scholarly journals Theoretical and Numerical Study on Electrical Resistivity Measurement of Cylindrical Rock Core Samples Using Perimeter Electrodes

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4382
Author(s):  
Ji-Won Kim ◽  
Chang-Ho Hong ◽  
Jin-Seop Kim ◽  
Song-Hun Chong
Keyword(s):  
Numerical Simulation ◽  
Electrical Resistivity ◽  
Hydraulic Conductivity ◽  
Lower Bound ◽  
Electrical Resistance ◽  
Equipotential Surface ◽  
Theoretical Equation ◽  
Simulation Tool ◽  
Stress Strain ◽  
Core Samples

The estimation of hydraulic and mechanical properties of bedrock is important for the evaluation of energy-related structures, including high-level nuclear waste repositories, hydraulic fracturing wells, and gas-hydrate production wells. The hydraulic conductivity and stress–strain curves of rocks are conventionally measured through laboratory tests on cylindrical samples. Both ASTM standards for hydraulic conductivity and compressive strength involve the use of the planar bases of a cylindrical sample. Hence, an alternative test method is required for the simultaneous measurement of hydraulic conductivity and stress–strain curves. This study proposes a novel electrical resistivity estimation method using two perimeter electrodes for the estimation of hydraulic properties. The theoretical background for the perimeter electrode setup is derived and the COMSOL MultiPhysics® finite element numerical simulation tool is employed to verify the derived theoretical equation. The accuracy of the numerical simulation tool is first validated by simulating the ASTM standard testing method for electrical resistivity. The electrical resistance values derived from the theoretical equation and numerical simulation are compared for different electrical resistivity and electrode radius. The assumed equidistant, circular equipotential surface results in a theoretical lower bound for the measured electrical resistance in the cylindrical specimen. The introduction of a phenomenological distortion factor to correct for the theoretical equipotential surface results in a good fit with the numerical simulation results. The effects of electrode length and equivalent strap electrodes were investigated to assess the applicability of the suggested method for laboratory testing. Consequently, this study presents an effective alternative theoretical assessment method for the lower bound electrical resistivity of cylindrical rock core samples under confining conditions when the installation of base electrodes is infeasible.

Simplified estimation of unsaturated soil hydraulic conductivity using bulk electrical conductivity and particle size distribution

Soil Research ◽  
2013 ◽  
Vol 51 (1) ◽  
pp. 23 ◽  
Author(s):  
Mohammad Reza Neyshabouri ◽  
Mehdi Rahmati ◽  
Claude Doussan ◽  
Boshra Behroozinezhad
Keyword(s):  
Electrical Conductivity ◽  
Particle Size ◽  
Hydraulic Conductivity ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Unsaturated Soil ◽  
Soil Core ◽  
Soil Hydraulic Conductivity ◽  
Core Samples ◽  
Soil Hydraulic

Unsaturated soil hydraulic conductivity K is a fundamental transfer property of soil but its measurement is costly, difficult, and time-consuming due to its large variations with water content (θ) or matric potential (h). Recently, C. Doussan and S. Ruy proposed a method/model using measurements of the electrical conductivity of soil core samples to predict K(h). This method requires the measurement or the setting of a range of matric potentials h in the core samples—a possible lengthy process requiring specialised devices. To avoid h estimation, we propose to simplify that method by introducing the particle-size distribution (PSD) of the soil as a proxy for soil pore diameters and matric potentials, with the Arya and Paris (AP) model. Tests of this simplified model (SM) with laboratory data on a broad range of soils and using the AP model with available, previously defined parameters showed that the accuracy was lower for the SM than for the original model (DR) in predicting K (RMSE of logK = 1.10 for SM v. 0.30 for DR; K in m s–1). However, accuracy was increased for SM when considering coarse- and medium-textured soils only (RMSE of logK = 0.61 for SM v. 0.26 for DR). Further tests with 51 soils from the UNSODA database and our own measurements, with estimated electrical properties, confirmed good agreement of the SM for coarse–medium-textured soils (<35–40% clay). For these textures, the SM also performed well compared with the van Genuchten–Mualem model. Error analysis of SM results and fitting of the AP parameter showed that most of the error for fine-textured soils came from poorer adequacy of the AP model’s previously defined parameters for defining the water retention curve, whereas this was much less so for coarse-textured soils. The SM, using readily accessible soil data, could be a relatively straightforward way to estimate, in situ or in the laboratory, K(h) for coarse–medium-textured soils. This requires, however, a prior check of the predictive efficacy of the AP model for the specific soil investigated, in particular for fine-textured/structured soils and when using previously defined AP parameters.

