Investigating the impact of advective and diffusive controls in solute transport on geoelectrical data

Abstract

Abstract Multiple types of physical heterogeneity have been suggested to explain anomalous solute transport behavior, yet determining exactly what controls transport at a given site is difficult from concentration histories alone. Differences in timing between co-located fluid and bulk apparent electrical conductivity data have previously been used to estimate solute mass transfer rates between mobile and less-mobile domains; here, we consider if this behavior can arise from other types of heterogeneity. Numerical models are used to investigate the electrical signatures associated with large-scale hydraulic conductivity heterogeneity and small-scale dual-domain mass transfer, and address issues regarding the scale of the geophysical measurement. We examine the transport behavior of solutes with and without dual-domain mass transfer, in: 1) a homogeneous medium, 2) a discretely fractured medium, and 3) a hydraulic conductivity field generated with sequential Gaussian simulation. We use the finite-element code COMSOL Multiphysics to construct two-dimensional cross-sectional models and solve the coupled flow, transport, and electrical conduction equations. Our results show that both large-scale heterogeneity and subscale heterogeneity described by dual-domain mass transfer produce a measurable hysteresis between fluid and bulk apparent electrical conductivity, indicating a lag between electrical conductivity changes in the mobile and less-mobile domains of an aquifer, or mass transfer processes, at some scale. The shape and magnitude of the observed hysteresis is controlled by the spatial distribution of hydraulic heterogeneity, mass transfer rate between domains, and the ratio of mobile to immobile porosity. Because the rate of mass transfer is related to the inverse square of a diffusion length scale, our results suggest that the shape of the hysteresis curve is indicative of the length scale over which mass transfer is occurring. We also demonstrate that the difference in sampling scale between fluid conductivity and geophysical measurements is not responsible for the observed hysteresis. We suggest that there is a continuum of hysteresis behavior between fluid and bulk electrical conductivity caused by mass transfer over a range of scales from small-scale heterogeneity to macroscopic heterogeneity.