Effect Of Anisotropic Conductivity Research Articles

Thermo-poro-elastic analysis: The effects of anisotropic thermal and hydraulic conductivity on borehole stability in bedding formations

Laminated or layered structures exist widely in shales, which resulted in costly and laborious wellbore unstable problems. Due to the existence of bedding structures, not only the strength of rocks (like shale) is proved to be anisotropic, but also the hydraulic and thermal conductivity are tested to be anisotropic by many experiments in the literature. However, these effects are seldom illustrated by former studies when building a wellbore stability model. Aiming at the anisotropic conductivity effects (thermal and hydraulic), we derived a new model of wellbore stability: the effective thermal and hydraulic conductivity coefficients around the wellbore are first obtained based on coordinates transformation; the temperature and stress distributions in the surrounding rocks are then calculated according to thermoporoelastic theory; the failure area, the collapse and fracture pressures under different conductivity conditions are calculated and compared considering both the failure of bedding planes and rock matrix. The results show that the distributions of temperature and stresses around the wellbore, the collapse area, the collapse and fracture pressures calculated are quite different both in radial and circumferential directions under different conductivity (thermal and hydraulic) conditions. The effects of anisotropic conductivity condition (ACC) can evolve with time and at certain times these effects can be significant, which makes the consideration of ACC quite necessary. The thermoporoelastic solutions, incorporated with the effects of anisotropic conductivity, may lead to more accurate results of inclined wellbores when encountering bedding shale in drilling practice.

Evaluation of anisotropic tangential conduction in printed-circuit-board heated-thin-foil heat flux sensors

The effect of the tangential conduction contribution in a thermally anisotropic heated-thin-foil heat flux sensor is examined. A parameter to assess the degree of importance of tangential conduction in the sensor is defined and evaluated in order to justify the need of tangential conduction corrections. Printed circuit boards (PCBs) are typical examples of sensors with anisotropic thermal conduction properties, due to the different conductance values in the directions either parallel or orthogonal to the copper tracks which are placed onto a fiberglass substrate. A parametric study on PCBs with different tracks coverage fraction and copper-to-fiberglass heat conductance ratio is carried out. A revised heated-thin-foil formulation, including a correction for anisotropic thermal properties of the PCB, is experimentally tested. The selected thermo-fluid-dynamic test case is the convective heat transfer of a normally impinging round jet for which axisymmetric maps of the Nusselt number are expected. The anisotropic tangential conduction results in non-axisymmetric temperature distributions. Consequently, if anisotropy is not properly accounted for, non-axisymmetric Nusselt number maps are obtained. The anisotropic conduction effects are shown to be weakly sensitive to the copper tracks coverage fraction while strongly dependent on a parameter called degree of anisotropy, which accounts for the copper-to-fiberglass heat-conductance ratio. Anisotropic conduction effects are found to be almost negligible in PCBs with low values of the degree of anisotropy and/or low values of the tangential conduction degree of importance. Accounting for the anisotropic tangential conduction in the heated-thin-foil formulation allows minimizing the differences between the Nusselt number profiles measured in the directions parallel and orthogonal to the copper tracks. For all the considered PCBs, differences after correction are found to be below the measurement uncertainty expected for an equivalent thermally-isotropic sensor. The proposed approach also allows reducing below the measurement uncertainty the spread between the Nusselt number values measured with all the considered printed circuit boards, providing measurements practically independent of the sensor characteristics.

The Evaporation and Survival of Cluster Galaxies’ Coronae. II. The Effectiveness of Anisotropic Thermal Conduction and Survival of Stripped Galactic Tails

Abstract We simulate anisotropic thermal conduction between the intracluster medium (ICM) and the hot coronal interstellar medium (ISM) gas in cluster galaxies. In Paper I, we simulated the evaporation of the hot ISM due to isotropic (possibly saturated) conduction between the ISM and ICM. We found that hot coronae evaporate on timescales, significantly shorter than the gas loss times due to ram pressure stripping. No tails of stripped gas are formed. This is in tension with the observed ubiquity and implied longevity of compact X-ray coronae and stripped ISM tails, and requires the suppression of evaporation, possibly due to magnetic fields and anisotropic conduction. We perform a series of wind tunnel simulations similar to that in Paper I, now including ISM and ICM magnetic fields. We simulate the effect of anisotropic conduction for a range of extreme magnetic field configurations: parallel and perpendicular to the ICM wind, and continuous and completely disjointed between the ISM and ICM. We find that when conduction is anisotropic, gas loss due to evaporation is severely reduced; the overall gas loss rates with and without anisotropic conduction do not differ by more than 10%–20%. Magnetic fields also prevent stripped tails from evaporating in the ICM by shielding, and providing few pathways for heat transport between the ICM and ISM. The morphology of stripped tails and magnetic fields in the tails and wakes of galaxies are sensitive to the initial magnetic field configuration.

