Stochastic and deterministic analysis of dispersion in unsteady flow at the Borden Tracer-Test site, Ontario, Canada

Abstract In this work, recently collected water-level data from the Borden aquifer are applied to two recent models to determine whether they predict the observed horizontal transverse dispersion observed at the aquifer. The collected water-level data are first detrended using a combination of ordinary least-squares and generalized least-squares methods. The trend surface information shows that the hydraulic head gradient is transient. A geostatistical analysis is performed on the time series of the components of the hydraulic head gradient to determine the variances and integral scales present. Assuming the data represent earlier behaviour at the aquifer, the results of the geostatistical analysis are combined with those obtained from the Stanford-Waterloo tracer experiment and the combination used to evaluate Rehfeldt's equations for the asymptotic macrodispersivity due to unsteady flow conditions. The computed range in asymptotic transverse horizontal macrodispersivity is found to be 0.0014 m ⩽ A 22 ⩽ 0.054 m . This computed range is in good agreement with the measured dispersivity values for the Borden acquifer. Spectral analysis is also performed on the component of hydraulic head gradient perpendicular to the mean flow direction and these results, along with those obtained from the Stanford-Waterloo tracer experiment, are incorporated into Naff et al.'s moment model to predict the horizontal transverse moments at the site. The moments, computed using Naff et al.'s model, are found to significantly under-predict the observed moments at the site. The analysis shows that flow transients contribute to the transverse macrodispersion at the Borden site.

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