Incorporation of Effects of Diffusion into Advection-Mediated Dispersion in Porous Media

The distribution of solute arrival times, W(t;x), at position x in disordered porous media does not generally follow Gaussian statistics. A previous publication determined W(t;x) in the absence of diffusion from a synthesis of critical path, percolation scaling, and cluster statistics of percolation. In that publication, W(t;x) as obtained from theory, was compared with simulations in the particular case of advective solute transport through a two-dimensional model porous medium at the percolation threshold for various lengths x. The simulations also did not include the effects of diffusion. Our prediction was apparently verified. In the current work we present numerical results related to moments of W(x;t), the spatial solute distribution at arbitrary time, and extend the theory to consider effects of molecular diffusion in an asymptotic sense for large Peclet numbers, Pe. However, results for the scaling of the dispersion coefficient in the range 1<Pe<100 agree with those of other authors, while results for the dispersivity as a function of spatial scale also appear to explain experiment.