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All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Role of crystallographic orientation on intragranular void growth in polycrystalline FCC materials

In this study, we study the effect of crystallographic orientation and applied triaxiality on the growth of intragranular voids. Two 3D full-field micromechanics methods are used, the dilatational visco-plastic fast-Fourier transform (DVP-FFT) and the crystal plasticity Finite Elements (CP-FE), both of which incorporate a combination of crystalline plasticity and dilatational plasticity. We demonstrate with several select cases that predictions of void growth from both formulations agree qualitatively. With the more computationally efficient DVP-FFT, additional effects of polycrystalline microstructure and the influence of nearest neighborhood are investigated. Crystals bearing a single intracrystalline void are studied in three types of 3D microstructural environments: isolated single crystals, individual equal-sized grains within a regular polycrystal, and individual variable sized grains within a polycrystal with grains and voids randomly located. We show that loading type plays a significant role. In strain-rate controlled conditions, voids in the hardest [111]-crystals grow the fastest in time, whereas in stress-controlled conditions, voids in the softest [100]-crystal grow the fastest in time. The analysis reveals that on average void growth is slower for the same starting orientation in the polycrystal than in the single crystal. We find that at the highest triaxiality tested that the correlation between crystal orientation and void growth rate in the polycrystal strengthens, drawing closer to that seen in the isolated single crystals. These results and model can help guide the microstructural design of polycrystalline materials with high strength and damage-tolerance in high-rate deformation.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Integrating Experiments and Well Logs to Predict Caney Shale Static Mechanical Properties During Production with Supervised Machine Learning

Caney shale is one of the emerging oil reservoirs in Oklahoma. Understanding the impact of effective stress on its mechanical properties is critical for predicting hydraulic fracture geometry and overall hydrocarbon production. The objective of our study is to evaluate the impact of effective stress on the dynamic Young’s modulus using ultrasonic velocity measurements for Caney shale samples. A triaxial cell was utilized to measure ultrasonic (P-wave and S-wave) velocities for ten downhole Caney shale samples under various effective stresses to indirectly assess the impact of pore pressure change. The dynamic Young’s moduli estimated from these measurements were integrated with available conventional well logs (excluding sonic logs) and triaxial test results from Benge et al. (2021) to predict the static Young’s modulus using Random Forest (RF) and Extreme Gradient Boosting (XGBoost) models. The results showed that the estimated dynamic Young’s moduli from ultrasonic measurements were higher than the corresponding static Young’s modulus of cores from the same vertical well at similar depths. With increasing effective stress, the dynamic Young’s modulus increased for all samples. The estimated dynamic-to-static correction factor tended to be higher in zones of high neutron porosity (PHIN) and low density compared to other zones. Finally, SHapley Additive exPlanations (SHAP) for RF and XGBoost models identified depth, gamma ray (GR), and PHIN as key features for predicting the static Young’s modulus. This study enhances our understanding of the dynamic and static Young’s moduli for the Caney shale interval, as a function of effective stress and conventional well logs. The findings from this study can improve predictions of production throughout the well's lifespan by offering insights into the mechanical property degradation resulting from pore pressure depletion.

Kholy, Sherif M.↗
DOE OSTI2025

Predicting Dynamic-to-Static Correction Factor from Petrophysical Data and Chemostratigraphy using Unsupervised Machine Learning

Estimating static mechanical properties of stratigraphic layers is critical for optimizing subsurface engineering applications. To estimate dynamic-to-static correction factor F ds (static-to-dynamic Young’s modulus ratio) across the Caney shale interval in Oklahoma, USA, we integrated triaxial test measurements and petrophysical data, including well logs and X-ray fluorescence (XRF) using unsupervised machine learning (ML). We used a novel workflow that includes principal component analysis (PCA) to reduce data set dimensionality of well logs and XRF data sets—both separately and combined—creating three scenarios, and later applied inverse distance weighting (IDW) to derive F ds profiles for these scenarios. Furthermore, we applied K-means clustering on each scenario to predict depositional facies, and built a stiffness zonation profile through chemostratigraphic analysis of the terrigenous elements to validate the predicted F ds . The predicted F ds profile from each scenario using the PCA-IDW method was compared with the constant F ds approach from our previous study by calculating the root mean square error (RMSE). The combined data sets scenario yielded the lowest RMSE value of 0.113, while the RMSE values for the well logs and XRF scenarios were 0.131 and 0.129, respectively. In addition, the predicted F ds from the XRF scenario well-matched the stiffness zonation from the chemostratigraphic analysis that was built using the optimized K-means clustering of nine clusters for that scenario. These methods and findings offer a valuable tool for refining lithological classification and improving the F ds profile, potentially enhancing drilling and stimulation strategies for subsurface energy engineering applications.

