Abstract
We discuss the convective dispersion of passive tracer in a stratified porous medium consisting of an infinite number of parallel layers, an idealization of geologically heterogeneous oil and water reservoirs first discussed by Matheron and de Marsily. There is assumed to be a random, horizontal velocity in each layer, reflecting variations in permeability, and the tracer undergoes molecular diffusion between layers coupled to convection plus diffusion in the horizontal direction. The resulting tracer motion is superdiffusive, 〈X2(t)〉→t3/2 at large times, with analogous behavior for higher moments, and a non-Gaussian probability distribution. We discuss the origin of this effect using both intuitive and exact arguments, give an asymptotic estimate for the tracer concentation distribution, and consider the first-passage-time aspects of the problem. [This work was done in collaboration with A. Georges, J.-P. Bouchaud, F. Leyvraz, A. Provata, and S. Redner.]
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