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

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. Plain Language Summary In many geologic settings, the migration of chemicals in groundwater does not appear to obey the classical theory of advective-dispersive transport in porous materials. Instead, it is necessary to represent the rock or soil through which water moves as comprising two overlapping domains, one in which water and chemicals move (the mobile domain), and the other in which water is stagnant and chemicals are trapped for some period of time (the immobile domain). Such dual-domain models are used to reproduce tracer data and describe transport observations from contaminated sites, water-resource investigations, and aquifer management operations; however, estimating the parameters for dual-domain models is difficult because the immobile domain is inaccessible to conventional sampling. Electrical geophysical methods have been shown to be sensitive to the immobile domain and exchange between mobile and immobile domains. Previous experimental studies indicate that a time-varying, or hysteretic, relation can develop during transport of electrically conductive tracers through dual-domain materials. Here, we (1) provide a micro-scale mechanistic explanation for such observations and verify the electrical signature of transport in dual-domain materials, and (2) present a new petrophysical model to link electrical measurements and the electrical conductivity of pore fluids.