<10000), the buoyancy ratio (2<N<100), Dykstra-Parsons coefficient (0<V_dp<0.85), and a fixed Lewis number. How permeability variation in vertical (k_z) to horizontal (k_x) direction affects the CO₂ dissolution is discussed by performing numerical simulation for different ratios of k_z/_kx(0-0.8). Results of different cavity aspect ratios (0.5<A<2) are also presented. A sinusoidal perturbation is added for the initial top boundary condition as numerical computations do not exhibit natural convection effects for flat initial conditions. It is found that heterogeneous media renders increased mass transfer of CO₂ than the homogeneous media. CO₂ dissolution is enhanced with increasing both Ra_s and V_dp. N, which represents geothermal effect, has negligible impact on overall dissolution process.  The results have implications in enhanced oil recovery and CO₂ based geothermal systems.