Double diffusive natural convection of CO_2 in a brine saturated geothermal reservoir: Study of non-modal growth of perturbations and heterogeneity effects

摘要

In a recent study (Islam et al., 2013) double diffusive natural convection of CO_2 in brine saturated homogeneous permeable geothermal reservoir was investigated. Here we have shown the study of heterogeneous reservoirs. Firstly, we present the non-modal stability theory to analyze time-dependent double diffusive convection. Linear stability analysis is performed and the maximum amplification of perturbations optimized over the entire space of initial perturbations is examined. These provide us onset time of convection (or the critical time) and the structure of the most-amplified perturbations. Secondly, we investigate numerical simulation of an anisotropic and layered reservoir with permeability variations, which is impervious from the sides, and is open to CO_2 at the top. We show the propagation of CO_2 plumes over long period of time by analyzing different combination of problem parameters: solutal Rayleigh number (100≤Ra_s≤ 10,000), 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 CO_2 dissolution is discussed for different ratios of k_z/k_x (0.1 ≤ k_z/k_x ≤ 0.8). Results of different cavity aspect ratios (0.5 ≤ A ≤ 2) are also presented. It is found that heterogeneous porous reservoir renders better mass transfer of CO_2 than the homogeneous one. CO_2 dissolution is enhanced with increasing both Ra_s and V_(dp). N, which represents geothermal effect, has minor impact on overall dissolution process. The results have implications in enhanced oil recovery and CO_2 based geothermal systems.