Multiphysics simulation of the electrical signature of dual-domain mass transfer in a pore-scale microfluidics experiment

Abstract

Dual-porosity models are often used to describe solute transport in heterogeneous media, but the parameters within these models are difficult to identify experimentally or relate to measurable quantities. Here, we developed synthetic, pore-scale microfluidics experiments that coupled fluid flow, solute transport, and electrical resistivity (ER) measurements to explore relations between dual-porosity model parameters and the hydrogeologic system. A conductive-tracer test and the associated geoelectrical signatures were simulated for four flow rates in two distinct pore-scale model scenarios: one with intergranular porosity, and a second with an intragranular porosity also defined. With these models, we explore how the effective characteristic-length scale estimated from a best-fit DDMT model compares to geometric aspects of the flow field. In both model scenarios we find that: (1) mobile domains and immobile domains are interpreted to exist in a DDMT system even in a system that is explicitly defined with one domain; (2) the ratio of immobile to mobile porosity is larger at faster flow rates as is the mass transfer rate; and (3) a comparison of length scales associated with the mass-transfer rate (Lα) and those associated with calculation of the Peclet number (LPe) show LPe is commonly larger than Lα. These results suggest that estimated immobile porosities from a DDMT model are not only a function of physically mobile or immobile pore space, but also are a function of advective versus diffusive transport defined by the average linear pore water velocity, whereas the mass-transfer rates between mobile and immobile pore space are a function of the average linear pore water velocity. This work demonstrates that the definition of “immobile” is a function of the relation between pore water velocity and domain geometry (i.e., stagnant zones around pore constrictions), where physical obstructions to flow can drive the interpretation of immobile porosity even in single-porosity domains.