Mixing in the presence of convective instabilities in an homogeneous porous media is governed by the behavior of stagnation points where the fluid interface is stretched and compressed. It has been shown that an interface compression model is able to predict the behavior of the scalar dissipation rate. The mixing regimes experienced by these kind of systems are linked to the dependency of compression on diffusion and the interaction between stagnation points and the correlation structure of the velocity field. We apply this approach to an heterogeneous porous media in which the variations in heterogeneity distorts the convection patterns and the way the fluid interface is compressed. We consider a Rayleigh-Bénard instability in which the stagnation points are at a fixed interface and Rayleigh-Taylor instability in which the interface is mobile. Using a stochastic approach we perform a series of numerical simulations using randomly generated conductivity fields realizations with varying statistical properties. Numerical results are used to analyze the impact of variance and spatial correlation of conductivity fields on the way the fluid interface is compressed and on the mixing behavior of the system. The flow structures are visualized by the strain rate and characterized by their correlation length.
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