Constitutive and numerical modeling of anisotropic quasi-brittle shales

Understanding the hydro-mechanical behavior of shale is fundamental to assess the safety of deep geological nuclear repository sites. Several countries have adopted argillaceous formations as host geological media for the repository. In Switzerland, the candidate for hosting the deep geological repository site is Opalinus Clay. This thesis aims at improving the current predicting and modeling capabilities of the hydro-mechanical behavior of shale by: (1) developing proper constitutive models; (2) validating the developed models against experimental findings. First, thermo-hydro-mechanical (THM) couplings at the constitutive level are addressed. A constitutive model that accounts for suction and temperature dependent failure is presented. Additionally, the model accounts for the true triaxial nature of strength. Numerical results showed that not accounting for true triaxial strength of geomaterials in unsaturated and non-isothermal conditions can lead to an overestimation of its strength. Then, a new constitutive model combining damage and plasticity theory for quasi-brittle geomaterials is developed. Comparison between numerical results at material point level and experimental results in triaxial compression tests show good agreement. The constitutive model is furtherly developed and modified to improve the calibration scheme and to represent a wider range of confinements. The new constitutive model is implemented with an implicit scheme in the Finite Element solver Code_Aster. Validation examples give good results and the model proves to be a powerful tool to describe the hydro-mechanical behavior of shale. The developed constitutive model is furtherly extended to account for anisotropy and true triaxial strength, both typical features of shale. Both extensions are compared separately against experimental data on several materials. The performance of the constitutive model in terms of failure stress predictions is compared to other failure criteria common in geomechanics. Results demonstrate how the proposed model gives a global smaller error between predictions and data compared to the other criteria. To avoid pathological mesh dependency, the Finite Element analyses must be carried out with a proper regularization technique. The one employed in this study is the second gradient of dilatancy formulation, which was available in Code_Aster. A series of numerical examples are presented to highlight the main characteristics of the structural response of the proposed constitutive model in combination with a second gradient of dilatancy formulation. Results demonstrate how the parameter controlling the non-associated plastic potential, the softening response, the anisotropic failure surface and the size of the problem play a major role in the final solution in presence of localized inelastic strains. Results show as well that the pathological mesh dependency is removed. A Finite Element analysis of tunnel excavation in coupled hydro-mechanical conditions is presented. The developed anisotropic plastic-damage model is employed along with the second gradient of dilatancy. Pore water pressure, tunnel walls displacement and damage around the tunnel are compared with in-situ recorded data during the excavation of the FE-tunnel at the Mont Terri site, Switzerland. The comparison between numerical predictions and recorded data is consistent and validates the concepts developed in the thesis

Multiphysical behaviour of shales

The involvement of shales in new energy-related fields such as the extraction of gas shale and shales oil, the deep geothermal energy capture, the sequestration of CO2 and the nuclear waste geological storage, has raised a new and growing interest in the geomechanical behaviour of the material. In this context, fundamental issues come along with the complex multiphysical conditions in which the geomaterial is found where temperature, chemistry and unsaturated conditions play a major role. As a consequence the study of the coupled thermo-hydro-chemo-mechanical (THCM) behaviour of shales is strongly sought. This lecture introduces the most recent advances in the experimental testing and modelling of the THCM behaviour of shales. Such testing under complex multiphysical conditions come along with the need to develop advanced experimental tools and techniques to reproduce the extreme multiphysical conditions experienced by shales in the context of the latest engineering developments. The lecture addresses the devices developed and methodologies established to study the water retention properties of shales and gas shales, the water and gas transport properties, the 1D volumetric behaviour, the thermo-mechanical couplings, the impact of the pore water composition on the mechanical response and the unsaturated behaviour of shales. A workflow established for the analysis of the water retention behaviour of shales in non-isochoric conditions is introduced; the method allows for the determination of the main drying and wetting paths and of the volume change response upon total suction variations (Ferrari et al. 2014)

An elasto-plastic-damage model for quasi-brittle shales

A constitutive model that couples elastic-plastic and damage theories is developed to predict the mechanical behavior of a shale from the Mont Terri rock laboratory (Opalinus Clay). The framework of continuum damage mechanics allows to predict the degradation of the elastic parameters with strains, while the coupling with plasticity correctly reproduces the irreversible strains typical of hard clayey materials. The yield surfaces (one for damage and one for plasticity) are postulated and the evolution equations of the internal variables are derived throughout the application of normality rule. Thermodynamic consistency of the model is investigated. The plastic behavior is described with a non-linear strain hardening function and is coupled with an isotropic damage model suitable for brittle and quasi-brittle geomaterials. The model is integrated with an implicit scheme that guarantees convergence and accuracy. Numerical simulations carried out with the proposed model in triaxial conditions well reproduced observed behavior from experiments

