Thermal refraction: implications for subglacial heat flux

In this study, we explore small-scale (~1 to 20 km) thermal-refractive effects on basal geothermal heat flux (BGHF) at subglacial boundaries resulting from lateral thermal conductivity contrasts associated with subglacial topography and geologic contacts. We construct a series of two-dimensional, conductive, steady-state models that exclude many of the complexities of ice sheets in order to demonstrate the effect of thermal refraction. We show that heat can preferentially flow into or around a subglacial valley depending on the thermal conductivity contrast with underlying bedrock, with anomalies of local BGHF at the ice–bedrock interface between 80 and 120% of regional BGHF and temperature anomalies on the order of ±15% for the typical range of bedrock conductivities. In the absence of bed topography, subglacial contacts can produce significant heat flux and temperature anomalies that are locally extensive (>10 km). Thermal refraction can result in either an increase or decrease in the likelihood of melting and ice-sheet stability depending on the conductivity contrast and bed topography. While our models exclude many of the physical complexities of ice behavior, they illustrate the need to include refractive effects created by realistic geology into future glacial models to improve the prediction of subglacial melting and ice viscosity.

A grain size auto-classification of Baikouquan Formation, Mahu Depression, Junggar Basin, China

The borehole electrical imaging log offers general visual borehole wall, leaving no doubt that the conductivity contrast is sufficient to obtain a qualitative gain-size distribution of rocks. In this study, an automatic grain-size classification method is proposed using gray values of borehole electrical images from Baikouquan Formation in Mahu Depression. The first stage is comparing electrical images with cores. Gravels, sands, silts and clays are all discovered in the cores. The gravels are “mottled” in electrical images, and the bigger the spots, the coarser the gravels. The images of sands are homogeneous bright colored, and the coarser the sandy grains, the brighter the images. The electrical images of silts and clays are homogeneous brown and dark-brown colored. The second stage is auto-discriminating four categories of grain sizes roughly using averages and variances of gray values. The variances of gray values of gravels are high, whereas those of sands are medium. The gray averages of silts are between 160 and 220, whereas those of clays are larger than 200. The third stage is auto-classifying three kinds of gravels or sands finely using frequency distribution of gray values. The gray values of frequency peaks of cobbles are less than 50 and frequencies are larger than 15%, whereas those of pebbles are less than 50 or larger than 200 and frequencies are between 10% and 20%; almost gray frequencies of granules are less than 10%. The dominated gray values of coarse sandstones, medium sandstones and fine sandstones are less than 50, between 50 and 160 and ranged from 160 to 240, respectively. The proposed method is demonstrated to be useful and fast to auto-classify grain size of various rocks in conglomeratic environments.

A parametric analysis of oilfield design factors affecting the detectability and characterization of electrically conductive hydrofracks

Electrical responses in the vicinity of energized steel-cased well sources offer significant potential for monitoring induced fractures. However, the high complexity of well-fracture-host models spanning multiple length scales compels analysts to simplify their numerical models due to enormous computational costs. This consequently limits our understanding regarding monitoring capabilities and the limitations of electrical measurements on realistic hydraulically fracturing systems. Here, we use the hierarchical finite element approach to construct geoelectric models in which geometrically complex fractures and steel-cased wells are discretely represented in 3D conducting media without sacrificing the model realism and computation efficiency. We have discovered systematic numerical analyses of the electrical responses to evaluate the influences of borehole material conductivity and the source type as well as the effects of well geometry, conductivity contrast, source location, fracture growth, and fracture propagation. The numerical results indicate that the borehole material property has a strong control on the electrical potentials along the production and monitoring wells. The monopole source located at a steel-cased well results in a current density distribution that decays away from the source location throughout the well length, whereas the dipole source produces a current density that dominates mainly along the dipole length. Moreover, the conductivity contrast between the fractures and host does not change the overall pattern of the electrical potentials but varies its amplitude. The fracture models near different well systems indicate that the well geometry controls the entire distribution of potentials, whereas the characteristics of the voltage difference profiles along the wells before and after fracturing are insensitive to the well geometry and the well in which the source is located. Further, the hydraulic-fracturing models indicate that the voltage differences along the production well before and after fracturing have strong sensitivity to fracture growth and fracture set propagation.

The Levenberg–Marquardt Method for Acousto-Electric Tomography on Different Conductivity Contrast

The stability and convergence performance of Levenberg–Marquardt method for acousto-electric tomography (AET) applied to different levels of conductivity contrast is studied in this paper. As a multi-physical imaging modality, acousto-electric tomography (AET) provides high spatial imaging resolution while also conserving the high contrast property of electrical impedance tomography. The Levenberg–Marquardt method is a well known iteration scheme which can be applied for the nonlinear problem of AET. However, the influence of the conductivity contrast on the stability and convergence performances of this conductivity reconstruction method is rarely discussed in the literature. In this paper, the performance of the Tikhonov regularization-based Levenberg–Marquardt method is applied to reconstruct conductivity map with different conductivity contrast between different regions of the domain of interest (DOI). Numerical investigations are carried out for phantoms with different conductivity contrast. Reconstructed results with different levels of noise are presented and discussed in detail.

