Electrical-Hydraulic Relationships Observed for Unconsolidated Sediments in the Presence of a Cobble Framework

摘要

Mechanistic models now exist to predict hydraulic conductivity (K) from the spectral-induced polarization (SIP) response of granular media. We examined the predictions of such a model on unconsolidated coarse fluvial sediments and compared them to those obtained with a modified Kozeny-Carman (KC) model. Samples were retrieved from the Boise Hydrogeophysical Research Site (BHRS), located on a gravel bar adjacent to the Boise River, Idaho. A sample holder (0.102 m diameter and 0.12 m in length) was designed to include the cobble framework in reconstituted samples representing the primary stratigraphic units defined based on porosity variation at this site. SIP (0.001–1000 Hz) and K (from Darcy tests) measurements were recorded for 12 samples, with SIP measurements made as a function of pore fluid conductivity (3–300 mS/m), grain size distribution (GSD), and total porosity. K prediction with the KC model was improved after discounting of the cobble framework and multiplying by the tortuosity resulting from matrix “capillaries” around the cobbles, resulting in estimates within a factor of 5 of the measurements. K prediction with a mechanistic SIP model based on Stern layer polarization (SLP model) that requires an estimate of the GSD also required discounting for the cobble framework to obtain estimates within 0.5 orders of magnitude of the measurements. Similarly, the SLP model overpredicts the measured imaginary conductivity ( σ″) unless the cobble framework is discounted, which then results in estimates of σ″ within a factor of 2 of the measurements. This can be explained by the fact that the cobbles polarize at frequencies well below the minimum measurement frequency (0.001 Hz). The SLP model for K prediction parameterized in terms of the formation factor and imaginary conductivity performed well for the 10 samples with a cobble framework without modification as the imaginary conductivity directly senses the matrix grain size characteristics, whereas the formation factor captures the porosity reduction and tortuosity resulting from the presence of the cobble framework (capillary tortuosity). Our findings suggest that the estimation of contrasts in K in coarse sediments may be achievable through measurements of electrical properties after appropriate consideration of the cobble fraction.