Anomalous transport in laboratory‐scale, heterogeneous porous media

Abstract

We analyze measured breakthrough curves in a laboratory model which consists of a uniformly heterogeneous porous medium; these curves were previously shown to be indicative of scale‐dependent transport and therefore inconsistent with the (macroscopic) advection‐dispersion equation [ Silliman and Simpson , 1987]. Our analysis is based on an analytical expression for the first‐passage time distribution (FPTD) of migrating contaminants in random media, developed with the use of a continuous time random walk (CTRW) formalism. The general CTRW has been shown to be effective in quantifying anomalous transport patterns frequently observed in fractured and strongly heterogeneous porous media [ Berkowitz and Scher , 1997, 1998]. We calculate a family of FPTD curves, usually referred to as “breakthrough curves,” which are a function of an exponent β; this exponent is related to the low‐velocity tail of the velocity distribution. The FPTD curves fit well the measured data, with a single value of the β exponent over the spatial/temporal scale of the experiment. This is in contrast to previous analyses using solutions of the Gaussian‐based advection‐dispersion equation with time‐independent parameters in a uniform flow field. We conclude that the CTRW may allow analysis of transport in porous media subject to complex heterogeneities at large scale, which may not be amenable to analysis using classical advection‐dispersion theory. Hence the CTRW represents a potentially valuable tool in the assessment of dispersive processes in heterogeneous porous media.