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Stress-Dependent Voltage Offsets From Polymer Insulators Used in Rock Mechanics and Material Testing
Dielectric insulators are used in a variety of laboratory settings when performing experiments in rock mechanics, petrology, and electromagnetic studies of rocks in the fields of geophysics,material science, and civil engineering. These components may be used to electrically isolate geological samples from the experimental equipment, to perform a mechanical compliance function between brittle samples and the loading equipment, to match ultrasonic transducers, or perform other functions. In manyexperimental configurations the insulators bear the full brunt of force applied to the sample but do not need to withstand high voltages, therefore the insulators are often thin sheets of mechanically tough polymers. From an instrument perspective, transduction from various types of mechanical perturbation has beenqualitatively compared for a number of polymers [1, 2] and these error sources are readily apparent duringhigh-impedance measurements if not mitigated. However even when following best practices, a force dependent voltage signal still remains and its behavior is explored in this presentation. In this experimenttwo thin sheets (0.25 mm) of high-density polyethylene (HDPE) were set up in a stack, held alternatelybetween three aluminum bars; this stack was placed on the platen of a 60T capacity hydraulic testingmachine. The surface area, A, over which the force is applied to the PE sheets in this sandwich is roughly 40 square cm, each sheet forming a parallel-plate capacitor having roughly 320 pF [3], assuming therelative dielectric permittivity of PE is approximately 2.3. The outer two aluminum bars were connected to the LO input ofthe electrometer and the central aluminum bar was connected to the HI input of a Keithley model 617 electrometer. Once the stack is mechanically well-seated with no air gaps, the voltage offset is observed tobe a linear function of the baseline voltage for a given change in applied force. For a periodically appliedforce of 66.7 kN the voltage offsets were measured as a function of initial voltage, and these data were fitwith a linear function that was constrained to pass through the origin. The best fit solution had a correlation coefficient of R=0.85 and a slope of approximately -0.0228 volts/volt. The voltage offset when normalizedis demonstrated to be constant -2.28% for both positive and negative polarities over nearly 3 orders ofbaseline voltage magnitude. From this, the voltage-force coefficient is derived to be -0.34 ppm/N. Thiscorrelates well to a first-order parallel plate capacitor model that assumes constant area, and smalldeformation such that the polymer may be mechanically modeled by a spring that obeys Hookes law. Thissimple model predicts that the coefficient of proportionality is a function of Youngs modulus E= 0.8 GPaand surface area of the insulator, theoretically -1EA= -0.31 ppm/N. The outcome of this work is animproved insulator made from ultra-high molecular weight (UHMW) polyethylene and other approachestoward the minimization of and compensation for these experimental artifacts.
Evolving physical and mechanical rock properties during exposure at Earth's surface
Rocks at Earth's surface experience progressive damage due to exposure to environmental conditions. Although environmental damage to rocks is recognized as being time-dependent, our quantitative understanding of its effects on physical and mechanical properties remains limited by field and laboratory studies constrained to short timescales. In this study, we aim to rigorously quantify how these properties evolve under longer natural environmental exposure spanning from the Holocene to the late Pleistocene. We conducted a ‘time series’ analysis of key physical and mechanical rock properties using multiple interior samples from 10 cogenetic granitoid boulders exposed for different amounts of time at two sites in Eastern California, USA. We find that over the late Pleistocene (~30 ka), rocks exhibit porosity increases of 40 ± 4 % and seismic velocity decreases of 7 ± 1 % at both sites. Similarly, over the same time period, rock tensile and compressive strengths declined by an average of 11 ± 4 %, and rock permeability increased on average by 104 ± 50 %. Microscopic analysis of thin sections of the same rocks indicates that microfracture density and intensity also progressively increased over the same timescales. These results suggest that time-dependent fracture propagation due to environmental exposure is likely a central contributor to the observed changes in rock properties. This study provides quantitative documentation that pronounced changes in the physical and mechanical properties of rock progressively occur within thousands of years of exposure.
