[1] We measured the electric parameters for four different configurations of unconsolidated homogeneous and layered sands as a function of frequency, water saturation, and salinity under fluid flow conditions. Our objective is to determine if the effect of heterogeneities at scales much smaller than the skin depth can be captured by introducing effective frequency-dependent electrical values whose behavior can be described by simple functions. We employed the parallel plate capacitor technique to measure the complex impedance over a broad frequency range, from 100 kHz up to 3 MHz. We conducted main drainage and secondary imbibition cycles at atmospheric pressure and temperatures between 21°C and 22°C. The hysteretic effect in the real part of the effective complex permittivity at higher concentrations of NaCl is more pronounced for the homogeneous configurations than for the heterogeneous samples. Effective medium theory works well for dry and saturated layered sand, when the NaCl solution concentration is 1 mmol/l. It fails for fully saturated layered sands at salinities of 10 mmol/l or more. It also does not work for partially saturated sands, independent of salinity. A description of the electric properties of a layered sand at all saturation levels by means of an effective homogeneous medium will therefore require a dependence on frequency, saturation level, and salinity of the pore fluid. An extended version of the Cole-Cole model fits the nonmonotonic behavior of the real part of permittivity versus saturation.Citation: Kavian, M., E. C. Slob, and W. A. Mulder (2011), Hysteresis in the nonmonotonic electric response of homogeneous and layered unconsolidated sands under continuous flow conditions with water of various salinities, 100 kHz to 2 MHz,

Macroscopic measurements of electrical resistivity require frequency-dependent effective models that honor the microscopic effects observable in macroscopic measurements. Effective models based on microscopic physics exist alongside with empirical models. We adopted an empirical model approach to modify an existing physical model. This provided a description of electrical resistivity as a function of not only frequency, but also water saturation. We performed two-electrode laboratory measurements of the complex resistivity on a number of fine and medium-grained unconsolidated sand packs saturated with water of three different salinities. For frequencies between 0.1 and 1 MHz, the data were fitted with the new model and compared to fits with Archie's law. Our model described the relaxation times and DC resistivity values as negative exponential functions with increasing water saturation. All data could be accurately described as a function of frequency and water saturation with nine parameters.

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