Solute dilution under imbibition and drainage conditions in a heterogeneous structure: Modeling of a sand tank experiment

Abstract

This study aims at modeling the transport of a conservative tracer in two dimensions, as experimentally observed in a strongly heterogeneous medium under conditions of variable water saturation during drainage and imbibition. Solute transport experiments were conducted in a sand tank containing an artificial packing of three quartz sands of different particle sizes. The packing was characterized by the presence of numerous homogeneous layers (0.5 × 5 × 5 cm) inclined at 45° and randomly distributed in a tank. Six different stationary flow conditions were sequentially established during imbibition and drainage. When a stationary flow regime was reached, several solute pulses were applied at different positions at the upper surface of the sand structure. The transport regime was studied by monitoring the tracer plumes injected as point-like pulses at the surface, as they travelled through the sand bedding. A textural map was generated from a digital image of the sand bedding. The Richards equation was solved with the experimental boundary conditions assuming homogeneity of the individual sand layers. The hydraulic properties of the three quartz sands were deduced from multistep-outflow column experiments [Ursino N, Gimmi T. Combined effect of heterogeneity, anisotropy and saturation on steady state flow and transport: structure recognition and numerical simulation. Water Resour Res 2004;40. doi:10.1029/2003WR002180]. The convection–dispersion equation was solved on the resulting flow fields for solute pulses of given solute mass applied onto the top boundary at the same positions as in the experiment. The simulated and observed solute concentration distributions were then compared. In agreement with the experimental observations, the simulations reproduced the existence of preferential pathways in those stationary flow fields at low saturation degrees. The values of the vertical and horizontal macroscopic dispersivities obtained from the simulations are smaller than experimentally observed, especially at low flow rates. The simulated solute concentration distributions show a realistic degree of solute dilution quantified as reactor ratio.