Relating Topological and Electrical Properties of Fractured Porous Media: Insights into the Characterization of Rock Fracturing

Abstract

Numerous laboratory and field experiments suggest that electrical properties of fractured rocks may provide critical information regarding the topological properties of the underlying fracture networks. However, a lack of numerical studies dedicated to realistic fractured media prevents us from assessing, in a systematic manner, the relationships between electrical and topological properties in complex domains for which a representative elementary volume may not exist. To address this issue, we conduct an extended numerical analysis over a large range of realistic fractured porous media with an explicit description of the fractures that takes into account the fracture-matrix interactions. Our work shows that the fracture density determines the suitability of Archie's law for describing effective electrical properties with complex behavior associated with small fracture densities. In particular, for fracture networks at the percolation threshold surrounded by a low-porosity matrix, the effective petrophysical relationships are impacted by the assumed fracture-length distribution and the exchange of electric current between the fractures and surrounding matrix. These results help in understanding experimental observations that were difficult to explain so far, suggesting that the effective electrical properties of fractured rock may be used to obtain insights into the properties of their geological structures.

Monitoring the Drainage Efficiency of Infiltration Trenches in Fractured and Karstified Limestone via Time-Lapse Hydrogeophysical Approach

“…Particularly in low-porosity fracture-matrix systems, simplified fracture network models, such as Archie's law, are not representative of realistic field conditions and may not be adequate to model the electrical properties of the medium; on the contrary, high fracture densities lead to simplified behaviors that can be described with Archie's law [40].…”

“…In the specific study case, Archie's model was suited to describe the electrical properties of the fractured rock for three main reasons: (1) the contribution of the surface conductivity was assumed to be negligible because of the cyclic drying-wetting phases, which have been occurring since the start of plant operation in 2016, and should have washed out the clayey filling in the fractures; (2) the fracture density estimated on the excavation walls of the trench is about 10, which is above the percolation threshold defined in [40]; (3) the fluid electrical conductivity σ w did not change over time because, during the monitoring, the water circulating in the rock formation is solely the treated wastewater that percolates through the trenches. In addition, in the two temporal windows considered for the ERT monitoring the electrical conductivity of infiltrated water was steady around 1.020 mS cm −1 , making dual domain effects negligible to the overall conductivity.…”

Self‐Potential as a Predictor of Seawater Intrusion in Coastal Groundwater Boreholes

“…The bulk electrical conductivity of the aquifer was simulated using equation , with a value of 2.5 for the cementation exponent m below the unnamed marl and a value of 1.5 above this, reflecting an increased degree of fracturing at shallow depths and, hence, greater connection between pores (Glover, ; Roubinet et al, ). For marl seams, equation was applied, reflecting the contribution of surface conductance in clay minerals.…”

Predicting Electrokinetic Coupling and Electrical Conductivity in Fractured Media Using a Fractal Distribution of Tortuous Capillary Fractures

“…Petrophysical relationships relating electrical conductivity and structural properties in fractured media are not abundant in the literature. Among other works, Bernabe [32] uses crack networks and percolation to study the transport properties, while Roubinet et al [33] revisited the classic model of Archie [34] to relate topological and electrical properties. To the best of the authors knowledge, no analytical petrophysical relationships for fractured media exist in the literature.…”