Université de Rennes1
Campus de Beaulieu
35042 Rennes Cedex
02 23 23 60 76
par- 2 juillet 2012
Date : 2 juillet 2012, 15 h
Titre : Mixing and reactions in porous media.
Lieu : Salle de Conférences de l’OSUR (Bât. 14B, RdC)
In this thesis we use a stochastic approach to address the upscaling of mixing dominated reactions in flows thorough heterogeneous porous media. For the case where the transport is represented only by diffusion, fluctuations in spatial concentration distribution lead to segregation of chemicals and thus to anomalous kinetics. We show that the transition from the expected behavior shown by well mixed systems to this anomalous kinetics is intimately linked to the evolution of the concentration PDF from a Gaussian to non-Gaussian shape. This fact establishes a direct relationship between anomalous reaction kinetics, incomplete mixing and the non-Gaussian nature of the concentration PDF.
Introducing advective transport processes in our analysis, we studied the impact of incomplete mixing on effective reaction kinetics at the front between two solutes, one displacing the other, in a 2d heterogeneous porous medium. While classical Fickian models predict a scaling for the mass production as t0.5, we show that the kinetics follow 2 non-Fickian regimes. An early times the invading reactant is organized in fingers and the mass production scales as t2. For later times the mass production slows down, but it is still faster then the t2 . It does not depends on diffusion and is totally controlled by advective spreading. In this regime, anomalous kinetics is directly related to superdiffusive advective spreading. In order to relate the pore scale flow heterogeneity to advective spreading and subsequently to anomalous kinetics, we analyse the distribution and correlation of Lagrangian velocities. We show the existence of long range temporal correlation of Lagrangian accelerations, which are at the root of the breakdown of classical Fickian dispersion models. Thus, similarly to turbulent media, flow through porous media displays strong intermittent properties. We demonstrate that they can be quantified by a correlated Continuous Time Random Walk approach, which provides a consistent upscaling framework.
We finally perform a laboratory experiment where a quasi 2D system is studied through an Hele-Shaw cell in which two reactive chemicals are injected, one displacing the other. A new experimental set up based on chemiluminescence reactions allows high resolution quantification of the pore scale concentration pdf and reaction rate. The anomalous kinetics of the reactive front is observed and is very consistent with our theoretical predictions.
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