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Abstract
The efficiency of mixing in density-driven natural-convection is largely governed by the aquifer permeability, which is heterogeneous in practice. The character (fingering, stable mixing or channeling) of flow-driven mixing processes depends primarily on the permeability heterogeneity character of the aquifer, i.e., on its degree of permeability variance (Dykstra-Parsons coefficient) and the correlation length. Here we follow the ideas of Waggoner et al. (1992) to identify different flow regimes of a density-driven natural convection flow by numerical simulation. Heterogeneous fields are generated with the spectral method of Shinozuka and Jan (1972), because the method allows the use of power-law variograms. We observe from our simulations that the rate of mass transfer of CO2 into water is higher for heterogeneous media.

1. Introduction
Efficient storage of carbon dioxide (CO2) in aquifers requires dissolution in the aqueous phase. Indeed the volume available for gaseous CO2 is less than for dissolved CO2. The inverse partial molar volume (virtual density) of dissolved CO2 is around 1300 kg/m3 (Gmelin, 1973) leading to more efficient storage than CO2 remaining in the supercritical state (< 600 kg/m3) at relevant storage temperatures. Moreover, dissolution of CO2 in water decreases the risk of CO2 leakage. The mass transfer between CO2 and underlying brine in aquifers causes a local density increase (Gmelin, 1973), which induces convection currents accelerating the rate of CO2 dissolution (Yang and Gu, 2006; Farajzadeh et al, 2006, 2009). This system is gravitationally unstable and leads to unstable mixing enhancement in the aquifer (Riaz et al, 2006; Meulenbroek et al, 2010; Hassanzadeh et al, 2007; Farajzadeh et al, 2007).

The effect of natural convection increases with increasing Rayleigh number, which, for a constant-pressure CO2-injection scheme, mainly depends on the permeability. This means that the efficiency of the mixing (caused by natural convection) is largely governed by the aquifer permeability (Green et al, 2009; Farajzadeh et al, 2007a), which is subject to spatial and directional variations in practice. Previous studies on this subject are mostly concerned with homogeneous porous media and despite attention of a few papers (e.g. Farajzadeh et al., 2008; Green et al, 2009; Nield and Simmons, 2007; Ranganathan et al, 2010) the effect of heterogeneity on the CO2 mass transfer in aquifers is not fully understood.