The Modeling of Time-Dependent Deformation and Fracturing of Brittle Rocks Under Varying Confining and Pore Pressures

Xu, Tao; Zhou, Guanglei; Heap, Michael; Yang, Sheng‐Qi; Konietzky, Heinz; Baud, Patrick

doi:10.1007/s00603-018-1491-4

Cited by 75 publications

(16 citation statements)

References 72 publications

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“…In this work, creep strain rate is expressed as Norton-Bailey power law using the parameters used for Halites by Carter law 10 as presented in Table 1 . Using Carter law and under multiaxial stress condition the creep strain is expressed as 41 , 71 , The above formulation incorporates temperature dependency as expressed by the Arrhenius law. here s is deviatoric part of the stress tensor, and Q , R and T denote the activation energy, Boltzmann’s constant and temperature, respectively 8 , 13 , 27 .…”

Section: Governing Equationsmentioning

confidence: 99%

Geomechanical simulation of energy storage in salt formations

Kumar

Makhmutov

Spiers

et al. 2021

Sci Rep

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A promising option for storing large-scale quantities of green gases (e.g., hydrogen) is in subsurface rock salt caverns. The mechanical performance of salt caverns utilized for long-term subsurface energy storage plays a significant role in long-term stability and serviceability. However, rock salt undergoes non-linear creep deformation due to long-term loading caused by subsurface storage. Salt caverns have complex geometries and the geological domain surrounding salt caverns has a vast amount of material heterogeneity. To safely store gases in caverns, a thorough analysis of the geological domain becomes crucial. To date, few studies have attempted to analyze the influence of geometrical and material heterogeneity on the state of stress in salt caverns subjected to long-term loading. In this work, we present a rigorous and systematic modeling study to quantify the impact of heterogeneity on the deformation of salt caverns and quantify the state of stress around the caverns. A 2D finite element simulator was developed to consistently account for the non-linear creep deformation and also to model tertiary creep. The computational scheme was benchmarked with the already existing experimental study. The impact of cyclic loading on the cavern was studied considering maximum and minimum pressure that depends on lithostatic pressure. The influence of geometric heterogeneity such as irregularly-shaped caverns and material heterogeneity, which involves different elastic and creep properties of the different materials in the geological domain, is rigorously studied and quantified. Moreover, multi-cavern simulations are conducted to investigate the influence of a cavern on the adjacent caverns. An elaborate sensitivity analysis of parameters involved with creep and damage constitutive laws is performed to understand the influence of creep and damage on deformation and stress evolution around the salt cavern configurations. The simulator developed in this work is publicly available at https://gitlab.tudelft.nl/ADMIRE_Public/Salt_Cavern.

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Section: Governing Equationsmentioning

confidence: 99%

Geomechanical simulation of energy storage in salt formations

Kumar

Makhmutov

Spiers

et al. 2021

Sci Rep

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“…Finally, viscoplascitiy is incorporated for the shale rock model. Power-law 44 is employed for modelling creep in both salt rock and sandstone. The sandstone plasticity is modeled by using the MCC as a yield criterion and the consistency algorithm, as presented in 50 .…”

Section: Introductionmentioning

confidence: 99%

Simulation of the inelastic deformation of porous reservoirs under cyclic loading relevant for underground hydrogen storage

Kumar

Honório

Hajibeygi

2022

Sci Rep

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Subsurface geological formations can be utilized to safely store large-scale (TWh) renewable energy in the form of green gases such as hydrogen. Successful implementation of this technology involves estimating feasible storage sites, including rigorous mechanical safety analyses. Geological formations are often highly heterogeneous and entail complex nonlinear inelastic rock deformation physics when utilized for cyclic energy storage. In this work, we present a novel scalable computational framework to analyse the impact of nonlinear deformation of porous reservoirs under cyclic loading. The proposed methodology includes three different time-dependent nonlinear constitutive models to appropriately describe the behavior of sandstone, shale rock and salt rock. These constitutive models are studied and benchmarked against both numerical and experimental results in the literature. An implicit time-integration scheme is developed to preserve the stability of the simulation. In order to ensure its scalability, the numerical strategy adopts a multiscale finite element formulation, in which coarse scale systems with locally-computed basis functions are constructed and solved. Further, the effect of heterogeneity on the results and estimation of deformation is analyzed. Lastly, the Bergermeer test case—an active Dutch natural gas storage field—is studied to investigate the influence of inelastic deformation on the uplift caused by cyclic injection and production of gas. The present study shows acceptable subsidence predictions in this field-scale test, once the properties of the finite element representative elementary volumes are tuned with the experimental data.

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“…However, laboratory experiments have demonstrated that the deformation of rock materials (e.g., sandstone, basalt, granite) can progress with time under constant stress that is below their short-term failure strength. Rock held under a constant stress can eventually fail, with the time-to-failure depending inversely on the magnitude of the differential stress, amongst other factors such as temperature and the nature of any pore fluid that is present [1,[4][5][6][7][8]; a phenomenon known as static fatigue in the engineering literature and brittle creep in the geoscience literature. This time-dependent deformation is often explained in terms of time-dependent subcritical crack growth [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model

Heap

et al. 2020

Computers and Geotechnics

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A three-dimensional discrete element grain-based stress corrosion model incorporating the theories of subcritical crack growth and chemical reaction rate was built to explore the time-dependent behavior of damage evolution and fracture patterns of brittle rocks on a mesoscopic scale. The model was first validated and the model accurately captured the evolution of damage (tensile and shear microcracks) on the mesoscopic scale and the macroscopic mechanical behavior (the strength, and failure patterns) observed in laboratory experiments. The subcritical parameters of the model were calibrated to match the time-dependent damage deformation behavior observed in laboratory experiments. The timedependent numerical results replicated the typical deceleratingaccelerating axial strain behavior seen in laboratory experiments. The crack propagation pattern in the simulation indicated that tension cracks were dominant. The results of numerical simulation showed that the timeto-failure during brittle creep decreased with the increase of the stress level, while the initial strain value, initial damage value, and minimum creep strain rate increased, as observed previously in the laboratory. We conclude therefore that the presented model supports a rich set of grainscale discontinuities that can be related to microstructural features and provides a deeper understanding of the evolution of time-dependent damage on the mesoscale.

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The Modeling of Time-Dependent Deformation and Fracturing of Brittle Rocks Under Varying Confining and Pore Pressures

Cited by 75 publications

References 72 publications

Geomechanical simulation of energy storage in salt formations

Geomechanical simulation of energy storage in salt formations

Simulation of the inelastic deformation of porous reservoirs under cyclic loading relevant for underground hydrogen storage

Mesoscopic time-dependent behavior of rocks based on three-dimensional discrete element grain-based model

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