clastic rock↗
DOE OSTI2022

A Geomechanical Model for Gas Hydrate Bearing Sediments Incorporating High Dilatancy, Temperature, and Rate Effects

The geomechanical behavior of methane hydrate bearing sediments (MHBS) is influenced by many factors, including temperature, fluid pressure, hydrate saturation, stress level, and strain rate. The paper presents a visco-elastoplastic constitutive model for MHBS based on an elastoplastic model that incorporates the effect of hydrate saturation, stress history, and hydrate morphology on hydrate sediment response. The upgraded model is able to account for additional critical features of MHBS behavior, such as, high-dilatancy, temperature, and rate effects. The main components and the mathematical formulation of the new constitutive model are described in detail. The upgraded model is validated using published triaxial tests involving MHBS. The model agrees overly well with the experimental observations and is able to capture the main features associated with the behavior of MHBS.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Utah FORGE 2439: A Multi-Component Approach to Characterizing In-Situ Stress

Core-based in-situ stress estimation, Triaxial Ultrasonic Velocity (labTUV) data, and Deformation Rate Analysis (DRA) data for Utah FORGE well 16A(78)-32 using triaxial ultrasonic velocity and deformation rate analysis. Report documenting a multi-component approach to characterizing in-situ stress at the U.S. DOE FORGE EGS site: laboratory, modeling and field measurement. Core-based methods for in-situ stress estimation were applied using samples from 5 intervals within the Utah FORGE 16A(78)-32 well. At three of these locations, Triaxial Ultrasonic Velocity (labTUV) tests were performed, resulting in experimentally-determined relationships between wave velocities and stresses. Non-monotonic increase in the velocity-stress relationships are inferred provide evidence of stress history and are therefore used to estimate in-situ stress magnitudes. Additionally, Deformation Rate Analysis (DRA) tests were run on core plugs from various orientations at each of the 5 sampling locations. These, too, provide evidence of stress history based on stress-strain behavior. A novel Weight of Evidence (WoE) method was developed as a means of synthesizing in-situ stress evidence from these two types of tests. Results indicate the minimum horizontal stress gradient ranges from 0.58 psi/ft to 0.69 psi/ft, with 4 of the 5 values between 0.66 psi/ft and 0.69 psi/ft. The vertical stress gradient ranges from 1.05 psi/ft to 1.12 psi/ft, with 4 of the 5 zones given results between 1.09 psi/ft and 1.12 psi/ft. The maximum horizontal stress gradient ranges from 0.98 psi/ft to 1.34 psi/ft, with 4 of the 5 zones falling between 0.98 psi/ft and 1.24 psi/ft. The stress regime thus appears to be on the edge between normal faulting and strike-slip faulting, potentially flipping back and forth between the two regimes due to variability of rock properties, structures such as faults, and/or thermal anomalies.

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Utah FORGE 5-2557: Trixial Shear and Wellbore Breakout Tests Report and Data

Included are a report and data from triaxial shear tests on simulated Sierra White fault gouge and a borehole stimulation experiment. This serves as a progress report for the Role of Fluid and Temperature in Fracture Mechanics and Coupled Thermo-Hydro-Mechanical-Chemical (THMC) Processes for Enhanced Geothermal Systems project by Purdue University (Utah FORGE R&D project 5-2557). Tests were done with Sierra White granite (SWG) to investigate slip mechanisms and to evaluate the fracture initiation and propagation from a geothermal borehole. Raw data is provided alongside a report on all experimental testing protocols, experimental design, and results.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Geophysical Signatures of Crack Network Coalescence in Rocks at Multiple Length Scales

