Concentration fluctuations in transport by groundwater: Comparison between theory and field experiments

In a recent work [Dagan and Fiori, 1997] we developed a Lagrangian theoretical framework to compute the concentration variance in transport of a conservative solute in a heterogeneous formation of random stationary structure. This variance, a measure of concentration fluctuations in the plume, depends on the spreading effect of advection and on the mixing effect of pore-scale dispersion. Comparison between theory and the numerical simulations of Graham and McLaughlin [1989] showed very good agreement. Here we compare the same theoretical formulae with the field measurements at Borden Site and Cape God. We rely on the analysis of these experiments carried out by Fitts [1996], who characterized the concentration fluctuations by a global measure. The latter is the standard deviation of the logarithm of the ratio between measured and modeled concentrations over the entire plume and at different times. The theoretical relationships require computing the two particles trajectories' covariances. We simplify the computations considerably by taking advantage of the anisotropy of the heterogeneous structures of the two aquifers. Thus the major effect of advection is in the shearing of the plume in the longitudinal direction, whereas pore-scale dispersion acts mainly through its transverse effect in the vertical direction. We found a good agreement between theory and experiments by using parameter values determined independently in the past, provided that the values of transverse pore-scale dispersivities were 0.5 mm for Cape Cod and 0.44 mm for Borden Site. These values are somewhat smaller than the vertical macrodispersivities inferred from measurements.