scholarly journals Fatal Void Size Comparisons in Via-Below and Via-Above Cu Dual-Damascene Interconnects

2004 ◽  
Vol 812 ◽  
Author(s):  
Z. -S. Choi ◽  
C. L. Gan ◽  
F. Wei ◽  
C. V. Thompson ◽  
J. H. Lee ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Failure Mechanisms ◽  
Simulation Tool ◽  
Void Size ◽  
Dual Damascene ◽  
Preferential Nucleation ◽  
Failure Correlation ◽  
Void Volumes ◽  
Damascene Interconnects ◽  
Critical Void

AbstractThe median-times-to-failure (t50's) for straight dual-damascene via-terminated copper interconnect structures, tested under the same conditions, depend on whether the vias connect down to underlaying leads (metal 2, M2, or via-below structures) or connect up to overlaying leads (metal 1, M1, or via-above structures). Experimental results for a variety of line lengths, widths, and numbers of vias show higher t50's for M2 structures than for analogous M1 structures. It has been shown that despite this asymmetry in lifetimes, the electromigration drift velocity is the same for these two types of structures, suggesting that fatal void volumes are different in these two cases. A numerical simulation tool based on the Korhonen model has been developed and used to simulate the conditions for void growth and correlate fatal void sizes with lifetimes. These simulations suggest that the average fatal void size for M2 structures is more than twice the size of that of M1 structures. This result supports an earlier suggestion that preferential nucleation at the Cu/Si3N4 interface in both M1 and M2 structures leads to different fatal void sizes, because larger voids are required to span the line thickness in M2 structures while smaller voids below the base of vias can cause failures in M1 structures. However, it is also found that the fatal void sizes corresponding to the shortest-times-to-failure (STTF's) are similar for M1 and M2, suggesting that the voids that lead to the shortest lifetimes occur at or in the vias in both cases, where a void need only span the via to cause failure. Correlation of lifetimes and critical void volumes provides a useful tool for distinguishing failure mechanisms.

Research on Hydraulic Conductivity of Coarse Sandstone under Triaxial Compression

2011 ◽  
Vol 94-96 ◽  
pp. 1146-1151 ◽  
Author(s):  
Guan Rong ◽  
Xiao Jiang Wang
Keyword(s):  
Hydraulic Conductivity ◽  
Circumferential Strain ◽  
Triaxial Compression ◽  
Confining Pressure ◽  
Test Results ◽  
Stress Strain ◽  
Deformation And Failure ◽  
Maximum Value ◽  
Strain Process ◽  
Peak Value

Permeability test for complete stress-strain process of coarse sandstone were carried out in triaxial test instrument. On the basis of test results, the influence of confining pressure and strain on the hydraulic conductivity was discussed. It is shown that in the complete stress-strain process, hydraulic conductivity changes in the law that presents the same character with the curve of stress-strain. The hydraulic conductivity reduces slightly with the increase of deviatoric stress in the stage of micro fracture compressing and elastic; In the elastoplastic stage, along with the expansion of new fractures, the hydraulic conductivity increases slowly at first and then reaches sharply to the maximum value after peak point; In the post-peak stage, the fracture which controls the hydraulic conductivity of coarse sandstone is compressed because of the confining pressure and the hydraulic conductivity decreases. During the process of deformation and failure, the hydraulic conductivity is more sensitive to the change of circumferential strain. With the increase of confining pressure, the increased value from initial to peak value and the decreased value from peak to residual value decreases.

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