Systematic deviations in source direction estimates of Q‐bursts recorded at Nagycenk, Hungary

AbstractQ‐bursts are globally detectable extremely low frequency (ELF, 3–3000 Hz) band wave packets produced by intense lightning discharges. Q‐bursts recorded in the Széchenyi István Geophysical Observatory (NCK, 16.7°E, 47.6°N), Hungary, on 1 and 2 August 2012 have been analyzed to find azimuths of their sources. The location of parent lightning strokes of 320 and 205 Q‐bursts on the 2 days, respectively, have been identified in the records of the World Wide Lightning Location Network (WWLLN) using the detection times at NCK. ELF data‐based source azimuths were found to differ systematically from source azimuths obtained from WWLLN lightning locations. The difference between the corresponding azimuth values depends on the azimuth of the source. This variation of the source azimuth error mirrors the symmetry of the conductance of the Earth's crust inferred from magnetotelluric measurements around NCK. After correction for the azimuthal dependence, the variation of the residual error shows a diurnal pattern with positive azimuth deviations occurring near midnight, local time. Füllekrug and Sukhorukov (1999) suggested that the anisotropic conductivity in the Earth's crust below the observatory and the different daytime and nighttime conductivities in the lower ionosphere, respectively, may cause the identified error terms. Our results emphasize the substantial effect of anisotropic conductivity in the Earth's crust around the recording station on the accuracy of ELF direction finding. The need for theoretical approach and more measurements is pointed in understanding the underlying mechanisms quantitatively and in investigating whether ELF observations can be used in geophysical prospecting.

Anisotropic subvoxel-smooth conduction model for bioelectromagnetism analysis

The bioelectric conduction model plays a key role in bioelectromagnetism analysis, such as solving electromagnetic forward and inverse problems. This paper is aimed to develop an anisotropic subvoxel-smooth conduction model (ASCM) to characterize the electrical conductivity tensor jump across the tissue interface, which is derived based on the interfacial continuity condition with asymptotic analysis method. This conduction model is furthermore combined with finite volume method to improve the numerical accuracy for solving electromagnetic forward problem. The performance of ASCM for electrical potential analysis is verified by comparison with analytic solution. The method is also applied to investigate the effect of anisotropic conduction on EEG analysis in a realistic human head model.

Numerical Study of Magnetoacoustic Signal Generation with Magnetic Induction Based on Inhomogeneous Conductivity Anisotropy

Magnetoacoustic tomography with magnetic induction (MAT-MI) is a noninvasive imaging modality for generating electrical conductivity images of biological tissues with high spatial resolution. In this paper, we create a numerical model, including a permanent magnet, a coil, and a two-layer coaxial cylinder with anisotropic electrical conductivities, for the MAT-MI forward problem. We analyze the MAT-MI sources in two cases, on a thin conductive boundary layer and in a homogeneous medium, and then develop a feasible numerical approach to solve the MAT-MI sound source densities in the anisotropic conductive model based on finite element analysis of electromagnetic field. Using the numerical finite element method, we then investigate the magnetoacoustic effect of anisotropic conductivity under the inhomogeneous static magnetic field and inhomogeneous magnetic field, quantitatively compute the boundary source densities in the conductive model, and calculate the sound pressure. The anisotropic conductivity contributes to the distribution of the eddy current density, Lorentz force density, and acoustic signal. The proposed models and approaches provide a more realistic simulation environment for MAT-MI.

