On the Dagan model of solute transport in groundwater: Foundational aspects
The convection-dispersion equation (CDE) developed by Dagan  to predict the ensemble-average concentration of a conservative solute in groundwater has been used successfully to interpret recent tracer experiments in a sand aquifer at the Borden site in Canada. This successful application encouraged further investigation of the Dagan model in respect to its physical basis and predictive characteristics. It is shown in the present paper, which deals with the first topic, that the Dagan model CDE can be derived through an extension of the cumulant expansion technique applied previously by Chu and Sposito  to develop a mean CDE for solute transport in homogeneous porous media. This technique also leads directly to the mean CDE developed by Gelhar and Axness  as an asymptotic (large time) limit and to model dispersion coefficients derived by Mather on and de Marsily  and Güven and MoIz . The Dagan CDE then is considered in detail in respect to which conceptualization of the solute concentration, resident or flux, the model may utilize in predictive applications. General mathematical expressions relating the two conceptualizations are derived for an arbitrary solute transport problem and then are applied to the Dagan model for point and prism source inputs. Finally, the Dagan model is interpreted physically using data from the recent tracer experiments of Roberts and Mackay  at the Borden site. It is shown that model predictions of resident and flux concentrations are numerically indistinguishable on any time scale over which field solute concentration measurements typically are made. The model prediction of dispersion coefficients, on the other hand, leads to dramatic differences in predicted plume behavior depending on whether finite time expressions or their asymptotic limits are used. According to the Dagan model, the asymptotic transverse dispersion coefficient cannot replace the time-dependent coefficient on any realistic time scale for solute movement at the Borden site.
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Record created on 2005-12-09, modified on 2016-08-08