Effects of material texture and packing density on the interfacial polarization of granular soils

Many electrical and electromagnetic (EM) methods operate at MHz frequencies, at which the interfacial polarization occurring at the solid-liquid interface in geologic materials may dominate the electrical signals. To correctly interpret electrical/EM measurements, it is therefore critical to understand how the interfacial polarization influences the effective electrical conductivity and permittivity spectra of geologic materials. We have used pore-scale simulation to study the role of material texture and packing in interfacial polarization in water-saturated granular soils. Synthetic samples with varying material textures and packing densities are prepared with the discrete element method. The effective electrical conductivity and permittivity spectra of these samples are determined by numerically solving the Laplace equation in a representative elementary volume of the samples. The numerical results indicate that the effective permittivity of granular soils increases as the frequency decreases due to the polarizability enhancement from the interfacial polarization. The induced permittivity increment is mainly influenced by the packing state of the samples, increasing with the packing density. Material textures such as the grain shape and size distribution may also affect the permittivity increment, but their effects are less significant. The frequency characterizing the interfacial polarization (i.e., the characteristic frequency) is mainly related to the electrical contrast of the solid and water phases. The model based on the traditional differential effective medium (DEM) theory significantly underestimates the permittivity increment by a factor of more than two and overestimates the characteristic frequency by approximately 1 MHz. These inaccurate predictions are due to the fact that the electrical interactions between neighboring grains are not considered in the DEM theory. A simple empirical equation is suggested to scale up the theoretical depolarization factor of grains entering the DEM theory to account for the interaction of neighboring grains in granular soils.

Characterization of an electrically conductive proppant for fracture diagnostics

Fracture diagnosis with electromagnetic (EM) and electrical tools requires proppants with high electrical conductivity and mechanical strength. Lab measurements of the electrical and hydraulic conductivity of proppants are critical for selecting the best candidates. Such measurements greatly benefit simulations, field tests, and the ultimate application of such proppants in the field. To that end, a new lab protocol is developed for measuring the electrical and hydraulic conductivity of proppants. The lab setup, which mainly includes a resistivity core holder and a Hassler sleeve core holder, allows for simulation of realistic pressure and temperature conditions when making measurements. Petroleum coke (PC) is proposed as a candidate proppant because of its widespread availability and low cost. Lab measurements show that the effective electrical conductivity of pure PC in a model fracture is approximately 5000 S/m, under a closure stress greater than [Formula: see text] (4000 psi). When PC is mixed with sand, the effective electrical conductivity of the mixture decreases with an increasing weight percentage of sand. Although sand degrades the contact between PC particles, the electrical conductivity stays reasonably high (approximately 1700 S/m) when 50% sand is added. Hydraulic conductivity measurements show that when a fracture is propped with pure PC, the measured fracture conductivity is greater than [Formula: see text] ([Formula: see text]) (dimensionless fracture conductivity greater than 100 for a shale with [Formula: see text] or 100 nD permeability) under a confining pressure of [Formula: see text] (6000 psi). This means that a fracture propped with PC is infinitely conductive in a typical shale formation. When sand is added, the fracture’s hydraulic conductivity becomes even higher, which clearly shows PC’s ability of sustaining high stresses. The proposed protocol provides a robust and effective method that can be generalized for lab testing for other candidate proppants. The data presented clearly show that PC has the potential for field-scale applications in EM hydraulic fracture diagnostics.