비등방 균질 댐의 정상상태에서의 침투면과 신뢰성지수

균질한 재료로 설계된 댐에서 수직 수평 투수계수가 서로 다를 경우에 이 비등방성 비율이 침투수의 침투면과 신뢰성지수에 어떤 영향을 주는지를 분석하였다. 정상상태에 있는 포화-불포화 침투수 현상을 유한요소법을 사용하여 분석하였다. 수평방향 투수계수를 고정한 상태에서 수직방향 투수계수만을 줄여주는 방법으로 여러가지 다른 비등방성 비율을 해석하였다. 댐제체의 전단강도는 수정된 모어-쿨롱 파괴기준을 사용하여 결정하였다. 해석 결과에 따르면 비등방성 비율이 증가함에 따라 침투면의 거리와 신뢰성지수는 증가하는 것으로 나타났으나 댐 상하류의 전체 수두차에 따라 차이를 보였다. 이러한 침투면과 신뢰성지수의 차이는 비등방성 비율이 변동함에 따라 등가수두선도 변화하는 현상에 의한 것으로 판단된다. This paper evaluates the effect of anisotropic conductivity on the seepage face and reliability index of an homogeneous dam with and without toe drain. The analysis are conducted under steady state saturated-unsaturated seepage condition using finite element method. Various anisotropic conductivity ratios were interpreted under such conditions as the vertical conductivity is reduced while the horizon conductivity is fixed. The shear strength of soil is defined by the modified Mohr-Coulomb failure criterion. The analysis results demonstrate that the length of seepage face and reliability index at the downstream and upstream of the dam increase with an increasing anisotropic ratio. These results of the seepage face and reliability index, however, depend on the total head difference between the upstream slope and downstream toe. The difference in seepage face and reliability index is attributed to the different equipotential head with different anisotropic ratios of the dam material.

Effect of anisotropic conductivity on suction and reliability index of unsaturated slope exposed to uniform antecedent rainfall

The authors discuss the effect of anisotropic conductivity on the suction and reliability index of an unsaturated embankment for uniform rainfall whose intensity is lower than the saturated hydraulic conductivity. The analysis is performed on good-drainage soil of a specific horizontal conductivity and various anisotropic ratios such that the vertical conductivity is reduced. The initial suction profile for the unsaturated zone is 15 kPa. The effect of the shear strength caused by matric suction in the unsaturated zone is explained by the modified Mohr–Coulomb failure criteria. The uncoupled approach of finite element method and limit equilibrium method is used to evaluate the reliability index at different elapsed time of an antecedent rainfall. The anisotropic conductivity ratios affect the volumetric water content and the suction profile. The reliability index remains practically unchanged at high anisotropic ratios but decreases noticeably at low ratios when the wetting front reaches and elevates the water table level.

3D simulation of the effects of growth parameters on the growth of sapphire crystals using heat exchanger method

Abstract3D simulations using the commercial CFDRC and FIDAP code, which are based on finite element techniques, were performed to investigate the effects of anisotropic conductivity on the convexity of the melt–crystal interface and the hot spots of sapphire crystal in a heat‐exchanger‐method crystal growth system. The convection boundary conditions of both the energy input to the crucible by the radiation as well as convection inside the furnace and the energy output through the heat exchanger are modeled. The cross‐sectional flow pattern and the shape of the melt–crystal interface are confirmed by comparing the 3‐D modeling results with previous 2D simulation results. In the 3D model, the “hot spots” in the corners of the crucible are donut shaped, and the shape changes with the value of the conductivity of anisotropic crystal. The outline of the crystal becomes more convex as the conductivity in the z direction (ksz) increases. The outline of melt–crystal interface is elliptical when the anisotropic conductivity is moving in the radial direction (ksx and ksy). The portion at the outline touching the bottom of the crucible is smaller than the maximum outline of the crystal, meaning that the shape at the “hot spot”, changes with the value of the conductivities of anisotropic crystal. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The Influence of Anisotropic Conductivity on the EEG Source Localization Investigated with an FEM Volume Conductor of an Animal Model