The main goal of the research project was to identify the geophysical signatures of fracture growth in natural rocks by utilizing novel geophysical techniques. The research objectives were to (a) investigate the potential for geophysical methods to determine when cracks initiate, the types and locations of propagated cracks, and the coalescence of networks of cracks in natural rocks at multiple scales, (b) determine how damage at the microscale evolved into damage at the macroscale and then link the microscopic and macroscopic observations, (c) quantify crack coalescence in rocks under realistic stress conditions using coupled mechanical-geophysical-optical visualization, and (d) identify the precursors in geophysical signals to crack coalescence. The following research thrusts were explored to achieve the research objectives: (1) uniaxial compression testing of rock specimens with and without a set of pre‐existing flaws and (2) triaxial compression testing of natural rock specimens. These thrusts allowed for exploring fracturing in rocks under realistic in situ environments and at multiple scales. This project provided educational opportunities for nine graduate and undergraduate students and resulted in 27 peer-reviewed publications. This first research thrust focused on investigating the micromechanics of fractures in rocks through uniaxial compression testing combined with advanced geophysical and imaging techniques, specifically acoustic emission (AE) monitoring, ultrasonic imaging, and 2-dimensional Digital Image Correlation (2D-DIC). By examining damage processes under time-independent and time-dependent loading conditions, insights into damage localization, crack initiation, and fracturing mechanisms were gained. It was observed that the AE signals and the strain-based measurements directly reflect the state of damage in the rock specimen and could be used to identify the cracking levels, such as the crack initiation (CI) and crack damage (CD), and the mode of deformation. A novel calibration apparatus was developed to enhance the accuracy of AE sensors, allowing for the estimation of key parameters such as magnitude, source dimension, stress drop, and radiated seismic energy associated with the fractures. The findings highlighted significant variations in the temporal evolution of AE source parameters during the primary, secondary, and tertiary stages of creep, identifying tensile cracking as the primary deformation mode. The second research thrust focused on enhancing the understanding of fracturing processes in natural rocks through triaxial compression testing, real-time AE monitoring, and ultrasonic monitoring. We investigated the impact of various factors such as fracture propagation regimes, injection parameters, rock types, and pre-existing conditions on the hydraulic fracture (HF) behavior using scaled true-triaxially loaded specimens of Barre granite and Lyons sandstone. Custom sensor housing facilitated concurrent active and passive monitoring to analyze hydro-mechanical responses and microseismicity associated with different HF scenarios. A coupled investigation of passive microseismicity and active signal attributes permitted a detailed comprehension of the various HF processes (aseismic deformation, fracture initiation and propagation, fluid permeation, and leak-off) and their dependence on the specific rock type. The findings of this research demonstrated the effectiveness of AE monitoring techniques in providing valuable insights into the impact of various factors on the behavior and dynamics of HF processes. The advancements in monitoring techniques, offering a more thorough and precise approach, represent a significant step towards optimizing HF practices and ensuring sustainable resource extraction.

58 GEOSCIENCES↗
DOE OSTI2023

Utah FORGE: Triaxial Direct Shear Results

This submission contains a report and associated data from triaxial direct shear tests conducted by Los Alamos National Laboratory. The samples used were sourced from 16A(78)-32 well core. The primary objectives of this test were to determine the shear strength in both intact and residual states, evaluate dilation against displacement, assess permeability in relation to displacement, time, and normal stress, understand the relationship between aperture and normal stress, and monitor the effluent chemistry as a function of time.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Utah FORGE: Triaxial Direct Shear Results - February 2025

This dataset contains results from nine triaxial direct shear tests conducted by Los Alamos National Laboratory on samples from FORGE Well 16A(78)-32. The primary objectives of this work were to determine the shear strength in both intact and residual states, evaluate dilation against displacement, assess permeability in relation to displacement, time, and normal stress, understand the relationship between aperture and normal stress, and monitor the effluent chemistry as a function of time. The data includes time-series measurements of stress, displacement, permeability, and effluent chemistry, with and without experimental dilution corrections. Additional materials include profilometry data, photographic documentation of the experimental setups and apparatus, and test notes. The dataset is organized into folders corresponding to each test, containing hydromechanical data, effluent chemistry measurements, and images. The hydromechanical data consists of detailed time-series records capturing parameters such as shear force, confining pressure, permeability, and temperature. Effluent chemistry data tracks fluid composition changes over time. Also included are conference papers, presentation slides, and a summary document outlining the experiments.

