A model is proposed regarding the polarization of dispersed metallic conductors (e.g., pyrite and magnetite) in porous media free of redox-active ionic species in the pore water. We studied two cases corresponding to having a background material with or without chargeability. The model was based on the polarization mechanism of a single particle using well-established bounds for the reflection coefficient entering the definition of the dipole moment of the metallic grains. We used the Maxwell-Clausius-Mossotti mixing equation to obtain the complex conductivity of the mixture of dispersed metallic particles in the background porous material composed of the pore water and the insulating grains coated by an electric double-layer. This equation can be generalized to a mixture of various types of metallic particles (with their own properties) dispersed in the background porous material. Our model led to a very simple linear relationship between the chargeability and the volume content of metallic particles in the material. In addition, the chargeability depended weakly only on the shape of the spheroidal metallic particles as long as their orientation was random. The relaxation time defined from the phase peak frequency related to the diffusion coefficient of the $n$- and $p$-charge carriers in the metallic particles. This diffusion coefficient was consistent with the mobility of the charge carriers derived from theoretical considerations or electric conductivity measurements. In the presence of a polarizable background (e.g., a clayey matrix), we found that the total chargeability of the material can be determined from the chargeability of the metallic particles and the chargeability of the background material.

We have derived a set of new relationships describing polarization parameters in porous materials with disseminated particles made of a semiconductor, such as pyrite or magnetite. We have compared various predictions of this model to a broad set of experimental data. The chargeability was found to be controlled only by the volume fraction of metallic particles in agreement with the experimental data. The relaxation time, defined from the peak frequency of the phase, was observed to be proportional to the square of the size of the metallic particles and was independent of the salinity of the pore water solution. The relationship between the peak frequency and the grain size could be used to determine the diffusion coefficient of the $n$- and $p$-charge carriers in the semiconductor. This diffusion coefficient was consistent with the mobility of the charge carriers derived from theoretical considerations or electric-conductivity measurements. The resistivity of a mixture of a porous matrix characterized by a low-chargeability and dispersed semiconductors does not depend on the content of metallic grains, as long as the grains are below a percolation threshold (< 22 vol.%). Various experiments were performed using magnetite and pyrite at different grain sizes, weight fractions, and with/without porous materials (i.e., suspended in agar gel). These data were used to test some additional aspects of the model. We found excellent agreement between the model predictions and these experimental data.

This paper investigates optimal sampling times of drawdowns for the analysis of hydraulic tomography (HT) survey. The investigation was carried out by analyzing the spatial and temporal evolution of cross‐correlations between the head responses at an observation well and transmissivity (T) and storage coefficient (S) properties during a pumping test in homogeneous and heterogeneous aquifers. The analysis shows that the cross‐correlation between the head and S values is limited to the region between the observation and the pumping well in the aquifers: It reaches the highest value near the early time (t_m), and decays to zero afterwards. The time t_m is approximately equal to the time t₀ at which the extrapolated drawdown from the first straight line portion of an observed drawdown‐log time plot becomes zero. At early times, the high cross‐correlation between the head and T is confined to the region between the observation and the pumping well. This region then evolves into two humps: One on each side of the circular region encompassing the observation well and the pumping well. The size of the two humps expands and their values reach the maximum as flow reach steady‐state. As a consequence, we hypothesize that pairs of head data at t₀ and those at either the steady‐state or a late time during an HT survey could yield the best estimates of the heterogeneous T and S fields. Results from numerical experiments have verified this hypothesis and demonstrated that this sampling strategy is generally applicable even when the boundary condition is unknown. We, therefore, recommend in principle that (1) carrying out pumping tests of HT surveys for sufficiently long period of time such that drawdown reaches the entire area of interest and (2) using a constant head or zero drawdown for all boundaries during the inverse modeling analysis.