Two-scale modeling of solute transport in an experimental stratigraphy

A high-resolution non-stationary hydraulic conductivity map is generated based on an experimental stratigraphy. A heterogenous model is created, incorporating the complete conductivity variation. A hydrostratigraphic model (HSM) is also created which divides the space into discrete lithofacies units. For each unit, an equivalent conductivity is estimated using numerical up-scaling. Under a lateral hydraulic gradient, steady-state, incompressible groundwater flow experiments are conducted in both models. Within each flow field, conservative pulse-input line-source tracer is simulated. In the heterogeneous model, the tracer exhibits both scale-dependency in the observed longitudinal macrodispersivity and persistent long tailing associated with anomalous, non-Fickian dispersion. In comparison, HSM-predicted, global mean relative error of hydraulic head is 1.5%, that of groundwater flux is 0.77%. Using (small) hydrodynamic dispersivities, the HSM closely predicts the evolution of the tracer moments. A certain degree of tailing is also predicted, as this model has captured the largest scale, between-unit velocity variations. However, detailed plume shape is knot captured, nor are the arrival and tailing of the breakthrough, curves. Using macrodispersivity (both unit-specific and time-dependent), the breakthrough prediction has improved, especially the solute arrival time. Both macrodispersion models also capture the development of breakthrough asymmetry as well as power-taw tailing. However, the development of a steep front and multiple peak concentrations are not captured. Similar observations are also found for a continuous-source injection. Overall, for the chosen boundary condition, the advection-dispersion equation can be used by the lithofacies model to capture certain key aspects of the bulk flow and transport behaviors, although displacement mapping reveals that heterogeneity-induced dispersion is correlated both in time and space, a likely result of the correlated velocity field. (c) 2007 Elsevier B.V. All rights reserved.