15 GEOTHERMAL ENERGY↗
DOE OSTI2022

Directional Cooling-Induced Fracturing: Directional Cooling Data Under True-Triaxial Stress State

Data includes Directional Cooling-Induced Fracturing (DCIF) testing data using westerly granite blocks. This submission includes data from two samples of westerly granite, lab sample 7 and 8. Files contain stress, temperature and acoustic emission data acquired during polyaxial, laboratory testing of westerly granite blocks for each sample. FILES: .tradb -- files containing acoustic emission waveforms; sqlite3 database .pridb -- files containing basic acoustic emission information (no waveforms); sqlite3 database .geom -- geometry of the AE sensor network (ASCII)

15 GEOTHERMAL ENERGY↗
DOE OSTI2023

Assessing continuum plasticity postulates with grain stress and local strain measurements in triaxially compressed sand

Critical state and continuum plasticity theories have been used in research and engineering practice in soil and rock mechanics for decades. These theories rely on postulated relationships between material stresses and strains. Some classical postulates include coaxiality between stress and strain rates, stress–dilatancy relationships, and kinematic assumptions in shear bands. Although numerical and experimental data have quantified the strains and grain kinematics in such experiments, little data quantifying grain stresses are available. Here, we report the first-known grain stress and local strain measurements in triaxial compression tests on synthetic quartz sands using synchrotron X-ray tomography and 3D X-ray diffraction. We use these data to examine the micromechanics of shear banding, with a focus on coaxiality, stress-dilatancy, and kinematics within bands. Our results indicate the following: 1) elevated deviatoric stress, strain, and stress ratios in shear bands throughout experiments; 2) coaxial principal compressive stresses and strains throughout samples; 3) significant contraction along shear bands; 4) vanishing volumetric strain but nonvanishing stress fluctuations throughout samples at all stages of deformation. Our results provide some of the first-known in situ stress and strain measurements able to aid in critically evaluating postulates employed in continuum plasticity and strain localization theories for sands.

42 ENGINEERING↗
DOE OSTI2023

Improved Compaction Experiments and Modeling of Waste Isolation Pilot Plant Standard, Non-degraded, Waste Containers

A credible simulation of disposal room porosity at the Waste Isolation Pilot Plant (WIPP) requires a tenable compaction model for the 55-gallon waste containers within the room. A review of the legacy waste material model, however, revealed several out-of-date and untested assumptions that could affect the model’s compaction behavior. For example, the legacy model predicted non-physical tensile out-of-plane stresses under plane strain compression. (Plane strain compression is similar to waste compaction in the middle of a long drift.) Consequently, a suite of new compaction experiments were performed on containers filled with surrogate, non-degraded, waste. The new experiments involved uniaxial, triaxial, and hydrostatic compaction tests on quarter-scale and full-scale containers. Special effort was made to measure the volume strain during uniaxial and triaxial tests, so that the lateral strain could be inferred from the axial and volume strain. These experimental measurements were then used to calibrate a pressure dependent, viscoplastic, constitutive model for the homogenized compaction behavior of the waste containers. This new waste material model’s predictions agreed far better with the experimental measurements than the legacy model’s predictions, especially under triaxial and hydrostatic conditions. Under plane strain compression, the new model predicted reasonable compressive out-of-plane stresses, instead of tensile stresses. Moreover, the new model’s plane strain behavior was substantially weaker for the same strain, yet substantially stronger for the same porosity, than the legacy model’s behavior. Although room for improvement exists, the new model appears ready for prudent engineering use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2025

Hyperelastic nature of the Hoek–Brown criterion

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Experimental study of fracture slip due to stress perturbation in fractured geo-resources

Anthropogenic activities such as underground fluid injection/extraction, well stimulation, and dam impoundment will perturb the state-of-stress in the subsurface, which could activate critically stressed pre-existing fractures and faults. Fault and fracture activation can induce seismicity, change flow behavior, and damage asperities on the fracture surface to alter reservoir permeability. Here, in this study, triaxial shear tests were conducted on saw cut and rough fracture Barre granite specimens to better characterize how a decrease in normal stress and increase in shear stress will influence crystalline rock fracture hydromechanical properties. In a triaxial set up, confining pressure (CP) and differential stress (DS) were used to induce normal and shear stress on a 45° oriented fracture. Fracture slip and the corresponding stress relaxation was observed when the confining stress decreased. Fracture permeability increased when the fracture slipped. Moreover, new micro-cracks observed by x-ray images indicated the creation of new flow paths for fluid movement. The experimental outcomes of this study indicate that decrease in normal stress due to stress perturbations along the faults/fractures in the extensional stress regime can induce the slip along the fracture. This could have a significant influence on slope stability in quarries, stimulation and injection strategy in deep geo-resources, and potentially minimize the risk of induced seismicity. The observed stress dependency of hydraulic aperture in rough fracture during pre- and post-slip stages could provide key inputs for field-scale simulation of geo-resources.