Examination of Mean Stress Calculation Approaches in Rock Mechanics
The mean stress, as a fundamental statistical property of a group of stress data, is essential for stress variability characterisation. However, currently in rock mechanics, the mean stress is customarily and erroneously calculated by separately averaging the principal stress magnitudes and orientations. In order to draw the attention of our community to the appropriate approach for stress variability characterisation, here we compare the customary scalar/vector mean with that obtained by the mathematically rigorous tensorial approach—the Euclidean mean. Calculation of mean stress using both a small group of actual in situ stress measurement results and a large group of simulated stress data (obtained using the combined finite– discrete element method, FEMDEM) demonstrates that the two approaches yield different results. Further investigation of these results shows that the scalar/vector approach may yield non-unique and non-orthogonal mean principal stresses, and these may deviate significantly from those of the Euclidean mean. Our calculations and comparisons reveal that the scalar/ vector approach is deficient because it processes the principal stress magnitudes and orientations separately as independent quantities and ignores the connection between them. Conversely, the tensorial approach appropriately averages the tensors that simultaneously carry not only the information of stress magnitudes and orientations, but also the inherent relations between them. Therefore, arbitrarily using scalar/vector mean stress of in situ stress measurements as input in further rock engineering analyses may yield significantly erroneous results. Finally, we advise that stress data should be statistically processed in a tensorial manner using tensors referred to a common Cartesian coordinate system.
Assessing the carbon sequestration potential of basalt using X-ray micro-CT and rock mechanics
Mineral carbonation in basaltic rock provides a permanent storage solution for the mitigation of anthropogenic CO 2 emissions in the atmosphere. 3D X-ray micro-CT (XCT) image analysis is applied to a core sample from the main basaltic reservoir of the CarbFix site in Iceland, which obtained a connected porosity of 2.05–8.76%, a reactive surface area of 0.10–0.33 mm -1 and a larger vertical permeability (2.07 × 10 -10 m 2 ) compared to horizontal permeability (5.10 × 10 -11 m 2 ). The calculations suggest a CO 2 storage capacity of 0.33 Gigatonnes at the CarbFix pilot site. The XCT results were compared to those obtained from a hydromechanical test applied to the same sample, during which permeability, electrical resistivity and volumetric deformation were measured under realistic reservoir pressure conditions. It was found that permeability is highly stress sensitive, dropping by two orders of magnitude for a -0.02% volumetric deformation change, equivalent to a mean pore diameter reduction of 5 μm. This pore contraction was insufficient to explain such a permeability reduction according to the XCT analysis, unless combined with the effects of clay swelling and secondary mineral pore clogging. Here the findings provide important benchmark data for the future upscaling and optimisation of CO 2 storage in basalt formations.
Investigation of acoustic waves under subsurface conditions to improve the predictions of rock mechanical properties and natural fracture characteristics
Mechanical properties and natural fracture characteristics are critical to investigate for subsurface engineering applications, including carbon storage, well drilling, and stimulation, as they govern rock stability, fluid flow, and mechanical behavior under stress. This dissertation integrates experimental and machine learning approaches to enhance the prediction and understanding of these properties by analyzing acoustic wave behavior under varied subsurface conditions. First, the influence of temperature, pore pressure, and supercritical CO2 (scCO2) saturation on poroelastic properties is examined using Gray Berea sandstone samples. The results show that temperature and pore pressure significantly affect the bulk modulus and Biot’s coefficient, while scCO2 saturation impacts rock compressibility, informing strategies for effective geological carbon storage. The study extends this understanding by experimentally evaluating the impact of reservoir depletion on the dynamic mechanical properties of the emerging Caney shale in South Oklahoma with the employment of unsupervised machine learning to predict static mechanical properties across the Caney shale. Integrating petrophysical data and chemostratigraphy, the workflow—featuring K-means clustering, principal component analysis (PCA), and inverse distance weighting (IDW)—improves stratigraphic characterization and the estimation of static-to-dynamic modulus ratios, which is vital for optimizing drilling and stimulation strategies. Finally, the work explores how natural fracture characteristics in shale influence acoustic waveforms and shear wave splitting (SWS) analysis. Experimental data on fractured samples under different stress and temperature conditions, combined with machine learning models such as K-nearest neighbors (KNN) and extreme gradient boosting (XGBoost), reveal key fracture properties impacting SWS and wave propagation. Together, these studies provide a comprehensive framework for linking acoustic wave behavior with rock properties, advancing the methods for monitoring and predicting geomechanical changes. The insights offered valuable implications for safer, more efficient CO2 injection, hydrocarbon extraction, and subsurface management.
