Reversible Dispersion in Periodic Radial Subsurface Flow

Abstract:

Solute dispersion in groundwater flow is typically assumed to be irreversible; however, under conditions of high Peclet number and incomplete mixing at the pore scale, this assumption may not be valid. This study performs theoretical and experimental investigations of dispersion in porous media under periodic radial subsurface flows, alternating between injection (i.e., diverging flow) and extraction (i.e., converging flow) from a central well. This flow scenario mimics push-pull tests, which are used for site characterization for remediation design. In the experiment, a neutrally buoyant dye solution is injected into quasi-three-dimensional rectangular apparatus containing spherical beads in a hexagonal close packed configuration. Laser-induced fluorescence was used in conjunction with refractive index matched porous media and pore fluid to track the movement of the dye solution through the intensity of the fluorescence, a surrogate for solute concentration. The measured dye intensity is averaged over the vertical dimension of the apparatus, which encompasses 10 bead diameters. This averaging of concentration is similar to any practical measure of concentration in a field setting in which the sampling device homogenizes concentrations over multiple flow paths. Thus, the apparent dispersion of the measured concentrations is a result of the predominantly radial flow paths diverting around individual beads and of the averaging in the vertical dimension. Because of the time scales of the experiment and the characteristics of the pore fluid (glycerin), molecular diffusion is negligible in the experiment. The results of the experiment show strong evidence that mixing at the pore scale is incomplete, and, consequently, that dispersion that occurs during diverging flow is undone during converging flow. In other words, dispersion is reversible. Theoretical investigations are conducted to model the upscaling of the pore-scale processes to the vertically averaged concentrations through a dispersivity parameter.