Macrodispersion in heterogeneous aquifers. Numerical experiments

Macrodispersion is the name given to the mechanical dispersion due to the mixing effect of a heterogeneous velocity associated with the large-scale heterogeneities present in aquifers. Recent studies due to Dagan [1982, 1984, 1987] provide a conceptual model that relates the statistical properties of the hydraulic conductivity field and the dispersive properties of a nonreactive contaminant. Similar theoretical results have been obtained by Gelhar and Axness [1983] and Neuman and Zhang [1990]. These results describe the ensemble-average behavior of the displacement moments of a solute plume, which are related to the apparent dispersion coefficient. In dealing with a single aquifer, the ensemble-average solution is valid only when the solute plume covers a relatively large area (i.e., the ergodicity assumption is valid). However, since the minimum plume size required is not known, the conditions needed for the application of the theory to these problems are yet to be found. Carefully designed numerical experiments provide an expedient way to assess the conditions for the ergodicity assumption to hold. The basic experiment involves the simulation of solute transport in a single realization of a random velocity field. Preliminary simulation runs have been performed for two-dimensional velocity fields. Experimental results provide evidence of the validity of Dagan's theory for sufficiently large input zones.