Autor: Rima BENHAMMADI (PhD student | IDAEA-CSIC)

Rayleigh-Bénard instability in heterogeneous porous media. 

Abstract: Convective mixing is present in a plethora of natural and industrial phenomena as in seawater intrusion, geothermal energy storage and CO2 sequestration. This seminar presents the results of the study of convective mixing in heterogeneous porous media represented by 2-D multi-Gaussian log-Normally distributed anisotropic permeability fields in the case of the Horton-Rogers-Lapwood problem where convection is triggered by a Rayleigh-Bénard instability. We perform a parametric study in which we explore the effect of the variation of the Rayleigh number, the variance and the correlation length of the permeability field on the fingering patterns, the mixing state and the dissolution fluxes. Mixing is characterised by the scalar dissipation rate and the boundary fluxes. The mixing state is evaluated through the concentration probability density function (pdf), the intensity of segregation and the pdfs variance. We show the difference in behavior between the dissolution fluxes and the mixing state both in the case of homogeneous and heterogeneous porous media. We observe that as in the homogeneous case, increasing Ra decreases the fluxes and that for a weakly heterogeneous porous medium, fluxes depend weakly on the variance. However, as the correlation length of the permeability field is increased, fluxes tend to increase with the variance of the permeability and this increase is only considerable for the highest considered correlation length. As for the interface width, it tends to decrease as the variance and the correlation length of the permeability field are augmented suggesting that the interface undergoes a higher stretching in heterogeneous porous media compared to their homogeneous counterparts. Nonetheless, the concentration variance and the intensity of segregation take higher values, compared to their homogeneous analogues, when the correlation length and the variance are increased. Based on these observations, an upscaling of the Rayleigh number based on the effective longitudinal and transverse permeability as well as the dispersion coefficient is performed.

Keywords: convective mixing, Rayleigh-Bénard instability, heterogeneity, dissolution fluxes.  

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