Eur. Phys. J. B 80, 411-432 (2011)
https://doi.org/10.1140/epjb/e2011-10805-y

Dispersion of solutes in porous media

¹ Department of Physics and Department of Earth and Environmental Sciences, Wright State University, Dayton, OH, 45435, USA
² Department of Physics, Wright State University, Dayton, OH, 45435, USA
³ Department of Agronomy, Iowa State University, Ames, Iowa, 50011, USA
⁴ Department of Earth and Environmental Sciences, Wright State University, Dayton, OH, 45435, USA

Corresponding author: ^a allen.hunt@wright.edu

Received: 20 October 2010
Revised: 5 January 2011
Published online: 24 March 2011

Abstract

A recently introduced theory of solute transport in porous media is tested by comparison with experiment. The solute transport is predicted using an adaptation of the cluster statistics of percolation theory to critical path analysis together with knowledge of how the structure of such percolation clusters affects the time of transport across them. Only the effects of a single scale of medium heterogeneity are incorporated, and a minimal amount of information regarding the structure of the medium is required. This framework is used to find effectively the distributions of solute velocities and travel distances and thus generate arrival time distributions. The comparison with experiment focuses on the dispersivity (the ratio of the second to the first moment of the spatial solute distribution). The predictions of the theory in the absence of diffusion are verified by comparing with over 2200 experiments over length scales from a few microns to 100 km. At larger length scales (centimeters on up) about 95% of the data lie within our predicted bounds. At smaller length scales approximately 99.8% of the data lie where we predict. These comparisons are not trivial as the typical values of the dispersivity increase by ten orders of magnitude over ten orders of magnitude of length scale. Noteworthy is that the classical advection-dispersion (ADE) equation predicts that the dispersivity should be independent of length scale! This agreement with experiment requires rethinking of the relevance of diffusion and multi-scale heterogeneity and would also appear to signal the complete inappropriateness of using the classical ADE or any of its derivatives to model solute transport.