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Solutal Convection in Porous Media

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Solutal convection in porous media is thought to be controlled by the molecular Rayleigh number, Ram, the ratio of the buoyant driving force over dissipation by molecular diffusion. The mass flux should increase linearly with Ram and the finger spacing should decrease as Ram. Instead, our experiments show that the flux levels off at large Ram and the finger spacing increases with Ram. Here we show that the convective pattern is controlled by a dispersive Rayleigh number, Rad, balancing buoyancy and dispersion. Increasing the bead size of the porous medium increases Ram but decreases Rad and hence coarsens the pattern. While the flux is predominantly controlled by Ram, the anisotropy of mechanical dispersion leads to an asymmetry in the pattern that limits the flux at large bead sizes.

Numerical simulations at the Darcy scale reproduce both the trend in the convective pattern and quantitative fluxes of the pore-scale results, only adjusting anisotropy of mechanical dispersion. Our simulations show the flux recovers a linear scaling with reduced coefficient as dispersion becomes dominant, consistent with the recent laboratory experiments. However, sub-linear flux scaling arises either in a transitional regime where diffusion and dispersion are comparable or if grains become too coarse. In this case, the pore-scale simulations show that convective up- and downwellings arise in individual pores. This leads to additional mixing not accounted for in Fickian dispersion model on the Darcy scale. The buoyancy-driven pore-scale mixing observed here therefore has different characteristics from mixing processes in pressure-driven flows and requires a new approach to upscale them to the Darcy scale.

This talk is part of the BPI Seminar Series series.

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