Purpose: Source localization based on EEG/MEG data is a widely used technique to investigate neuronal activity. It tries to localize focal sources (dipoles) in order to represent the external measured signal (EEG/MEG) solving an inverse problem. Thereby the accuracy of the results depends on the given volume conductor model. Volume conductor modeling using the Finite Element Method (FEM) opens the possibility of taking into account the anisotropic conductivity of, e.g., the white matter tracts. In our study we investigated the influence of this anisotropy on solving the forward and inverse problem using an animal model. Material: Using a T1-weighted MR image, we segmented the head of a rabbit into four different tissue layers (skin, skull, grey and white matter). Additionally, we performed diffusion-tensors imaging to obtain the anisotropy of the white matter tissue. The orientation of the diffusion tensors was used to model anisotropic conductivity tensors in the white matter of the rabbit brain employing an adopted anisotropic ratio of 1:10. 650 dipoles in the cortical region in intervals of 1mm and radial orientation served as sources. Using the anisotropic model we performed EEG simulation to asses EEG potentials at 100 electrodes placed on the rabbit head. With the computed potentials we performed source localization using the same model but with isotropic conductivity tensors. This corresponds to the assumption of a source localization with an isotropic model and realistic measurement data, which include effects of anisotropic conductivity. Results: All dipoles were shifted in their location and changed in their orientation due to the isotropic model with data derived from the anisotropic model. The shift was up to 2mm with a mean of 0.69mm. The averaged orientation deviation was 23.7 degrees and the mean magnitude change of the dipole was determined with a value of 24.2 percent. Conclusion: In this study we have shown the influence of conductivity anisotropy on EEG source simulation and localization with the help of an FEM model of a rabbit head. Volume conductor modeling in EEG source localization procedures including anisotropy will improve accuracy of the localization results.

Effect of regional differences in cardiac cellular electrophysiology on the stability of ventricular arrhythmias: a computational study

Re-entry is an important mechanism of cardiac arrhythmias. During re-entry a wave of electrical activation repeatedly propagates into recovered tissue, rotating around a rod-like filament. Breakdown of a single re-entrant wave into multiple waves is believed to underlie the transition from ventricular tachycardia to ventricular fibrillation. Several mechanisms of breakup have been identified including the effect of anisotropic conduction in the ventricular wall. Cells in the inner and outer layers of the ventricular wall have different action potential durations (APD), and support re-entrant waves with different periods. The aim of this study was to use a computational approach to study twisting and breakdown in a transmural re-entrant wave spanning these regions, and examine the relative role of this effect and anisotropic conduction. We used a simplified model of action potential conduction in the ventricular wall that we modified so that it supported stable re-entry in an anisotropic model with uniform APD. We first examined the effect of regional differences on breakdown in an isotropic model with transmural differences in APD, and found that twisting of the re-entrant filament resulted in buckling and breakdown during the second cycle of re-entry. We found that breakdown was amplified in the anisotropic model, resulting in complex activation in the region of longest APD. This study shows that regional differences in cardiac electrophysiology are a potentially important mechanism for destabilizing re-entry and may act synergistically with other mechanisms to mediate the transition from ventricular tachycardia to ventricular fibrillation.

A NUMERICAL STUDY OF ANISOTROPY AND CONVECTION DURING SOLIDIFICATION

A fixed-grid enthalpy formulation is developed to model convection and anisotropic conduction during solidification from the side or top wall of a rectangular cavity containing pure gallium. The solid-liquid interface is tracked with the use of an interface energy-balance equation. An improved discretization method is developed to prevent nonphysical oscillations due to discontinuous temperature and velocity gradients in the vicinity of the solid-liquid interface. Numerical results are compared to experimental data from the literature on the morphology and positions of the interface. The effect of anisotropic conduction in the solid interacting with thermal convection in the liquid has been studied.

An investigation of β-alumina electrolytes by electric modulus spectroscopy

Various types of β-alumina (including single-crystal cylindrical boules, Monofrax flakes polycrystalline sinters) have been investigated by electric modulus spectroscopy. The complex electric modulus is identical with the inverse complex permittivity, ie M *  ( e *) −1, and also related to the complex impedance by the equation M *  jω C 0 Z *; the modulus spectra are obtained by plotting the imaginary component, M″, vs log (frequency). The single-crystal specimens of β-alumina have spectra markedly broader than simple Debye curves, and in this respect they resemble vitreous and molten electrolytes rather than alkali halide crystals. The more complicated spectra of the polycrystalline samples show the marked effects of anisotropic conductivity. At the lowest temperatures studied (−160°C), the current appears to follow a series pathway through crystals in two distinct orientations, and it is apparently not able to seek out a preferred pathway as is the case at higher temperatures.