Review of low salinity waterflooding in carbonate rocks: mechanisms, investigation techniques, and future directions
This review analyses the fundamental thermodynamic theory of the crude oil-brine-rock (COBR) interface and the underlying rock-brine and oil-brine interactions. Next, the available data are reviewed to outline potential mechanisms responsible for increased oil recovery from low salinity waterflooding (LSWF). We propose an approach to studying LSWF and identify the key missing links that are needed to explain observations at multiple length scales. The synergistic effect of LSWFon other chemical enhanced oil recovery methods such as surfactant, alkaline, nanoparticle and polymer flooding are also outlined. We specifically highlight key uncertainties that must be overcome to fully implement the technique in the field.
TOUGH-RFPA: Coupled thermal-hydraulic-mechanical Rock Failure Process Analysis with application to deep geothermal wells
This paper presents a coupled thermal-hydraulic-mechanical (THM) model for simulating failure processes in geological media. The coupling between stress/strain and heat transfer describing how thermal expansion affects stress is based on the theory of thermo-elasticity. Additionally, the coupling between stress/strain and fluid flow describing how pore-pressure affects stress is governed by Biot's consolidation theory. Stress/strain-dependent porosity/permeability/capillary-pressure defines the influence of stress on fluid flow and thermal fields. The THM model is implemented in the solver module that links the multiphase, multicomponent fluid flow simulator TOUGH2 with the geomechanical simulator RFPA (Rock Failure Process Analysis), which is based on the concept that heterogeneity leads to non-linearity and progressive failure behavior. Capability of TOUGH-RFPA simulator was verified by two benchmark problems related to hydraulic-mechanical and thermal-mechanical response in a hollow cylinder. Then the applicability of TOUGH-RFPA was demonstrated for modeling cooling-induced damage around a very deep geothermal well with mesoscopic heterogeneous properties, which showed complex damage evolution and fracturing during well cooling and fluid pressurization.
Modeling Distributed Fiber Optic Sensor Signals Using Computational Rock Mechanics
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Reference Stratigraphy Applied to Rock Mechanics Studies for the Waste Isolation Pilot Plant: A Review - January 11, 2017
Reference stratigraphy for the Waste Isolation discernible clay in the orange halite, and Pilot Plant (WIPP) was developed to provide a standard for comparing the results of different models of mechanical behavior of the WIPP underground (e.g., Krieg, 1984) (Figure 1). Munson et al. (1989) revised the reference stratigraphy (Figure 2), and they concluded that mechanical behavior at WIPP was better represented by a different distribution of lithologies, in particular by assigning most of the units in the reference stratigraphy to “argillaceous halite” rather than as “clean halite.” Here I re-evaluate the background for these reference stratigraphies and lithology by examining core and other data.
Subsidence‐Derived Volumetric Strain Models for Mapping Extensional Fissures and Constraining Rock Mechanical Properties in the San Joaquin Valley, California
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Determining the eect mechanical rock properties have on variability in fracture gradients.
Abstract not provided.
Stress-sensitivity of fracture conductivity of Tuscaloosa Marine Shale cores
Production decline from wells producing from shale rocks is typically quite rapid. One possible factor responsible for such decline is loss in fracture conductivity. This is true in the case of the Tuscaloosa Marine shale reservoir. In this work, the stress-dependent fracture conductivity of TMS core samples is investigated using five propped cores under varying stress conditions. In addition, the effects of static rock mechanical properties and rock mineralogy on conductivity decline are investigated. The mineralogy of each core sample was determined by X-ray Diffraction analysis. Fracture conductivity was measured using a Hassler-type pressure core holder with a pressure rating of 15,000 psi (103.42 MPa). Estimated rock mechanical properties showed that shale anisotropy could affect fracture conductivity. The time decline in conductivity revealed two possible decline trends, a) decline from the reduction in induced fracture width, and b) decline from the healing of developed micro-cracks. An exponential decline in fracture conductivity with increasing confinement pressure was observed with an average decline rate constant of 3.15 x 10 -10 mPa -1 . While rock mineralogy did not have any clear relationship with conductivity decline, the effects of rock mechanical properties were only important at 10.34 MPa confinement pressure and above. The observation showed that a high Young's modulus correlate to high conductivity, whereas a high Poisson's ratio correlate to low conductivity. This study provides useful observations for optimizing fracture design to enhance well productivity in the TMS.
