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, 1997Scher, , 1998]. We calculate a family of FPTD curves, usually referred to as "breakthrough curves," which are a function of an exponent/3; 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/3 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.
Field observations by other authors indicate that dispersivity is dependent on distance from source. In this study, tests were conducted under controlled laboratory conditions to investigate the changes in dispersivity caused by the presence of heterogeneities. The experiments were conducted in a 2.4 × 1.07 × 0.10 m “sandbox” with measurements of tracer concentration taken at various distances from the input. Results for various sand‐packing arrangements were as follows: (1) Breakthrough curves for a uniform coarse sand showed a constant dispersivity of approximately 0.02 m. (2) Breakthrough curves for a three‐layer arrangement of coarse‐fine‐coarse deviated from the homogeneous results only in the late‐time tails. (3) The middepth fine‐sand layer was then replaced by small blocks of fine sand surrounded by coarse sand. Two distinct portions of the breakthrough curves could be identified: one for the coarse‐sand matrix and one for the heterogeneous layer. (4) Small blocks of fine sand were uniformly distributed through the entire coarse‐sand matrix. Results indicated a continuous increase in dispersivity with distance and a change in the shape of the breakthrough curve at each of five measurement sections. These results are in general agreement with several recent theoretical developments regarding transport.
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