Dual-domain mass-transfer parameters from electrical hysteresis: Theory and analytical approach applied to laboratory, synthetic streambed, and groundwater experiments

Abstract

Models of dual-domain mass transfer (DDMT) are used to explain anomalous aquifer transport behavior such as the slow release of contamination and solute tracer tailing. Traditional tracer experiments to characterize DDMT are performed at the flow path scale (meters), which inherently incorporates heterogeneous exchange processes; hence, estimated "effective" parameters are sensitive to experimental design (i.e., duration and injection velocity). Recently, electrical geophysical methods have been used to aid in the inference of DDMT parameters because, unlike traditional fluid sampling, electrical methods can directly sense less-mobile solute dynamics and can target specific points along subsurface flow paths. Here we propose an analytical framework for graphical parameter inference based on a simple petrophysical model explaining the hysteretic relation between measurements of bulk and fluid conductivity arising in the presence of DDMT at the local scale. Analysis is graphical and involves visual inspection of hysteresis patterns to (1) determine the size of paired mobile and less-mobile porosities and (2) identify the exchange rate coefficient through simple curve fitting. We demonstrate the approach using laboratory column experimental data, synthetic streambed experimental data, and field tracer-test data. Results from the analytical approach compare favorably with results from calibration of numerical models and also independent measurements of mobile and less-mobile porosity. We show that localized electrical hysteresis patterns resulting from diffusive exchange are independent of injection velocity, indicating that repeatable parameters can be extracted under varied experimental designs, and these parameters represent the true intrinsic properties of specific volumes of porous media of aquifers and hyporheic zones. Key Points Mass-transfer parameters are determined analytically from electrical hysteresis Analytical parameter estimates are local and insensitive to experimental design Model parameters are comparable to physically measured characteristics