Modeling of rock scour using coupled 3-D discrete element and Lattice Boltzmann Methods
Copyright © 2018 ARMA, American Rock Mechanics Association. Scour of rock in unlined rock spillway channels is a critical issue facing many of the world’s dams. From a modeling point of view this poses a challenging and interesting problem that combines rock mechanics and hydraulics of turbulent flow. We analyze this interaction between the blocky rock mass and water by directly modeling the solid and fluid phases—the individual polyhedral blocks are modeled using the Discrete Element Method (DEM) while the water is modeled using the Lattice Boltzmann Method (LBM). The LBM mesh is entirely independent of the DEM discretization, making it possible to refine the LBM mesh such that transient and varied fluid pressures acting of the rock surface are directly modeled. This provides the capability to investigate the effect of water pressure inside the fractured rock mass, along potential sliding planes, and can be extended to rock falls and slides into standing bodies of water such as lakes and reservoirs. Herein we present preliminary results to demonstrate the capabilities of the methodology.
Extended Barton–Bandis model for rock joints under cyclic loading: Formulation and implicit algorithm
In this paper, the Barton–Bandis model for rock joints is extended to cyclic loading conditions, without any new material parameter. Also developed herein is an implicit solution algorithm for the extended Barton–Bandis model, which can also be used for the original Barton–Bandis model for which an implicit algorithm has been unavailable. To this end, we first cast the Barton–Bandis model into an incremental elasto-plastic framework, deriving an expression for the elastic shear stiffness being consistent with the original model formulation. We then extend the model formulation to cyclic loading conditions, incorporating the dependence of shear stress and dilation on the joint position and the shearing direction. The extension is achieved by introducing a few state-dependent variables which can be calculated with the existing material parameters. For robust and accurate utilization of the model, we also develop an implicit algorithm based on return mapping, which is unconditionally stable and guarantees the satisfaction of the strength criterion. We verify that the proposed model formulation and algorithm produce virtually the same results as the original Barton–Bandis model under monotonic shearing conditions. Here, we then validate the extended Barton–Bandis model against experimental data on natural rock joints under cycling loading conditions. The present work thus enables the Barton–Bandis model, which has been exceptionally popular in research and practice, to be applicable to a wider range of problems in rock mechanics and rock engineering.
Stress and Strain Heterogeneity and Persistence in Uniaxially‐ and Triaxially‐Loaded Sandstone
Two critical questions in brittle rock mechanics are how rocks developed localized strains and to what extent internal stress heterogeneity controls this localization and subsequent macroscopic failure. Definitive answers have not yet been found, but would provide insight into rock fracture mechanics as relevant to hydrocarbon extraction and sequestration. Here, we use synchrotron X‐ray tomography (XRT) and 3D X‐ray diffraction (3DXRD) during uniaxial and triaxial tests on Nugget and Bentheimer sandstones to examine strain and stress localization prior to mechanical failure. 3DXRD was used to measure intra‐granular lattice strains which were used to compute elastic stress tensors of each grain. Digital volume correlation (DVC) was applied to XRT images to determine the strain field in the sample. Both samples featured marked spatial heterogeneity, localization, and temporal persistence of elevated stresses and strains during their mechanical deformation toward failure. Both samples featured a majority of grains with at least one principal stress component that was tensile, a signature of the influence of heterogeneity on stress transmission. Measurements further revealed that compressive stress orientations and statistics evolved in a similar manner to those of inter‐particle forces in loose granular materials, with triaxially‐compressed rock exhibiting enhanced grain stress heterogeneity compared to uniaxially‐compressed rock. Our results complement recent work by others who employed XRT and scanning 3DXRD to study triaxially‐compressed sandstone, but extend those results to uniaxial compression, sandstones of varied porosity, and grain stress measurements throughout the 3D full extent of the samples rather than in a single layer examined with scanning 3DXRD.