Pore network modeling of the electrical signature of solute transport in dual‐domain media

Abstract

Dual‐domain models are used to explain anomalous solute transport behavior observed in diverse hydrologic settings and applications, from groundwater remediation to hyporheic exchange. To constrain such models, new methods are needed with sensitivity to both immobile and mobile domains. Recent experiments indicate that dual‐domain transport of ionic tracers has an observable geoelectrical signature, appearing as a nonlinear, hysteretic relation between paired bulk and fluid electrical conductivity. Here we present a mechanistic explanation for this geoelectrical signature and evaluate assumptions underlying a previously published petrophysical model for bulk conductivity in dual‐domain media. Pore network modeling of fluid flow, solute transport, and electrical conduction (1) verifies the geoelectrical signature of dual‐domain transport, (2) reveals limitations of the previously used petrophysical model, and (3) demonstrates that a new petrophysical model, based on differential effective media theory, closely approximates the simulated bulk/fluid conductivity relation. These findings underscore the potential of geophysically based calibration of dual‐domain models.

Direct Observations of Hydrologic Exchange Occurring With Less‐Mobile Porosity and the Development of Anoxic Microzones in Sandy Lakebed Sediments

“…When plotted in fluid/bulk EC concentration space, the resulting hysteresis pattern shows approximate mirror symmetry, indicating that similar less‐mobile exchange processes were observed during the enrichment and flush phases of the injection experiment (Figure c). This symmetry also suggests that the electrical averaging of mobile and less‐mobile fluid EC components of bulk EC appears approximately arithmetic (Day‐Lewis et al, ), a basic assumption of the graphical less‐mobile exchange parameter analysis techniques presented by Briggs, Day‐Lewis, et al () and utilized here. Due to incomplete tracer replacement in the overlying water column during the flush injection phase, the hysteresis loop closes at a more conductive point than the background porewater condition and continues to drop slowly at late time (Figure c).…”

“…Using the experimental hysteresis, the parameter β , or the ratio of less‐mobile/mobile fractions of total porosity, was estimated graphically as described in detail by Briggs, Day‐Lewis, et al () and shown in Figure c by projecting hysteresis hinge points. Based on Day‐Lewis et al (), we expect the falling limb to conform more closely to the arithmetic‐averaging (parallel conduction) assumption underlying the graphical analysis; hence, we focus on that limb first (Figure ). Considering the linear portion of the falling limb (i.e., bulk EC > 25 μS/cm), β was determined by linear fit to be 0.97 and by least‐squares linear regression to be 1.03.…”

The Dual‐Domain Porosity Apparatus: Characterizing Dual Porosity at the Sediment/Water Interface

“…Additionally, flowpath lengths on the scale of meters or greater are needed for such experiments; such length scales are ill-suited for the characterization of shallow SWI sediments (Briggs et al 2013b). These experiments are based on methods developed and demonstrated by Singha et al (2007) and Day-Lewis and Singha (2008) and confirmed by pore-scale simulations (Day-Lewis et al 2017). These experiments are based on methods developed and demonstrated by Singha et al (2007) and Day-Lewis and Singha (2008) and confirmed by pore-scale simulations (Day-Lewis et al 2017).…”

Simulation of less‐mobile porosity dynamics in contrasting sediment water interface porous media

“…Our graphical analysis of β is based on the assumption that the mobile and less‐mobile zones function as electrical conductors in parallel during ionic tracer breakthrough. Day‐Lewis et al () recently found this assumption likely to be most valid for the tracer flush limb of the hysteresis loop, when less‐mobile porosity is temporarily more conductive than mobile porosity. This situation contrasts the tracer injection phase, when the less‐mobile zones are more resistive; both scenarios impact the bulk electrical averaging process differently.…”

“…In a heterogeneous medium with spatially differential conductive tracer loading, changes in bulk EC are expected to lag behind fluid EC, resulting in a hysteresis between fluid and bulk concentration histories during tracer step perturbations (Briggs et al, ; Singha et al, ). Day‐Lewis et al () investigated the nonlinear hysteresis relation using a pore‐network model with geoelectrical simulation to mechanistically explain the electrical patterns observed in laboratory experimental data.…”