Two-scale modeling of solute transport in an experimental stratigraphy

Abstract

Summary 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 not 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-law 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.