58 GEOSCIENCES↗
DOE OSTI2020

Petrophysical and geomechanical properties of gas hydrate-bearing sediments recovered from Alaska North Slope 2018 Hydrate-01 Stratigraphic Test Well

Knowledge of petrophysical and geomechanical properties of gas hydrate-bearing sediments are essential for predicting reservoir response due to gas production from gas hydrate reservoirs. That information will be critical parameters for designing production well completion such as specification of depressurization pump, water storage tank, and mesh size of sand screen. In December 2018, Stratigraphic Test Well Hydrate-01 was drilled in the western part of the Prudhoe Bay Unit, Alaska North Slope as part of the technical planning effort for a future long-term production test by collaborative team of DOE/NETL, USGS, and MH21-S (Boswell et al., 2020, Collett et al., 2020, Okinaka et al., 2020). Data set of logging-while-drilling (LWD) were acquired (Haines et al., 2020, Suzuki et al., 2019) and core sampling depth was determined on-site.Side-wall pressure coring was conducted to recover gas hydrate-bearing sediments from two reservoir sections named Unit-B and Unit-D. A total of 34 cores were successfully recovered by 5 runs of a wire-line deployed pressure corer (CoreVault® System - Halliburton). Core analysis scheme of this project are shown in Figure 1. All cores were quenched in liquid nitrogen while at high pressure in the laboratory of Stratum Reservoir, LLC. at Anchorage (Figure 1, a)). And the cores were removed from the pressure corer autoclave with temperature support of dry ice and stored under liquid nitrogen at atmospheric pressure. 19 damaged cores were processed to index property measurements directly such as grain size, grain density. 4 of another 17 cores were depressurized and trimmed for making a plug to analyze petrophysical properties of host sediments. Unsteady-state permeability test was conducted to obtain relative water permeability to gas and core scale NMR T2 distribution measurement was performed for evaluating pore size distribution at Houston (Figure 1, b)). Remained high quality 13 cores were preserved with gas hydrate for advanced laboratory analysis. National Institute of Advanced Industrial Science and Technology, as a part of the Japanese National Hydrate Research Program (MH21-S, funded by Ministry of Economy, Trade and Industry), received the samples at Sapporo, Japan for advanced core analysis. High-resolution X-ray CT was used to analyze the quality of the samples, which showed undisturbed lithological layers. Cores were lathed into cylindrical shape and distributed for multi property measurements (Figure 1, c)).<p>As a result, sediment from Unit-D is categorized as silty sand at ~37% porosity with ~80% gas hydrate saturation. An average hydration number n = 6.16 was measured by Raman spectroscopy. An average intrinsic permeability of ~400 mD and in situ effective permeability (with hydrate) on the order of ~10 mD. The Unit B recovered cores consisted of well sorted sand at ~40% porosity with ~95% gas hydrate saturation. An average intrinsic permeability of ~1 Darcy and in situ effective permeability on the order of ~30 mD was measured for the Unit B cores. There was a small permeability reduction due to porosity loss with increasing effective stress that simulated consolidation behavior along with depressurization in the highly permeable sandy sediment. The apparent minimum change in porosity and permeability may be caused by the low compressibility of quartz sand grains in the recovered cores. XRD and thermal conductivity analysis also suggested high quartz content. Triaxial compression tests established internal friction angles based on the Mohr-Coulomb's failure criterion, which are 40° for hydrate-bearing sediment and 29.8° for hydrate free sediment.</p>

Yoneda, Jun↗
DOE OSTI2022

Graphene nanoplatelets reinforced cement as a solution to leaky wellbores reinforcing weak points in hydrated Portland cement with graphene nanoparticles improves mechanical and chemical durability of wellbore cements