On the role of microgeometry in conductivity substitution

Conductivity substitution is the process of predicting the change in the effective electrical conductivity of a rock upon a change in conductivity of the mineral or fluid phase. Conductivity substitution is nonunique — only a range of conductivities can be predicted from knowledge of the initial effective conductivity, the porosity, and the initial and final compositions. The precise change depends strongly on the rock microstructure, which is seldom adequately known. Rigorous bounds on the change in effective conductivity upon changes in the phase conductivities for two-phase isotropic composites are used to gain insights into the roles of microgeometry and phase conductivity contrast. When the conductivity contrast between phases is high, the conductivity substitution predicted by Archie’s law corresponds approximately to the upper bound on the change of conductivity upon substitution. Inclusion modeling suggests that vuggy, highly tortuous, or partially disconnected pore space could account for conductivity changes smaller than those predicted by Archie’s law. Substitution behavior computed analytically for known microgeometries correlates with measures of microgeometry, including the fraction of connected fluid phase and variance of electric field strength in each phase. Comparison of the conductivity substitution bounds with brine-saturated sandstone data reveals that the position of measured data with respect to the conductivity substitution bounds can be indicative of the effective clay content. The bounds provide a template for better prediction of effective conductivity if we have at least some knowledge of the pore microstructure. Similarly, multiple conductivity measurements on the same rock might be used to extract more information about the rock and pore space properties than is possible with only a single measurement.

Mathematical modeling of cathodic protection of electric fields for major pipelines in anisotropic terrains

The authors consider the problem of the computational investigation of cathodic protection electric fields measured for an underground pipeline taking into account the anisotropic nature of soil specific electrical conductivity. A computational experimental method was used to compare the figures for anisotropic soils against the current distribution for a homogeneous half-space; the influence of anisotropy factors and the azimuth conductivity tensor rotation angle for pipeline-enclosing soil on the electrical parameters of cathodic protection of the pipeline were investigated. It was demonstrated that protective capacity can vary significantly for areas close to the drainage points of cathode stations and for defective segments. It was concluded that there is a need to take into account terrain structure (its electrical anisotropy) when there are prerequisites of soil lamination/fracturing, or if its specific electrical conductivity contrast in the lateral direction is in excess of 2–2.5 times.

A comparative study of inline and broadside time-domain controlled-source electromagnetic methods for mapping resistive targets on land

The land-based controlled-source electromagnetic (CSEM) method is an important tool in mapping subsurface resistivity contrast, especially for conductive target embedded in a resistive environment. For resistive targets on land, choosing an appropriate configuration to a specific field observation is quite confusing, due to the lack of systematic comparisons of different methods. We have conducted a comparison between the broadside and inline time-domain CSEM methods, using the short-offset transient electromagnetic (SOTEM) method and multitransient electromagnetic (MTEM) method as representatives respectively. We first compared the resolution of these methods by analyzing the relative target response and the misfit space of the designed models. We found that the inline MTEM method had advantages over the SOTEM method in resolving the thin resistive layer. We have developed a weighted joint inversion scheme to enhance the vertical resolution of the MTEM method. We then applied the methods to the investigation of a giant molybdenum deposit. The orebody, which is the real target of the exploration, does not have a conductivity contrast with its host. However, it sits on top of the granite porphyry, which is resistive compared with its surroundings, and so the granite porphyry becomes the resistive target for EM exploration. The results indicated that both methods are effective in locating large resistive target, yet the MTEM method outperforms the SOTEM method when a thick conductive overburden is presented.

Method of Measurement Representativeness Assessment for Spatial Conductometric Sensors as Applied to Investigation of Hydrodynamics in Single Phase Flows

The well-known method of spatial conductometry is widely used for hydrodynamical investigations in the frame of validation benchmarks. The aim of the work was to develop the method of representativeness substantiation for use of the conductometric sensors in single-phase applications.The paper presents aspects of wire-mesh sensors (WMS) applications in non-uniform conductivity fields. The equivalent electrical circuits for the measurement cell and WMS are proposed and investigated. The methods of translation from measured conductance to conductivity of the water are discussed. Decomposition of the uncertainty sources and their propagation through measurements are investigated.To obtain the «cross-talk» effect of the measurements the fi model of WMS fl domain was created. The results of calculations showed the dependence of the measurement results on the conductivity contrast in the cells as well as on the size of the contrast domain. The proposed method of the measurement uncertainty estimate was applied to the real WMS and it’s measurement system. The obtained results are topical for validation tests with the use of tracer methods and WMS.

Computational Thermal Model of Unidirectional Composites with Random Fiber Array

The purpose of this work was to study the influence of microstructure on effective transverse thermal behavior of unidirectional fiber reinforced composites. Three types of microstructures are taken into account, including square periodic, hexagonal periodic and random arrangements of circular fibers. Unlike classical results at low fiber volume fractions and low thermal conductivity contrast between fibers and matrices, results provided by finite elements simulations for copper matrix composite reinforced with Carbon T-300 fibers have shown that random microstructures strongly affect the effective thermal properties of unidirectional composites for both high volume fractions and thermal conductivity contrast and can give closer predictions to the experimental results than the regular microstructures and the theoretical model.