Strength evolution of geomaterials in the octahedral plane under nonisothermal and unsaturated conditions

Current geomechanical applications imply nonisothermal processes of unsaturated geomaterials, in most cases following stress paths different from the classical triaxial compression often used in laboratory testing. Although the effects of temperature, suction, and stress-path direction (Lode's angle) on the strength of geomaterials have been investigated independently, an integrated analysis combining the three effects has not yet been performed. In this paper, a thermoplastic constitutive model for unsaturated conditions that accounts for the effect of Lode's angle on the strength of geomaterials is presented. The yield surface evolves-shrinking for increasing temperature and expanding for increasing suction-and has its maximum strength for triaxial compression and its minimum for triaxial extension. Examples that can be related to geoenergy applications highlight the importance of accounting for the effects of temperature, suction, and Lode's angle on the evolution of the strength of geomaterials. Numerical results show that not considering these effects may give rise to misleading predictions of the strength of geomaterials. © 2017 American Society of Civil Engineers.V.V. acknowledges support from the ‘EPFL Fellows’ fellowship programme co-funded by Marie Curie, FP7 Grant agreement no. 291771. We would also like to acknowledge financial support from NAGRA (Swiss National Cooperative for the Disposal of Radioactive Waste).Peer reviewe

Combining geothermal energy production with CO2 storage in supercritical geothermal systems.

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Plastic-damage modeling of saturated quasi-brittle shales

The constitutive modeling of shales is an important topic in the geomechanics community as it is often encountered in advanced applications such as nuclear waste storage, CO2 sequestration, and unconventional oil and gas exploitation. The goal of this work is to describe, within a unique plastic-damage framework, the full mechanical behavior of shales such as pre-peak hardening plasticity, non-linearity in the onset of inelastic strains, dilatancy, post-peak softening, and degradation of the elastic parameters. The model validation against three sets of triaxial experimental results on shale demonstrates its capability to reproduce the main mechanical characteristics

Modeling Fluid Reinjection Into an Enhanced Geothermal System

Abstract The manuscript analyzes the stimulation for an Enhanced Geothermal System development in Acoculco, Mexico. Using an analytical penny-shaped hydraulic fracture model covering different propagation regimes, we computed the final fracture length and width by varying fluid properties with temperature. Our analysis indicates that for the given scenario, the fluid viscosity plays a minor role and instead flow rate and time of the stimulation are the controlling variables. We computed the fracture reopening as a consequence of water reinjection in the second stage of the stimulation through numerical computations based on the enriched discontinuity method. The computation shows that a single isolated fracture will not provide sufficient permeability, as the continuous injection will quickly fill and pressurize the crack. We demonstrate that the fracture needs to be connected to a permeable network to avoid excessive pressurization and achieve a commercially exploitable reservoir for Enhanced Geothermal System

On the formulation of anisotropic-polyaxial failure criteria: a comparative study

The correct representation of the failure of geomaterials that feature strength anisotropy and polyaxiality is crucial for many applications. In this contribution, we propose and evaluate through a comparative study a generalized framework that covers both features. Polyaxiality of strength is modeled with a modified Van Eekelen approach, while the anisotropy is modeled using a fabric tensor approach of the Pietruszczak and Mroz type. Both approaches share the same philosophy as they can be applied to simpler failure surfaces, allowing great flexibility in model formulation. The new failure surface is tested against experimental data and its performance compared against classical failure criteria commonly used in geomechanics. Our study finds that the global error between predictions and data is generally smaller for the proposed framework compared to other classical approaches

A novel CO2 storage concept that reduces the leakage risk

Geologic carbon storage is needed to reach carbon neutrality and eventually achieve negative emissions. In the classical concept of storing CO2 in deep sedimentary aquifers, supercritical CO2 has a lower density than the resident brine. CO2 is therefore buoyant and the safety and effectiveness of the storage concept rely on the caprock sealing capacity to prevent CO2 leakage. To reduce the risk of CO2 leakage and widen the CO2 storage options, we propose an innovative concept that consists in injecting CO2 in reservoirs where the temperature and pressure of the resident brine are above the critical point ( 373.95 ºC and 22.064 MPa for pure water). At such conditions, which can be found at depths between 3 to 5 km in volcanic areas, CO2 is denser than the resident water and thus, sinks. The sinking tendency reduces the risk of CO2 leakage to the surface even in case of damaged or absent caprock. CO2 storage in supercritical reservoirs can potentially become an additional option to the existing storage concepts aimed at significantly reduce CO2 emissions. We estimate that every 100 wells drilled into supercritical reservoirs could store between 50 to 500 Mt/yr of CO2.Peer reviewe