In this work, to improve the performance of wellbore cement under subsurface environments, graphene nanoplatelets (GNPs) were added in various percentages to Class-H cement slurry. Microstructural characterization of cement slurries cured at 90 °C and 95% RH indicates that GNP modifies the microstructure of hydrated cement by reinforcing pore spaces. As a result, the mechanical properties, such as Young's modulus and axial peak stress, obtained from high temperature triaxial compression tests are significantly improved based on different percentages of added GNPs. Furthermore, the hydrated 1 × 2 inch GNP- Portland cement cores tested under simulated deep wellbore conditions of high-temperature and high pressure (HTHP), appear to have a ductile-like behavior, when compared to a typical brittle nature of Portland cement pastes. From our observations and published data on graphene resistance to fracture, GNP addition to cement is evidently enhancing the flexibility of cement. These improvements would reduce the risks associated with wellbore cement deterioration and a consequent leakage in fossil fuel production, geothermal energy production, CO 2 storage as well as long-term sealing materials in plugging and abandonment of all wellbores at the end of their service life.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A B-spline based gradient-enhanced micropolar implicit material point method for large localized inelastic deformations

The quasi-brittle response of cohesive-frictional materials in numerical simulations is commonly represented by softening plasticity or continuum damage models, either individually or in combination. However, classical models, particularly when coupled with non-associated plasticity, often suffer from ill-posedness and a lack of objectivity in numerical simulations. Moreover, the performance of the finite element method significantly degrades in simulations involving finite strains when mesh distortion reaches excessive levels. This represents a challenge for modeling cohesive-frictional materials, given their tendency to experience strongly localized deformations, such as those occurring during shear band dominated failure. Hence, accurate modeling of the response of cohesive-frictional solids is a demanding task. To address these challenges, we present an extension of the material point method (MPM) for the unified gradient-enhanced micropolar continuum, aiming at the analysis of finite localized inelastic deformations in cohesive-frictional materials. The generalized gradient-enhanced micropolar continuum formulation is employed to tackle challenges related to localization and softening material behavior, while the MPM addresses issues arising from excessive deformations. The method utilizes a B-spline formulation for the rigid background mesh to mitigate the well-known cell crossing errors of the MPM. To demonstrate the performance of the method, 2D and 3D numerical studies on localized failure in sandstone in plane strain compression and triaxial extension tests are presented. A comparison with finite element results confirms the suitability of the formulation. Moreover, an efficient numerical implementation of the formulation is presented, and it is demonstrated that the additional MPM specific overhead is negligible.

B-spline↗
DOE OSTI2021

Experimental workflow to estimate model parameters for evaluating long term viscoelastic response of CO2 storage caprocks

Understanding the time-dependent behavior of reservoir and sealing formations is critical to assessing risks associated with geological carbon storage since time-dependent deformation strongly influences mechanical responses of some rock types. Many studies have evaluated the risk of CO2 leakage and induced seismicity by assuming poroelastic rheology in sealing formations. Few have considered viscoelastic or other time-dependent responses, where the existing literature adopts 1D models to represent long-term time-dependent responses. This is primarily because to date, the general form of a reasonable 3D time-dependent model for rocks remains unclear. In this paper, we address this unclear issue by proposing a new workflow to select constitutive modeling parameters to evaluate if a 3D viscoelastic model is reasonable using several-hour-long experimental data and a power-law response to extrapolate to the decades-long time frames of interest in geologic carbon storage. To provide experimental data, we conducted multi-level loading/unloading triaxial relaxation tests with four rock types. The experimental results showed that the maximum load relaxation observed is approximately 49%, with some rock types showing as little as 1.4%. Using a simple linear viscoelastic model, parameters were chosen such that a maximum deviation of 1.5 MPa in axial stress and 7 MPa in radial stress was attained with the extrapolated 30-year data. We found that a reasonable parameter range for the normalized elastic modulus is 0.1~2 for rocks with significant time-dependent responses and 0.01~0.06 for those with small time-dependent responses. No matter how significant time-dependent responses are for rocks considered, our results showed that the relaxation time has a general range of 1~10^10 s, whose time scale can be one or two orders higher than a time frame typically envisioned for CO2 injection projects.

Stress relaxation, 3D time-dependent model, viscoe↗