The Impact of Head Gradient Transients on Transport in Heterogeneous Formations: Application to the Borden Site

A three-dimensional interpretation of the Borden Site experiment is proposed with the aid of a recently developed stochastic model that incorporates transiency of the piezometric head gradient. The behavior of the second-order central transverse plume moments is analyzed with the aim of explaining the underprediction of experimental results by existing steady state models. The model assumes uniformity in space, but time varying mean head gradient, stationary and anisotropic log conductivity, and a first-order approximation in the log conductivity variance. The solution for the trajectory covariances, assumed to be equal to the plume spatial second moments under ergodic conditions, is evaluated with the aid of a few quadratures. An analysis of the parameters and plume spatial moments found in the literature precedes application of the model. It is found that unsteadiness leads to an increase in the transverse, horizontal, second moment compared with the one based on a steady state flow model. Still, application of Borden Site data leads to values lower than the ones inferred from concentration measurements. We conclude that unsteadiness of the mean head gradient does not fully explain the magnitude of observed transverse spreading. However, the impact of transients on spreading is significant in the transverse direction, and the definition of a Fickian transverse dispersion coefficient may not be a simple task for transport occurring under natural flow conditions.